How did this come to be? We somehow have reached the final day of the Major League Baseball regular season. Unless, that is, there are overhang games tomorrow! Any tiebreakers to determine remaining postseason slots count as regular season games. And as we prepare for the start of play on this last scheduled day, there remain realistic scenarios in which we could get as many as three such games!

The AL Wild Card has turned into a mash-up, with four teams–all but one from the AL East (the Mariners, really?)–still having the potential to end in a tie for the two slots. Failing that, two or three could tie for the second WC. I am tempted to call this a crush of four mediocre teams, but that really would not be fair. All enter today with either 91 or 90 wins. If all four are tied at the end of the day, there will be two games in the AL on Monday to determine which two reach the first AL postseason game. If three tie for the second WC, there will be two games to break that tie, spread across two days, under the tiebreaker rules.

In the NL West, we could still see the Giants and Dodgers tie for the division; these two are absolutely not mediocre teams! The Giants enter the final day with 106 wins, the Dodgers 105. If you want to see mediocrity, see the NL East winning Braves, with only 87 wins but a guaranteed berth in the Division Series. While both West teams clinched a postseason berth a while ago, if they finish with identical records, they need a tiebreaker on Monday (in San Francisco, based on head-to-head records) to determine which one is the division winner and which is the first Wild Card. The latter then gets one shot at knocking off a hot Cardinals team that will have finished 14 or 15 games behind the first Wild Card. As I have said before (just click and see the series going back several years), this is a dumb format.

If the second place team in the NL West beats the Cards in the Wild Card Game, the Dodgers and Giants will play each other in the Division Series. I am tempted to say we’ve probably had enough Dodgers-Giants for the year, but I can’t deny that the old rivalry would be fun. However, it would be better if their next potential match-up (after the potential division tiebreaker) would be for the pennant itself, and not a qualifier to face the vastly inferior Braves or Brewers for the honor. That bad format again.

It will be a fun day, and with none of “my” teams in it, I am just rooting for maximum overhang!

In yesterday’s review of the German election outcome, I used the extended Seat Product Model (SPM) formula for two-tier PR systems. I have done this many times, and Rein Taagepera and I (in our 2017 book, Votes from Seats) do explicitly include mixed-member proportional (MMP) in the category of two-tier PR systems.

However, there is one problem with that characterization. All other two-tier PR systems that I can think of entail a single vote, which is then used both for allocating seats in the basic tier and pooled across districts for national (or sometimes regional) compensation.

MMP, of course, usually entails two votes–a nominal (candidate) vote used only in the basic tier, and a second, party-list, vote used for determining overall proportionality. (In MMP, the basic tier is a “nominal tier” because the vote there is cast for a candidate, and the district winner earns the seat solely on votes cast for him or her by name.) This two-vote feature is a complex feature of MMP that is actually emphasized in my more recent coauthored book, Party Personnel Strategies, but which I may have tended to underplay in my comparative work on modeling the effects of electoral systems on party systems. Of course, by being two-tier, it is already a non-simple system, as Taagepera and I define that term. But we also say that two-tier PR, including MMP, is as simple as an electoral system can be and still be included in the complex category (see p. 263 and 299 of Votes from Seats).

Maybe that is not an accurate statement for two-vote MMP. Our definition of simple (pp. 31-36) concentrates on two features: (1) all seats allocated within districts, and (2) adherence to the rank-size principle, such that the largest party gets the first seat in a district, and remaining seats are allocated in a way that respects their relative sizes (i.e., by any of the common PR formulas). We further say that for simple PR, “the vote for candidate and for party is one act” (p. 35). This latter condition still holds for any two-tier list-PR system, because there is a list vote that applies both for allocating seats within a district, and also for the “complex” feature of the supra-district compensation mechanism. Obviously, however, MMP as used in Germany violates the principle that “the vote for candidate and for party is one act.” So maybe it is not “simple enough” to qualify as an almost-simple complex system. (Yes, that was a complex statement, but that’s kind of the point.)

If MMP were to tend to produce a party system more fragmented than expected from the extended SPM, it might be due to the “second” vote, i.e., the list vote. To test this, one could aggregate all the nominal votes and use them as the notional list votes in a simulated compensation. (This is how MMP in Germany worked in 1949, albeit with compensation only at state level. It is also how MMP now works in Lesotho.) The aggregation of basic-tier votes should work better from the standpoint of modeling the party system impact of the key features of a given MMP system–the size of the basic tier and the share of seats in the compensation tier.

The catch in all this is that, of course, till quite recently German MMP was under-fragmented, according to the SPM, despite using a separate list vote. Thus the issue did not arise. The New Zealand MMP system also has matched expectations well, after the first three post-reform elections were over-fragmented relative to model prediction. The graph below shows the relationship over time between the expectations of the SPM and the observed values of effective number of seat-winning parties (N_S) in both Germany and New Zealand. For the latter country, it includes the pre-reform FPTP system. In the case of Germany, it plots N_S alternately, with the CDU and CSU considered separately. As I noted in the previous discussion, I believe the “correct” procedure, for this purpose, is to count the “Union” as one party, but both are included here for the sake of transparency. In both panels, the dashed mostly horizontal line is the output of the extended SPM for the countries’ respective MMP systems¹; it will change level only when the electoral system changes. (For New Zealand, the solid horizontal line is the expectation under the FPTP system in use before 1996.)

The German party system from 1953 through 2005 was clearly fitting quite poorly, due to how under-fragmented it was for the electoral system in use. The old CDU/CSU and SPD were just too strong and overwhelmed the considerable permissiveness of the electoral rules.² So clearly the question I am raising here–whether the two-vote feature of MMP means it should not be modeled just like any (other) two-tier PR system–is moot for those years. However, perhaps it has become an issue in recent German elections, including 2021. The underlying feature of voter behavior pushing the actual N_S to have risen to well above “expectation” would be the greater tendency of voters towards giving their two votes to different parties. At least that would be the cause in 2021, given that we saw in the previous post that the basic tier produced almost exactly the degree of fragmentation that the SPM says to expect. It is the compensation tier that pushed it above expectation, and the problem here (from a modeling perspective) is that the formula implicitly assumes the votes being used in the compensation mechanism are the same votes being cast and turned into seats in the basic (nominal) tier. But with two votes, they are not, and with more voters splitting tickets, the assumption becomes more and more untenable.

The previous planting on this matter emphasized that the SPM is actually performing well, even in this most recent, and quite fragmented, election. I am not trying to undermine that obviously crucial point! However, the marked rise in N_S since 2009–excepting 2013 when the FDP failed to clear the threshold–may suggest that the model’s assumption that the two votes are pretty similar could be problematic.

Maybe two-vote MMP is more complex after all than its characterization as a two-tier PR system–the simplest form of complex electoral system–implies. In fact, maybe I should stop referring to MMP as a sub-category of two-tier PR. Yet for various reasons, it is a convenient way to conceptualize the system, and as yesterday’s discussion of the recent German election showed, it does work quite well nonetheless. It could be based on a flawed premise, however, and the more voters cast their nominal and list votes differently, the more that flaw becomes apparent.

A work in progress… in other words (fair warning), more such nerdy posts on this topic are likely coming.

Notes

1. The “expected N_S” line for Germany takes the tier ratio to be 0.5, even though as I argued in the previous entry, we really should use the actual share of compensation seats in the final allocation. This would have only minimal impact in the elections before 2013; in 2021, it makes a difference in “expected” N_S of 0.36.

2. Partly this is due to the 5% list-vote threshold, which is not a factor in the version of the SPM I am using. In Votes from Seats, we develop an alternate model based only on a legal threshold. For a 5% threshold, regardless of other features, it predicts N_S=3.08. This would be somewhat better for much of the earlier period in Germany. In fact, from 1953 through 2002, mean observed N_S=2.57. In the book we show that the SPM based only on mean district magnitude and assembly size–plus for two-tier PR, tier ratio–generally performs better than the threshold model even though the former ignores the impact of any legal threshold. This is not the place to get into why that might be, or why the threshold might have “worked” strongly to limit the party system in Germany for most of the postwar period, but the permissiveness of a large assembly and large compensation tier is having more impact in recent times. It is an interesting question, however! For New Zealand, either model actually works well for the simple reason that they just happen to arrive at almost identical predictions (3.08 vs. 3.00), and that for the entire MMP era so far, mean N_S has been 3.14.

The German general election of 2021 has resulted in a situation in which neither major party can form a government without either the other, or more likely, a coalition that takes in both the liberal FDP and the Greens. With the largest party, the social-democratic SPD, under 30% of seats, it is an unusually fragmented result compared to most German elections. Naturally, this being Fruits & Votes, attention turns to how much more fragmented this outcome is than expected, given the electoral system. The answer may be a bit of a surprise: not all that much. I expected this outcome to be a significant miss for the Seat Product Model (SPM). But it is really not that far off.

For a two-tier PR system, of which Germany’s MMP can be thought of as a subtype, we need to use the extended version of the SPM developed in Votes from Seats.

N_S = 2.5^t(MS_B)^1/6,

where N_S is the effective number of seat-winning parties (here, meaning the expected N_S), M is the mean district magnitude of the basic tier, S_B is the total number of seats in the basic tier, and t is the “tier ratio” defined as the share of the total number of assembly seats allocated in the compensatory tier. For Germany, basic-tier M=1 and S_B=299. The tier ratio could be coded as 0.5, because the initial design of the system is that there are 299 list tier seats, allocated to bring the result in line with the overall party-list vote percentages of each party that clears the threshold. However, in Germany the electoral law provides that the list tier can be expanded further to the extent needed to reach overall proportionality. Thus t is not fixed; we should probably use the ratio that the final results are based on, as N_S would necessarily be lower if only 299 list seats had been available. In the final result, the Bundestag will have 735 seats, meaning 436 list seats, which gives us a tier ratio of t=436/735=0.593. Plug all this into the formula, and you get:

N_S = 2.5^0.593299^1/6=1.72*2.59=4.45.

Now, what was the actual N_S in the final result? We have to ask ourselves whether to count to two Christian “Union” parties, the CDU and the CSU, as one party or two. The answer really depends on the question being asked. They are separate parties, with distinct organization, and they bargain separately over portfolios and policy when they are negotiating a coalition with another party. However, for purposes of the SPM, I firmly believe that when two or more parties in a bloc do not compete against each other (or, alternatively, do so only within lists over which votes are pooled for seat-allocation¹), they should be treated as one. The SPM does not “care” whether candidates of the bloc in question are branded as CSU (as they are in Bavaria) or as CDU (the rest of Germany). It simple estimates the effective number of “agents of the electorate” given the electoral rules. In terms of national politics, these are the same “agent”–they always enter government together or go into opposition together, and they jointly nominate a leader to be their Chancellor candidate.

Taking the CDU/CSU as a “party” for this purpose, we get actual N_S =4.84 in the 2021 election. So, given an expectation of 4.45, the actual outcome is just over 8.75% higher than expected. That is nothing too extraordinary. For comparison purposes, we can just take the ratio of actual N_S to expected N_S. Here are some elections in the dataset used for Votes from Seats that are in the same range of over-fragmentation as Germany 2021:

      country   year   simple   Ns   exp_Ns   ratio 
     Barbados   1981        1    1.87   1.735597   1.077439  
       Norway   1965        1    3.51   3.255616   1.078137  
    Sri Lanka   1970        1    2.49   2.307612   1.079037  
Dominican Rep   1990        1    3.05   2.810847   1.085082  
     Trinidad   2002        1    1.98   1.824064   1.085488  
      Iceland   1963        0    3.33   3.060313   1.088124  
       Israel   1961        1    5.37   4.932424   1.088714  
     Trinidad   2001        1       2   1.824064   1.096452  
     Trinidad   2000        1       2   1.824064   1.096452  
      Iceland   1999        0    3.45   3.146183   1.096567  
      Denmark   1950        0    3.98   3.624933   1.097951  
     

(The table indicates as ‘simple’ those with a single tier; others are two-tier.)

The ratio variable has a mean of 1.021 in the full dataset and a standard deviation of 0.359. Its 75th percentile is 1.224 (and 25th is 0.745). So the German election of 2021 is actually very well explained by this method. The degree of fragmentation we saw in this election is not too surprising. It is about what should be expected with MMP consisting of 299 nominal-tier M=1 seats and a very generous and flexible compensation tier.

As an aside, if we used the initial tier size (299, so t=0.5) in the formula, we would get an “expected” N_S=4.09. This would mean a ratio of 1.183, still short of the 75th percentile of the 584 elections included in the book’s main statistical test. Here is the company it would be keeping in that neighborhood:

            country   year   simple   Ns   exp_Ns   ratio 
            Germany   2009        0    4.83   4.121066   1.172027  
St. Kitts and Nevis   2000        1    1.75   1.491301   1.173472  
         Luxembourg   2009        1    3.63   3.077289    1.17961  
             Canada   2004        1    3.03   2.560218   1.183493  
            Denmark   1998        0    4.71   3.965222   1.187828  
          Venezuela   1963        0    4.32    3.63006   1.190063  
        Korea South   1988        0    3.55   2.981969   1.190488  
     Czech Republic   2010        1    4.51   3.767128   1.197199  
            Iceland   1991        0    3.77   3.146183   1.198277  

This would put the German 2021 election about as “over-fragmented” as the Canadian election of 2004. In other words, still not a big deal. If we count the two “Union” parties separately, obviously the degree of over-fragmentation goes up considerably. As I have said already, I think for this purpose counting them as one is the correct decision.²

As far as size of the largest seat-winning party is concerned, the SPD has 206 seats, for 28.03%. The SPM would predict, given expected N_S=4.45, that the largest should have 32.6% (240 seats out of 735); that’s a ratio of 0.860 (which is a slightly bigger miss than the N_S ratio of 1.088, the reciprocal of which would be 0.919). It is worth pausing on this for a bit. Polling before the election said the largest party might be only on a quarter of the votes. This was accurate, as the SPD won 25.7%. The advantage ratio (%seats/%votes) is 1.09, which is rather high for an electoral system that promises as near-perfect proportionality as Germany’s current system does, with its compensation for overhangs (cases in which a party has won more nominal-tier seats in a state than its list votes would have entitled it to). This bonus is a result of a rather high below-threshold vote. Not as high in 2013, of course, when two parties (FDP and AfD) narrowly missed the nationwide 5% threshold. But still considerably high, at 8.6% combined for all parties that failed to win a seat.

It is also worth asking whether the logic behind the extended SPM for two-tier systems holds for this German election. The formula says that the basic tier produces an initial allocation of seats consistent with the SPM for simple systems, and then inflates it based on the size of the compensation tier. So we can ask what the effective number of seat-winning parties is in the basic tier alone. It should be N_S =(MS_B)^1/6= 299^1/6= 2.59. In fact, the basic-tier N_S in this election was 2.51 (as before, taking CSU/CSU as one party). The ratio of 0.969 is a pretty trivial miss. We should expect the largest party to have won 0.490 of these seats (about 146). Actually the Union parties, which together won the most single-seat districts, won 143 (0.478). Thus Germany’s MMP system, in the 2021 election, actually did produce a basic-tier (nominal-tier) party system pretty much just like it should, given 299 seats and M=1 plurality, and then augmented this through a large compensatory national tier. The actual inflator is a factor of 1.93=4.84/2.51, rather than the expected 1.72=2.5^0.593. Had it been 1.72 instead, the final effective number of seat-winning parties would have been 4.32, about “half a party” less than in reality, implying almost exactly one third of seats to the SPD instead of just 28%.

This surprised me (pleasantly, of course). When I saw that the Greens and AfD each had won 16 seats in the nominal tier, I thought that was too many! But in fact, it works out. Maybe sometimes even I think Duverger had a law, or something. But given 299 single-seat districts, this is pretty much in line with expectations.

The outcome is interesting in the many ways that it serves as a primer on details of the electoral system. Here I mean not only the substantial expansion of the Bundestag from 598 to 735 seats, due to the way the compensation mechanism works, but also the thresholds. One of the best known features of the German electoral system is the 5% nationwide threshold. But of course, the threshold is more complex than that. It is 5% of the national party-list vote or three single-seat wins, except if a party is an ethnic-minority party. All these provisions were on display. For instance, the Linke (Left) party fell below the 5.0% threshold, yet is represented at full proportionality. That is because it won three individual mandates, thus fulfilling the “or” clause of the threshold. There was a point on election night when it looked as if the Linke might hold only two single-seat districts. In that case, with less than 5% of the list votes nationwide, it would have held only those seats as its total. By winning three, it is entitled under the law to full proportional compensation, and as a result it was awarded 36 list seats. Then, for the first time in a very long time, an ethnic party has won a seat. The South Schleswig Voters’ Association (SSW), which had not contested federal elections in decades, ran in this one and was able to win a single (list) seat, because as a representative of the Danish and Frisian minorities, it is exempt from the usual threshold provisions, as long as its votes are sufficient to qualify it for a seat when the threshold is ignored. Its 0.1% of the national vote was good enough. The SSW has had some renewed success in state elections in Schleswig-Holstein recently, and now it has scored a seat in the federal parliament for the first time since 1949. In 1949, the MMP system was a bit different, in that the 5% threshold was determined state-by-state, rather than nationwide. If the threshold had been state-by-state in this election, one other party would have earned seats. The Free Voters won around 7.5% of party-list votes in Bavaria. However, they managed only 2.9% nationwide (and no district seat), so they are shut out.

Now attention turns to what the coalition will be. Two options are on the table: SPD+Greens+FDP (“traffic light”) or CDU/CSU+Greens+FDP (“Jamaica”). The possibility of a broad left coalition has been ruled out by the election results: SPD+Green+Linke is not a majority. It was never likely anyway; the SPD and Greens did not spend recent years convincing voters they were safe options near the center of German politics to team up with the far left. Nonetheless, had it been mathematically possible the SPD might have used it as leverage against the FDP. My guess is that the traffic light coalition will form. Despite some serious policy differences between the FDP and the other two, it would be a government made up of the winners of the election, as these three parties all gained votes compared to 2017. On the other hand, one led by the CDU/CSU would be led by a pretty big loser, even though it is mathematically possible and the Greens seem to have been positioning for it over the last several years.³ Following the election, the DW live blog has been reporting on comments by various prominent CDU and CSU politicians that could be interpreted as saying the bloc needs some time in opposition, after the disappointing result. I suspect this is the view that will prevail, and after a lot of intense and difficult bargaining, Germany will be led by a traffic light coalition for the first time.

____

Notes

1. Here I am thinking of cases like Chile, where alliance lists contain candidates of different parties, but for purposes of how the electoral system assigns seats between competing teams of candidates, we should count the alliances, not the component parties. The same condition applies in Brazil and Finland, only there it is essentially impossible to aggregate to a meaningful national alliance category because the combinations of parties are not always the same across districts. In Chile, and also in the FPTP case of India–as well as in the current case of Germany–there is no such problem, as the alliances are nationwide in scope and consistent across districts.

2. For the record, counting them separately yields N_S=5.51 in this election, which would put the ratio just barely above the 75th percentile.

3.To be clear, they are much happier working with the SPD, but what I mean is that their positioning for the possibility of a coalition with the CDU/CSU should make finding common ground with the FDP easier than it otherwise would have been.

The German federal election is today. Here’s an open planting hole for your thoughts as and after results come in.

Once again, Canadians have voted as if they had a proportional representation (PR) electoral system, but obtained almost exactly the party system they should be expected to get, given the first-past-the-post (FPTP) system that they actually use.

If voters are voting as if they had PR already, why not just give them PR? Of course, it does not work that way, as the decision to adopt a new electoral system is rarely separable from party politics. Nonetheless, it is worth asking what electoral system the country should have, based on how voters are actually voting. They certainly are not playing the game as if it were FPTP. Even though it is.

To get at an answer to this question, we can start with the average value of the effective number of vote-earning parties over recent elections. (For those just tuning in or needing a refresher, the effective number of parties is a size-weighted count, where each party’s “weight” in the calculation is its own size–we square the vote (or seat) share of each party, sum up the squares, and take the reciprocal. If there were four equal size parties, the effective number would be 4.00. If there are four parties of varying sizes, the effective number will be smaller than four. For instance, if the four have percentages of 40%, 35%, 20%, and 5%, the effective number would be 3.08.) From the effective number, we can work backwards through the Seat Product Model (SPM) to determine what electoral system best fits the distribution of parties’ votes that Canadians have actually been providing. The SPM lets us estimate party system outputs based on a country’s mean district magnitude (number of seats elected per district (riding)) and assembly size. As noted above, Canada currently tends to have a distribution of seats among parties in the House of Commons consistent with what the SPM expects from a district magnitude of 1 and a House size of 338. The puzzle is that it does not have a distribution of votes consistent with the SPM. Instead, its distribution of votes across parties looks more like we would expect from a PR system. But what sort of PR system? That is the question the following calculations aim to answer.

Over the past eight elections, going back to 2000, the mean effective number of vote-earning parties (dubbed N_V in systematic notation) has been 3.70. During this time, it has ranged from a low of 3.33 (2015 when Justin Trudeau won his first, and so far only, majority government) to a high of 3.87 (the second Conservative minority government of the period under leadership of Stephen Harper). In 2019 it was 3.79 and in 2021 it was very slightly higher (3.84, based on nearly complete results). Even the lowest value of this period is not very “two party” despite the use of FPTP, an electoral system allegedly favorable to two-party systems. (I say allegedly, because given FPTP with a House of 338 seats, we actually should expect N_V=3.04, according to the SPM. In other words, a “two-party system” is not really what the current electoral system should deliver. Nonetheless, it would not be expected to be associated with as fragmented a voting outcome as Canadians typically deliver.)

How to get from actual voting output to the PR system Canadians act as if they already had

The SPM derives its expectation for N_V via a phantom quantity called the number of “pertinent” vote-earning parties. This is posited in Shugart and Taagepera (2017), Votes from Seats, to be the number of parties winning at least one seat, plus one. It is theoretically expected, and empirically verifiable, that the effective number of seat-winning parties (N_S) tends to equal the actual number of seat winning parties (N_S0, with the 0 in the subscript indicating it is the unweighted, raw, count), raised to the exponent, 2/3. That is, N_S=N_S0^2/3. The same relationship logically would hold for votes, meaning N_V=N_V0^2/3, where N_V0 is the aforementioned number of pertinent vote-earning parties. We can’t measure this directly, but we take it to be N_V0=N_S0+1, “strivers equal winners, plus one.” In Votes from Seats we show that this assumption works for estimating the impact of electoral systems on N_V.

Thus we start with the recently observed mean N_V=3.7. From that we can estimate what the number of pertinent parties would be: given N_V=N_V0^2/3, we must also have N_V0=N_V^3/2. So N_V0=3.7^3/2 = 7.12. This number by itself is not so interesting, but it makes all the remaining steps of answering our question possible.

Our expected number of seat-winning parties from a situation in which we know N_V=3.7 works out to be 6.12 (which we might as well just round and call 6). We get that as follows. First, N_S0=N_V0-1: the number of pertinent vote-earning parties, minus one. We already estimated the pertinent vote-earning parties to be 7, so we have an estimated average of 6 parties winning at least one seat. This is realistic for current Canadian politics, as recently five parties have been winning seats (Liberal, Conservative, NDP, BQ, and since 2011, Greens). With PR, the PPC likely would win a few seats on current strength, and the Greens probably would continue to do so, assuming they either recover from their current doldrums (especially once PR were adopted) or that any legal threshold would not be applied nationally and thus even their 2.3% showing in the 2021 election would not lock them out of parliament. (In 2021, Greens still got 9.6% in PEI, 5.3% in BC and 5.2% in New Brunswick, for example (per Elections Canada).)

If we have an expected number of seat-winning parties, based actual mean N_V, that is equal to six, what would be the seat product (MS) that would be expected? Once again, the seat product is the mean district magnitude (M), times the assembly size (S). Given M=1 (single-seat districts) and S=338, Canada’s current seat product is 338. Based on one of the formulas comprising the SPM, a seat product of 338 should be expected to result in an effective number of seat-winning parties (N_S) of 2.64 and effective number of vote-earning parties (N_V) of 3.04. It is working out pretty close to that for seats (average N_S=2.8). Yet voters are voting more like they had a PR system given the average over recent elections of N_V=3.7.

One of the formulas of the SPM, which like all of those referenced here, is empirically accurate on a worldwide sample of election results, predicts that N_S0=(MS)^1/4. Thus if we have an expected value of seat-winning parties of around 6, as expected from N_V=3.7, we can simply raise it to the power, 4, to get what the seat product is expected to be: MS=6⁴=1296. In other words, based on how Canadian voters are actually voting, it is as if their country had an electoral system whose seat product is around 1300, rather than the actual 338. For a comparative referent, this hypothetical PR system would be quite close to the model of PR used in Norway.¹

Any electoral system’s mean district magnitude is M=(MS)/S,so taking a House of 338 seats,² our hypothetical PR system has M=1300/338=3.85. That is, based on how Canadian voters are actually voting, it is as if their country had an electoral system whose mean district magnitude is around 3.85. Comparatively, this is quite close to the Irish PR system’s mean magnitude (but it should be noted that Ireland has a seat product of closer to 600, due to a much smaller assembly).

So there we have it. The mean district magnitude that would be most consistent with Canada’s current vote fragmentation would be just under 4, given the existing size of the House of Commons.

If Canada adopted a PR system with a seat product of 1300, its expected effective number of seat-winning parties (N_S) would rise to 3.30, and its expected largest party would have, on average, 40.8% of the seats, or 138. (This is based on two other predictive formulas within the SPM: N_S=(MS)^1/6 and s₁=(MS)^–1/8, where s₁ is the seat share of the largest party.)

A largest party with 138 seats (as an average expectation) would then require another party or parties with at least 32 seats to have a majority coalition, or a parliamentary majority supporting a minority government. The NDP would reach this easily under our hypothetical PR system, given it can win around 25 seats on under 18% of the votes under FPTP (and 44 seats on just under 20% as recently as 2015).

The Bloc Quebecois also would be available as a partner, presumably for a minority government, with which to develop budgets and other policy, thereby preventing the NDP from being able to hold the Liberal Party “hostage” to its demands. The BQ won 32 seats in 2019 and 33 in 2021. However, because it is a regionally concentrated party, we should entertain the possibility that it might do worse under PR than under FPTP, which rewards parties with concentrated votes. The only way to estimate how it would do might be to run the SPM within the province.

Estimating Quebec outcomes under PR

Quebec has 78 seats total, such that 33 seats is equivalent to 42% of the province’s seats. On Quebec’s current seat product (78) its largest party should win 45 seats (58%). So it is actually doing worse than expected under FPTP!

If the province had a mean district magnitude of 3.85, its seat product would be 300, for which the expected largest party size would be 49%, or 38 seats. In other words, when the BQ is the largest party in Quebec, it could do a little better on the very moderate form of PR being suggested here than it currently is doing under FPTP. (Suppose the model of PR had a mean magnitude of 9 instead, then we’d expect the largest provincial seat winner to have 44.1%, or 34 seats, or roughly what it has won in the last two elections. Only if the mean M is 16 or higher do we expect the largest party in Quebec—often the BQ—to have fewer than 32 of 78 seats. Obviously, in 2011 when the BQ fell all the way to 23.4% within the province, PR would have saved many of their seats when FPTP resulted in their having only 4 of 75 in that election. In 2015 they did even worse in votes—19.3%, third place—but much better in seats, with 10 of 78. Under the PR model being considered here, it is unlikely they would not have won at least 10 seats, which is 12.8%, on that provincial share of the vote.)

Do Canadians actually ‘want’ a still more proportional system than this?
It is possible we should use a higher N_V as reflective of what Canadians would vote for if they really had a PR system. I have been using the actual mean N_V of recent elections under FPTP, which has been around 3.7. But in the final CBC polling aggregate prior to the 2021 election, the implied N_V was 4.12. It dropped by almost “half a party” from the final aggregate³ to the actual result either because some voters defected late from the NDP, Greens, and PPC, or because the polls simply overestimated the smaller parties. If we use 4.12 as our starting point, and run the above calculations, we’d end up with an estimated average of 7.4 parties winning at least one seat. Maybe this implies that the Maverick Party (western emulators of the BQ’s success as a regional party) might win a seat, and occasionally yet some other party. In any case, this would imply a seat product of 2939, for a mean M of 8.7. The largest party would be expected to have only 36.8% of the seats with such an electoral system, or about 125.

How to use this information when thinking about electoral reform

I would advise, as the way to think about this, that we start with what we’d like the parliamentary party system to look like. I am guessing most Canadians would think a largest party with only around 125 seats would be an overly drastic change, despite the fact that they are currently telling pollsters, in effect, that this is the party system they are voting for as of the weekend before the election!

The expected parliamentary party system from an average M around 4, yielding a largest party averaging just over 40% of the seats (around 138) is thus probably more palatable. Nonetheless, armed with the information in this post, drawn from the Seat Product Model, we could start with a desirable average share of the largest party, and work back to what seat product it implies: MS=s₁^–8, and then (assuming 338 seats in the House), derive the implied district magnitude from M=(MS)/S. Or one can start with how Canadians are actually voting, as I did above–or from how we think they would (or should) vote, using MS=[(N_V^3/2)–1]⁴, and followed by M=(MS)/S.

Whichever value of the seat product, MS, one arrives at based on the assumptions about the end state one is hoping to achieve, remember that we’d then expect the seat share of the largest party to be s₁=(MS)^–1/8. As we have seen here, that would tend to be around 40% if mean magnitude were just under 4. This implies a typical largest party of around 138 seats.⁴

But herein lies the rub. If you tell the Liberal Party we have this nifty new electoral system that will cut your seats by about 20 off your recent results, they probably will not jump at the offer. The parties that would benefit the most are the Conservatives (twice in a row having won more votes than the Liberals but fewer seats), NDP, and smaller parties, including apparently (based on above calculations) the BQ. But this isn’t a coalition likely to actually come together in favor of enacting PR. Thus FPTP is likely to stick around a while yet. But that’s no reason not to be thinking of what PR system would best suit Canadian voters, given that they have been voting for a while as if they already had a PR system.

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Notes

General note: At the time of writing, a few ridings remained uncalled. Thus the seat numbers mentioned above, based on who is leading these close ridings, could change slightly. Any such changes would not alter the overall conclusions.

1. More precisely, it would be almost identical in seat product to the Norwegian system from 1977 to 1985, after which point a small national compensation tier was added to make it more proportional.

2. I will assume electoral reform does not come with a change in the already almost perfect S for the population, based on the cube root law of assembly size, S=P^1/3, where P is population, which for Canada is currently around 38 million. This suggests an “optimal” number of seats of about 336.

3. This is based on the Poll Tracker final aggregate having vote shares of 0.315, 0.310, 0.191, 0.070, 0.0680, 0.035 for the six main parties (and 0.011 for “other”).

4. I am deliberately not going into specific electoral system designs in this post. I am stopping at the seat product, implicitly assuming a simple (single-tier) districted PR system, meaning one with no regional or national compensation (“top up” seats). Arriving at a seat product to produce the desired party system should be the first step. Then one can get into the important finer details. If it is a two-tier system–including the possibility of mixed-member proportional (MMP)–one can generate its parameters by using the result of the calculations as the system’s “effective seat product,” and take it from there.

The 2021 Canadian federal election turned out almost the same as the 2019 election. Maybe voters just really do not want to entrust Justin Trudeau with another majority government, as he led from 2015 to 2019. The early election, called in an effort to turn the Liberal plurality into a Liberal majority, really changed almost nothing in the balance among parties.

The result in terms of the elected House of Commons is strikingly close to what we expect from the Seat Product Model (SPM). Just as it was in 2019. The predictive formulas of the SPM suggest that when your electoral system is FPTP and there are 338 total seats, the largest one should win 48.3% of the seats, or about 163. They further suggest that the effective number of seat-winning parties (N_S) of around 2.64. In the actual result–with five districts still to be called–the largest party, the Liberals, has won or is leading in 159, or 47.0%., and N_S=2.78. These results are hardly different from expected. They also are hardly different from 2019, when the Liberals won 157 seats; in that election we had N_S=2.79.

While the parliamentary balance will be almost what the SPM expects, the voters continue to vote as if there were a proportional system in place. The largest party again has only around a third of the votes, and the effective number of vote-earning parties (N_V) is around 3.8. For a FPTP system in a House the size of Canada’s, we should expect N_V=3.04. Once again, the fragmentation of the vote continues to be considerably greater than expected.

Another bit of continuity from 2019 is the anomalous nature of FPTP in the current Canadian party votes distribution. For the second election in a row, the Conservative Party has won more votes than the Liberals, but will be second in seats. The votes margin between the two parties was about the same in the two elections, even though both parties declined a little bit in votes in 2021 compared to 2019. Moreover, as also has happened in 2019 (and several times before that), the third largest party in votes will have considerably fewer seats than the party with the fourth highest vote share nationwide. The NDP won 17.7% of the vote and 25 seats (7.4%), while the Bloc Quebecois, which runs only in Quebec, won 7.8% of vote and 33 seats (9.8%).

The Green Party and the People’s Party (PPC) more or less traded places in votes: Greens fell from 6.5% in 2019 to 2.3%, while the PPC increase from 1.6% to 5.0%. But the Greens’ seats fell only from 3 to 2, while the PPC remained at zero.

So, as in 2019, the 2021 election produced a good night for the Seat Product Model in terms of the all-important party balance in the elected House of Commons. However, once again, Canadians are not voting as if they still had FPTP. They are continuing to vote for smaller parties at a rate higher than expected–and not only in districts such parties might have a chance to win–and this is pushing down the vote share of the major parties and pushing up the overall fragmentation of the vote, relative to expectations for the very FPTP system the country actually uses.

In a follow up, I will explore what this tendency towards vote fragmentation implies for the sort of electoral system that would suit how Canadians actually are voting.

Below are the CBC screen shots of election results for 2021 and 2019. As of Thursday afternoon, there remain a few ridings uncalled. I may update the view for 2021 once they have all been called.

So election day is here already in the Canadian federal general election of 2021. The election was called in mid August, but otherwise would not have been due to 2023.

The final CBC Poll Tracker has the nationwide votes really close, at 31.5% to 31.0%, the Liberals being barely in front. The NDP is on 19.1%. For comparison, in 2019, these parties’ vote percentages were 33.1, 34.4, and 15.9, respectively. Note that the Conservatives led in the votes, but the Liberals led in seats (157 to the Conservative’s 121 and NDP’s 24). The Poll Tracker for the other parties has the following vote percentages (with last election’s results in parentheses) has the PPC on 7.0 (1.6), Bloc Quebecois on 6.8 (7.7), and Greens 3.5 (6.5).

The Poll Tracker’s seat projections currently have Liberals at 155, Conservatives 119, NDP 32, BQ 31, Green 1, PPC 0. The “likely” range for the Liberals extends to 168, which would be two seats short of the majority that PM Justin Trudeau was seeking by calling this election. If they have a really good result and there is some poling error or last-minute changes of minds (for those who have not already voted early), they might yet make it. On the other hand, the likely range for the party extends as low as 121 in the projection, while that for the Conservatives extends from 105 to 143. It would not be a surprise to see the NDP’s actual vote and seat numbers drop from the projection–their final “likely” range is 24 to 48 (indicating they also have some significant potential upside). They have been declining a little bit in projections in recent days, and they came short of the final projection in 2019.

So, unless there is a surprise, the results will not be fundamentally different from the last time. That would be good news for the Seat Product Model (SPM), as the projected outcome is an effective number of seat-winning parties (N_S) around 2.84. For an assembly the size of Canada’s, with M=1, the expected result is N_S=2.64. In 2019, the actual result was 2.79, a small excess over the model expectation. Additionally, the SPM expects the largest party to have 48.3% of the seats (163), and the projected outcome of this election is 45.9%, also a small deviation from the expectation, albeit a potentially consequential one politically. On the effective number of vote-earning parties, the current poll tracker projection works out to about 4.1! That is far above expectation. The SPM would expect 3.22; as was already the case in 2019 and indeed earlier, but even more so now, Canadian voters are not playing along with the FPTP game anymore, even if the translation of their votes into seats is still giving them the parliamentary party system expected for FPTP, given their assembly size.

News flash: Canada still needs a new electoral system! Only with some kind of PR will they get the parliamentary party system closer to the one they vote for, instead of the the SPM says they “should” have.

As results come in, or as you have any questions or thoughts about this election, here is the “open planting hole.”

Please be advised that I will not be monitoring it after about my local sundown, as the holiday of Sukkot starts tonight. But the virtual orchard is always open.

In the previous planting, I showed that there is a systematic relationship under FPTP parliamentary systems of the mean district-level effective number of vote-earning parties (N‘_V) to the nationwide effective number of seat-winning parties (N_S). Specifically,

N‘_V =1.59√N_S .

But why? I noticed this about a year after the publication of Votes from Seats (2017) while working on a paper for a conference in October, 2018, honoring the career of Richard Johnston, to which I was most honored to have been invited. The paper will be a chapter in the conference volume (currently in revision), coauthored with Cory Struthers.

In VfrS Rein Taagepera and I derived N‘_V =1.59S^1/12. And as explained in yesterday’s planting, it is simply a matter of algebraic transformation to get from expressing of N‘_V in terms of assembly size (S) to its expression in terms of N_S. But perhaps the discovery of this connection points the way towards a logic underlying how the nationwide party system gets reflected in the average district under FPTP. In the paper draft, we have an explanation that I will quote below. It is on to something, I am sure, but it remains imperfect; perhaps readers of this post can help improve it. But first a little set-up is needed.

To state clearly the question posed in the title above, why would the average district-level effective number of vote-winning parties in a FPTP system tend be equal to the square root of the nationwide effective number of seat-winning parties, multiplied by 1.59?

We can deal with the 1.59 first. It is simply 2^2/3, which should be the effective number of vote-earning party in an “isolated” district; that is, one that is not “embedded” in a national electoral system consisting of other seats elected in other districts (this idea of embedded districts is the key theme of Chapter 10 of VfrS). The underlying equation for N‘_V, applicable to any simple districted electoral system, starts with the premise that there is a number of “pertinent” parties that can be expressed as the (observed or expected) actual (i.e., not ‘effective’) number of seat-winning parties, plus one. That is, the number of parties winning at least one seat in the district, augmented by one close loser. For M=1 (as under FPTP), we obviously have one seat winning party, and then one additional close loser, for two “pertinent” parties. Thus with M=1 it is the same as the “M+1 rule” previously noted by Reed and Cox, but Taagepera and I (in Ch. 7 of our 2017 book) replace it with an “N+1″ rule, and find it works to help understand the effective number of vote-earning parties both nationwide and at district level. Raising this number of pertinent vote-earning parties to an exponent (explained in the book) gets one to N_V (nationwide) or N‘_V (district-level). When M=1, the number of pertinent parties is by definition two, and for reasons shown by Taagepera in his 2007 book, the effective number of seat-winning parties tends to be the actual number of seat-winning parties, raised to the exponent, 2/3. The same relationship between actual and effective should work for votes, where we need the “pertinent” number only because “actual number of parties winning at least one vote” is a useless concept. Hence the first component of the equation, 2^2/3=1.5874.

As for the second component of the equation, S^1/12, it is also an algebraic transformation of the formula for the exponent on the quantity defined as the number of seat-winning parties, plus one. At the district level, if M>1, the exponent is itself mathematically complex, but the principle is it takes into account the impact of extra-district politics on any given district, via the assembly size. The total size of the assembly has a bigger impact the smaller the district is, relative to the entire assembly. Of course, if M=1, that maximizes the impact of national politics for any given S –meaning the impact of politics playing out in other districts on the district of interest. And the larger S is, given all districts of M=1, the more such extra-district impact our district of interest experiences. With all districts being M=1, the exponent reduces to the simple 1/12 on assembly size (shown in Shugart and Taagepera, 2017: 170). Then, as explained yesterday we can express N‘_V in terms of N_S via the Seat Product Model. It should be possible to verify N‘_V =1.59√N_S empirically; indeed, we find it works empirically. I showed a plot as the second figure in yesterday’s post, but here is another view that does not add in the Indian national alliances as I did in yesterday’s. This one shows only Canada, Britain, and several smaller FPTP parliamentary systems. The Canadian election mean values are shown as open squares, and several of them are labelled. (As with the previous post’s graphs, the individual districts are also shown as the small light gray dots).

It is striking how well the Canadian elections, especially those with the highest nationwide effective number of seat-winning parties (e.g., 1962, 2006, and 2008) conform to the model, indicated with the diagonal line. But can we derive an explanation for why it works? Following is an extended quotation from the draft paper (complete with footnotes from the original) that attempts to answer that question:

Equation 4 [in the paper, i.e. N‘_V =1.59√N_S ] captures the relationship between the two levels as follows: If an additional party wins representation in the national parliament, thus increasing nationwide N_S to some degree, then this new party has some probabilistic chance of inflating the district-level voting outcome as well. It may not inflate district-level voting fragmentation everywhere (so the exponent on N_S is not 1), but it will not inflate it only in the few districts it wins (which would make the exponent near 0 for the average district in the whole country). A party with no seats obviously contributes nothing to N_S, but as a party wins more seats, it contributes more.^[1] According to Equation 4, as a party emerges as capable of winning more seats, it tends also to obtain more votes in the average district.

As Johnston and Cutler (2009: 94) put it, voters’ “judgements of a party’s viability may hinge on its ability to win seats.” Our logical model quantitively captures precisely this notion of “viability” of parties as players on the national scene through its square root of N_S component. Most of the time, viability requires winning seats. For a new party, this might mean the expectation that it will win seats in the current election. Thus our idea is that the more voters see a given party as viable (likely to win representation somewhere), the more they are likely to vote for it.^[2] This increased tendency to vote for viable national parties is predicated on voters being more tuned in to the national contest than they are concerned over the outcome in their own district, which might even be a “sideshow” (Johnston and Cutler 2009: 94). Thus the approach starts with the national party system, and projects downward, rather than the conventional approach of starting with district-level coordination and projecting upward.

[Paragraph on the origin of 2^2/3 =1.5874 skipped, given I already explained it above as stemming from the number of pertinent parties when M=1.³]

Thus the two terms of the right-hand side of Equation 4 express a district component (two locally pertinent parties) and a nationwide one (how many seat-winning parties are there effectively in the parliament being elected?) Note, again, that only the latter component can vary (with the size of the assembly, per Equation 2, or with a given election’s national politics), while the district component is always the same because there is always just one seat to be fought over. Consider some hypothetical cases as illustration. Suppose there are exactly two evenly balanced parties in parliament (N_S =2.00), these contribute 1.41=√2 to a district’s N’_V, while the district’s essential tendency towards two pertinent parties contributes 1.59=2^2/3. Multiply the two together and get 1.59*1.41=2.25. That extra “0.25” thus implies some voting for either local politicians (perhaps independents) not affiliated with the two national seat-winning parties or for national parties that are expected to win few or no seats.^[4] On the other hand, suppose the nationwide N_S is close to three, such as the 3.03 observed in Canada in 2004. The formula suggests the national seat-winning outcome contributes √3.03=1.74 at the district level; multiply this by our usual 1.59, for a predicted value of N’_V =2.77. […] this is almost precisely what the actual average value of N’_V was in 2004.^[5]

^[1] The formula for the index, the effective number, squares each party’s seat share. Thus larger parties contribute more to the final calculation.

^[2] Likely the key effect is earlier in the sequence of events in which voters decide the party is viable. For instance, parties themselves decide they want to be “national” and so they recruit candidates, raise funds, have leaders visit, etc., even for districts where they may not win. Breaking out these steps is beyond the scope of this paper, but would be essential for a more detailed understanding of the process captured by our logic. 

^[3] Because the actual number of vote-earning parties (or independent candidates) is a useless quantity, inasmuch as it may include tiny vanity parties that are of no political consequence.

^[4] A party having one or two seats in a large parliament makes little difference to N_S. However, having just one seat may make some voters perceive the party a somehow “viable” in the national policy debate—for instance the Green parties of Canada and the UK.

^[5] The actual average was 2.71.

One of the notable trends in polling leading up to the Canadian election of 20 September is the increasing vote share of the Peoples Party of Canada (PPC). At the same time, polls have captured a steady decline of the Green Party as the campaign reaches its end. These two small parties’ trends in national support appear to be happening in all regions of the country, albeit to different degrees (see the graphs at the previous link). That is, while these parties have different levels of support regionally, their trends are not principally regional. Rather, all regions seem to be moving together. This will be a key theme of this post–that politics is fundamentally national, notwithstanding real difference in regional strengths¹ and the use of an electoral system in which all seat winning is very local (in each of 338 single-seat districts or “ridings”).

The PPC is a “populist” party of the right. It seems that the Conservatives’ attempt to position themselves closer to the median voter during this campaign has provoked some backlash on the party’s right flank, with increasing numbers of these voters telling pollsters they will vote PPC.

At The Writ, Éric Grenier offers a look into what the polls say about the type of voter turning to the PPC, and whether they might cost the Conservatives seats. The PPC vote share ranges widely across pollsters but in the CBC Poll Tracker (also maintained by Grenier) it currently averages 6.7%. This would be quite a strikingly high figure for a party that is not favored to win even one seat and probably very unlikely to win more than one.² The Poll Tracker shows a stronger surge in the Prairies region than elsewhere (3.6% on 14 Aug. just before the election was called to 10.9% when I checked on 19 Sept.) and Alberta (4.6% to 9.0% now), but it is being picked up in polling in all regions (for example, from 2.2% to 4.4% in Quebec and 2.9% to 6.1% in Atlantic Canada).

What I wish I knew: Is a voter more likely to vote PPC if he or she perceives that the party is likely to win at least one seat? This question is central to the “all politics is national” model developed in Shugart & Taagepera (2017) Votes from Seats, in chapter 10. We do not mean “all” to be taken literally. Of course, regional and local political factors matter. We mean that one can model the average district’s effective number of parties based on the national electoral system. More to the point, we argue that the way to think of how party systems form under FPTP (or any simple districted system) is not to think in terms of local “coordination” that then somehow gets projected up to a national party system, but rather that the national electoral system shapes the national party system, which then sets the baseline competition in the district contests.

If the PPC or Greens are perceived as likely to have a voice in parliament–and perhaps especially if the parliament is unlikely to have a majority party– voters who like what a small party proposes may be more inclined to support it, even though few voters live in a district where it has any chance of winning locally. Below I will show two graphs, each based on a mathematical model, showing a relationship of local votes to national seats. The first is based on the total available seats–the assembly size–while the second will be based on the seat outcome, specifically the nationwide effective number of seat-winning parties. The formula derived in the book for the connection to assembly size states the following for FPTP systems (every district with magnitude, M=1, and plurality rule):

N‘_V=1.59S^1/12,

where N‘_V is the mean district-level effective number of vote-earning parties and S is the assembly size. Please see the book for derivation and justification. It may seem utterly nuts, but yes, the mean district’s votes distribution in FPTP systems can be predicted when we know only how many districts there are (i.e., the total number of seats). In the book (Fig. 10.2 on p. 156) we show that this sparse model accurately tracks the trend in the data across a wide range of FPTP countries, particularly if they are parliamentary. Here is what that figure looks like:

Of course, individual election averages (shown by diamonds) vary around the trend (the line, representing the above equation), and individual districts (the smear of heavily “jittered” gray dots) have a wide variation within any given election. But there is indeed a pattern whereby larger assemblies tend to be associated more fragmented district voting than is the case when assembly size is smaller. At S=338, Canada has a relatively large assembly (which happens to be almost precisely the size it “should be,” per the cube root law of assembly size).

The model for N‘_V under FPTP is premised on the notion that voters are less attuned to the likely outcome in their own district than they are to the national scene. There is thus a systematic relationship between the national electoral system and the average district’s votes distribution.

Moreover, by combining the known relationship between the national electoral system and the national party system, we can see there should be a direct connection of the district vote distribution to the national distribution of seats. The Seat Product Model (SPM) states that:

N_S=(MS)^1/6,

where N_S is the nationwide effective number of seat-winning parties. For FPTP, this reduces to N_S=S^1/6, because M=1. In terms of a FPTP system, this basically just means that because there are more districts overall, there is room for more parties, because local variation in strengths is, all else equal, likelier to allow a small party to have a local plurality in one of 400 seats than in one of 100. So, more seats available in the assembly (and thus more districts), more parties winning seats. The model, shown above, connecting district-level votes (N‘_V) to the assembly size (S) then suggests that the more such seat-winning opportunities the assembly affords for small parties, the more local voters are likely to give their vote for such parties, pushing N‘_V up. The process probably works something like this: Voters are aware that some small parties might win one or more seats somewhere, providing these parties a voice in parliament, and hence are likelier to support small parties to some degree regardless of their local viability. It is national viability that counts. “All politics is national.” The posited connection would be more convincing if it could be made with election-specific seat outcomes rather than with the total number of available seats. We can do that! Given the SPM for the national seat distribution (summarized in N_S) based on assembly size, and the model for district-level votes distribution (N‘_V), also based on assembly size, we can connect N‘_V to N_S algebraically:

N‘_V=1.59N_S^1/2.

(Note that this comes about because if N_S=S^1/6, then S=N_S⁶, giving us N‘_V=1.59(N_S⁶)^1/12, in which we multiply the exponents in the final term of the equation to get the exponent, 1/2, which is also the square root. A full discussion and test of this formula may be found in my forthcoming chapter with Cory Struthers in an volume in honor of Richard Johnston being edited by Amanda Bittner, Scott Matthews, and Stuart Soroka. Johnston’s tour de force, The Canadian Party System likewise emphasizes that voters think more in terms of national politic than their local contest.)

Here is how this graph looks:

By implication, this connection of district-level N‘_V to national N_S may arise because voters have some estimate of how the national parliament is going to look when they decide whether or not to support a party other than one of the two leading national parties. For instance, a voter wavering between the NDP and the Liberals might be more likely to support the NDP if she estimates that there will be no majority, thereby allowing a smaller party like the NDP to be more influential than if one of the big parties has a majority on its own.

A vote for a much smaller party, like the PPC, might be simply expressive–“sending a message” to the Conservatives that they are not sufficiently right wing or populist. For a purely expressive voter, the national seat outcome may be irrelevant. Such a voter simply wants to register a protest. There still might be a connection to expected national votes: If such a voter thinks the PPC can get 7% he might be likelier to vote for it than if it’s only 3%.³ If, however, the connection runs through thinking about the national parliament, and whether one’s party will have voice there, it should help the party win votes around the country if its potential voters perceive that it will win one or more seats–in other words, that it is viable somewhere. I hope there is some polling data that I can find some day that allows us to get at this question, as it would connect the aggregate outcome demonstrated here with individual-level voter behavior. As the Canadian 2021 campaign has developed, it would be an especially good test of the model’s underlying individual-voter premise, given the surge of a small national party that is probably not likely to have a voice in the House of Commons. (But maybe its voters believe it will! They might even turn out to be correct.)

I do not, however, currently know if any polling or voter surveys exist to get at these questions. Such a survey ideally would ask the respondent how many seats they believe the various parties will get in the election. This would allow a rough construction of voter-expected effective number of seat-winning parties even though no voter actually has to know what that concept means or how to calculate it for the premise of the model to work. Minimally, as noted, it would at least be useful to know if voters choosing a small party think that party will indeed get one or more seats.

I have so far focused on the PPC in the Canadian 2021 election, as a possible example of a wider phenomena connecting local voting to the (expected) national seat outcome. A similar logic on the left side of politics should apply for the Green Party. Does its perceived viability for seats in parliament affect the tendency of voters to vote for it outside the specific districts where it is locally viable? The very big wrinkle this time around for the Greens, however, is that the party is struggling mightily, with an ongoing conflict between its leader and much of the rest of the party. It is currently projected to win no more than two seats, and perhaps none. It might be expected to retain the former leader’s seat in British Columbia, but even that may be in jeopardy with the national party in such disarray.

It is even questionable whether the Green Party still meets the criteria of a “national” party this time around; I do not (yet) have a really precise working definition of how many districts the party must be present in to qualify as “national.” The Green Party has not fielded a candidate in about a quarter of the ridings nationwide. Grenier has reviewed the 86 Green-less constituencies and whether their absence could affect outcomes among the contesting parties. Obviously the connection between expected seat winning nationally and obtaining votes in contests around the country is broken in any district in which there is no candidate running for the party. No candidate, no possibility of the local voters augmenting the party’s aggregate vote total. In any case, the party has dropped in national polls from 5.4% on 14 August to 3.2% now.

Further emphasizing now the Greens may not be a “national” party in this election is the campaign behavior of the leader. The CBC recently noted that the leader, Annamie Paul, is not exactly campaigning like the leader of a national party:

Asked why she hasn’t campaigned in more ridings, Paul acknowledged Friday that some candidates may want her to steer clear. She has campaigned outside of her home riding of Toronto Centre twice so far — once in a neighbouring riding and then Monday, in P.E.I.

Candidates distancing themselves from the leader is not normally a good sign for a party, particularly in a parliamentary system. “All politics is national,” after all. As explained in Votes from Seats (ch. 10), the impact of national politics on local voting is likely enhanced by parties bringing resources into districts to “show the flag” even where they are not likely to win a seat. (The PPC leader is certainly doing this.) If your leader remains mostly ensconced in her own district, the party is not deploying what is normally one of its best resources–the leader making the case for her party.

Nonetheless, it still might matter for the party’s ability to get votes, even in ridings it surely will not win, whether its potential voters believe it is viable for seat-winning somewhere. The good news for the party–and there is little of that–is that the province where it currently holds two seats, BC, is one of those where its polling has declined least: 7.0% on 14 August to 6.3% now. So, politics is still at least a bit more regional for the Greens than for other “national” parties, perhaps.

In conclusion, the district-level extension of the Seat Product Model states that in FPTP systems, district-level effective number of vote-earning parties can be predicted from the national electoral system–specifically, the assembly size. By further extension (in the aforementioned chapter I am working on with Struthers for the volume honoring Johnston), it should also be tied to the nationwide effective number of seat-winning parties, and to voter perceptions in the campaign as to how parties are doing at the national level. The result would be that voters are more likely to vote for even a small party under FPTP to the extent that they expect it to have a voice in parliament, and to the extent that the parliament may not have a majority party. The Canadian 2021 election, with a surging small party (the PPC) and another one declining (the Greens) offers an excellent case study of the phenomenon that is behind these models.

___________

Notes:

1. Obviously, things are different for an explicitly regional party (one that does not present candidates outside its region) like the Bloc Quebecois, which I will leave aside for this current discussion.

2. Perhaps it has some chance of winning the leader’s riding of Beauce (in Quebec), but as Grenier notes in a post the day before the election:

There’s nothing about Bernier’s Beauce riding that makes it particularly open to a party that has been courting the anti-vaxxer, anti-vaccine mandates and anti-lockdowns crowd. It’s hard to know where in the country that crowd would be big enough to elect a PPC MP.

He does also note that one poll, by EKOS, has put the party second in Alberta, albeit with only 20% of the vote. Maybe they could get a local surge somewhere and pick up a seat there.

3. Indeed, it might seem that we could make a similar algebraic connection. The Seat Product Model expects national effective number of vote-earning parties to be N_V=[(MS)^1/4 +1]^2/3. This is confirmed in Votes from Seats. However, this can’t easily be expressed in terms of just S (even for FPTP, where the term for M drops out) and therefore is complicated to connect to the N‘_V formula. In any case, the theoretical argument works better from seats–that voters key on the expected outcome of the election, which is a distribution of seats in parliament and whether one or another party has a majority or not. These outcomes are summarized in the effective number of seat-winning parties.

4. This graph is a version of the one that will be shown in the previouysly mentioned Shugart & Struthers chapter.

What a relief. It turned out like the fundamentals of this state said it should all along. But the risk was high. Maybe those polls that showed the recall ahead or close were just rogues. But a process that lets a motivated minority potentially replace an effective but unexciting incumbent with someone elected by a small percentage of the vote is deeply undemocratic. 

It needs to be reformed before an extremist minority puts us through such an attempted power grab again, and maybe pulls it off. So this planting is all about brainstorming for some possible improvements to the process.

As I have noted before, I oppose recalls in principle, at least against the elected chief executive. I explained why in the first in my series on this recall. But for this discussion, I will assume we are stuck with a recall provision, and only focus on how it could be improved. I also am limiting myself to recalls of elected governors (or by extension, presidents), and not to all the other offices that are, or might be, subject to recall.

Minimal changes

The California process of initiating a recall is probably the most favorable to an incumbent’s opponents. Without undermining the principle of allowing the people to recall a governor, there are numerous ways the hurdle could be made higher. FiveThirtyEight has already done a helpful rundown of how California’s provisions compare to those of other US states.

Possible reforms, drawn from experiences of other states, include raising the petition signature requirement (currently just 12% of the number of voters who participated in the previous gubernatorial election) and shortening the time during which petitions can circulate (currently 160 days).

While reforms of this sort are probably a good idea, they are very minimal. There are more fundamental problems with the process, once qualified. These problems do not go away unless the qualification becomes so onerous that effectively a recall election is never triggered. And while some tightening of the criteria may now be likely, it is unlikely the conditions will be greatly restricted.

Somewhat more significant changes for recall

Somewhat more significant options including requiring a claim of malfeasance, rather than we just do not like you, as a basis for petitioning for a recall, or requiring a supermajority to vote in favor of the recall. I do not think the first of these ideas is easily enforceable. (What are the criteria, and who decides if they have been met and so an election is triggered?)

The supermajority idea is attractive. Obviously, a supermajority privileges the status quo, and that is why I normally do not approve of such rules other than perhaps for constitutional changes. Yet in a system based on fixed terms, privileging the status quo is not such a bad idea–the officeholder serves his or her original term unless a strict condition for termination has been met. Nonetheless, I would be concerned about the continued legitimacy and effectiveness of a governor whom a majority of voters–but less than three fifths or two thirds or whatever–had voted to oust.

One could also set a rule that says the recall has not succeeded unless it obtains a majority that is also a greater number of voters than originally voted for the governor in the last election. This is de-facto a supermajority requirement, but it sets the threshold according to the existing electoral base of the incumbent instead of at a fixed level. I retains the same problems I noted with a specific supermajority threshold, but I do rather like the idea nonetheless. See Frozen Garlic for a good statement of the general principle “that recalling an elected official should be significantly harder than electing that same official”; the post has some specific suggestions for implementing that principle. That blog is about elections in Taiwan, where there are recalls and there is a turnout requirement for it to be valid (but it is low, at 25%).

Reforms to the replacement election

Here is where the most important changes could be made. Currently, all state officeholders in California are elected by majority in a “top two” runoff election–unless they are replacing a recalled officeholder. Per Section 5(a) of the California Constitution, “The candidates who are the top two vote-getters at a voter-nominated primary election for a congressional or state elective office shall, regardless of party preference, compete in the ensuing general election.” However, Section 15(c), regarding recalls, says “If the majority vote on the question is to recall, the officer is removed and, if there is a candidate, the candidate who receives a plurality is the successor. The officer may not be a candidate…”

An obvious solution is to clean up this contradiction. Why should a replacement be eligible to be elected by only a plurality when the officeholder being replaced was elected by a majority? This violates the previously articulated principle by making it easier to replace than to initially elect. Among the strange things about recall-replacement elections in this state is that there is no primary. Of course, readers of this site know that we do not have primaries at all anymore (other than for presidential nominating delegates). What Section 5(a) calls a “primary” is actually not a primary; it is just the first round of a two-round majority election in which party affiliation is not a criterion regarding who advances to the runoff (as quoted previously, “regardless of party preference”). In any case, how we label this process is not the point–important though it is!. The point is that there is a prior qualifying round for general elections, but not for the special election that chooses a replacement. This should be corrected.

Any correction should also resolve the current undemocratic “trainwreck” criterion that a replacement can win fewer votes than the recalled officer had not merely when previously elected but also in the same election. If a majority is required to elect the replacement, this problem is mostly solved. But how to do it? Here are a few possibilities.

(1) Replicate the current general-election process, that is, have a preliminary round (“primary”) and then a top-two runoff, in the event a majority has voted to recall the incumbent.

A key problem with this is it could result in having three special election dates to complete the process: the recall, then if a majority votes for it, a qualifying election, and then if no candidate wins a majority, a runoff. Such a proposal is not likely to fly.

(2) An alternative would be to hold the qualifying round concurrent with the recall question. If the recall passes by majority, but no single replacement candidate wins a majority, then there is a top-two runoff a few weeks later. This would turn a potentially three-round process into a maximum of two, and might still allow it to be over in one round.

If this option were chosen, I would explicitly permit the recalled officer to run in the qualifying round on the same day. If he or she is one of the top two, then the recalled official proceeds to the runoff against a single challenger. If a majority votes to retain the previously recalled governor, so be it. A majority has decided it did not see a single replacement who was better than the incumbent after all. (This sub-option that I suggest is not necessary for the general principle of two rounds to be adopted.)

(3) Yet another possibility is to dispense with the recall question altogether. A successfully qualified recall petition simply triggers a special election in which the incumbent may stand alongside whatever replacement candidates have qualified. The incumbent survives unless a single replacement candidate earns a majority of votes cast. It is all over in one round, and on one question. It would have the advantage of forcing coordination among the opponents, because they need a majority and get only one chance at it.

A potential flaw is the incumbent could survive without even a plurality if coordination fails and there are many candidates, which raises those legitimacy questions again. But the goal is to make it hard to replace, not hard to continue. A twist would be to say there is a runoff if and only if the incumbent finishes second or worse to a challenger who has fallen short of a majority. (Such a runoff probably should include the incumbent even if he or she finished lower than second, but I don’t feel strongly about that particular sub-option.)

By now, some readers will be impatient that I have not mentioned the ranked-choice option. Okay, here you go.

(4) Using ranked-choice voting (RCV) is a simple solution that could be done in one round of voting either with, or without, two questions. The smallest change would be to have two separate questions like we currently do, but the replacement is by ranked-choice voting (alternative vote). A better–I think–option would be the single question: rank as many as the following candidates, including the incumbent, as you wish.

I d not favor these RCV options because we have seen we can have dozens of candidates enter. Asking voters to rank a huge field, where at least the major out-party may have several candidates, is asking a lot of the voters. Moreover, with many candidates, many voters will not rank them all, and the chances are high that the winner will still have only a plurality. This is a general problem with RCV in an effectively non-partisan context (i.e. when multiple parties have not each pre-selected a single candidate). I do not favor this, although I recognize it as an improvement over the status quo. Almost anything would be.

Abolish the replacement election

We have a Lieutenant Governor. The main point of such an office is to replace the incumbent Governor if the latter is unable to discharge his or her duties. If a recall passes, have the Lt.Gov. take over and there is no need to have a special replacement election. This makes a great deal of sense, and I’d be happy with it. Voters might not be, and so its chance of being enacted as a constitutional reform in California is likely not high.

Think big

As I explained earlier (see first linked post), one of my objections to gubernatorial (or presidential) recall is that it targets one officeholder. If we are talking impeachment for malfeasance, that’s fine. But in reality, a recall is a just another political process–even more than impeachment, which is also political. If the objection of the potential majority in favor of recall is discontent with policy, the problem is clearly not only with one person. So recall them all! Have a recall process that simply initiates an early election for the entire legislature as well as the governor. Sort of like an early dissolution in a parliamentary system. Go back to the people and get new policymakers, or if the voters prefer, reelect them all.

I do not actually favor this. But I mention to make a point–recalls are about attempting to reset the terms of delegation from voters to their agents in government. So it sensibly should not be used to target a single individual (again, unless there is some process specifically targeting only a corrupt individual officeholder).

So there you have it. These are the ideas I have come up. What are yours? What do you think of these? We desperately need to change this process before a minority power grab succeeds in the future, but how?

Heinz Brandenburg on Twitter walks readers through a very useful explainer on how the current Germany version of MMP deals with overhangs through a multi-layered compensation mechanism, and why it could mean the new Bundestag will top out at more than 800 seats!

It is best to read it in its native Twitter, but following is the text of most of it (courtesy of the ThreadReader app) . The starting point, not quoted here, is a poll of current party standing in the state of Bavaria.

[the remainder of this text is not mine, but Brandenburg’s; numbers correspond to tweets in the thread]

____________________________________________________________________________

Last time around, the CSU won 38.8% of the vote but all of the constituencies in Bavaria (they even swept all of Munich). That results in so-called overhang and compensatory seats.
How are these calculated?

1/ Well, there are 93 regular seats allocated to Bavaria, 46 of which are constituencies. CSU winning them all meant 46 seats, but they only had 38.8% of the list vote or about 42% of the vote once you discount votes for parties that did not get into the Bundestag.

2/ 42% of the vote would mean their proportional share of seats was 39, not 46. So they got 7 Ueberhangmandate (overhang seats), i.e. 7 more seats than their proportional share.

3/ Since 2013, these seats have to be compensated for. So other parties get additional seats, to the extent that the 46 seats the CSU won amount to 42% of the total number of seats in Bavaria.
So Bavaria actually had 108 seats in the Bundestag, not 93. 

4/ But that is not the end of it. Bavaria’s 93 seats are proportional to its population size. If the state’s seat share increases to 108, then the 15 other states also need a larger share. And it wasn’t only Bavaria. 

5/ Baden-Wuerttemberg got 96 instead of 76 because of the CDU winning all constituencies, Brandenburg 25 instead of 20 because CDU won all but one constituency, Hamburg 16 instead of 12 because SPD won all but one constituency, and so on.

6/ What happens then is that to keep the 16 states’ share of seats in the Bundestag proportional, not only overhang seats within states need to be compensated, but overhang and compensatory seats within states have to be compensated across states.

7/ So North Rhine-Westphalia (NRW), the biggest German state, did not produce any overhang seats, because SPD and CDU are more evenly balanced there. But it got 14 compensatory seats, to make up for additional seats given to other states. 

8/ It is not a perfect compensation across states. Bavaria and Baden-Wuerttemberg have 15 and 20 seats, respectively, more than their normal share in the 2017 Bundestag. NRW only 14, despite being the larger state.

9/ Berlin, Niedersachsen and NRW were the only states where no overhang seats were dished out in 2017, largely a reflection of dominance of the CDU in a fragmenting party landscape. 

10/ CDU won all seats in five states, almost all seats in over a dozen states, despite having their worst election result in history, with 33%.

Could be very different this time around, with them down to 20% and the SPD at 25%. More states could get away without overhang seats.

11/ But one single state can make a big difference, and if the result in Bavaria is anywhere close to the recent polls (CSU 28%) it could be a dramatic effect.

12/ Even at 28%, the CSU would like win almost all constituencies. These are the four most marginal seats. Muenchen-Nord and Nuernberg-Nord are most likely to fall to the SPD. But the others are not certain.

So the CSU could still end up with 42-44 seats, on just 28% of the vote, or 31% if we remove votes for parties that do not get into the Bundestag.

14/ By my calculations, that would mean Bavaria’s seat share increases to 129 seats from their current 108 (and their nominal allocation of 93).

Once other states are compensated, that would get us to possibly 840 seats. 

15/ A few changes have been made, which I have taken into account – the first three overhang seats will not be compensated, which would keep Bavaria’s share at 129 rather than 135 under 2017 rules.

16/ And overhangs can also be compensated against a party’s list seats in other states. But I don’t think that applies to the CSU. They won’t take CDU seats away in other states to compensate for CSU over-representations.

17/ So one such lop-sided result, under increasing fragmentation – where suddenly 28% of the vote share allow a party to win almost all constituencies – can have incredible effects on the size of the Bundestag.

18/ The nominal size of the Bundestag is 598. This one result in Bavaria could increase the size of parliament by 40%.

The parliament of Thailand has again adopted electoral system changes. However, the WaPo is confused (and confusing) about what has been done. On the one hand, it says it is a “system of mixed-member proportional representation” (MMP).

On the other hand, it also says the new system is “a throwback to the system implemented under a 1997 constitution that sought to disadvantage smaller parties.”

Only one of those statements can be true.

The 1997 system was definitely mixed-member majoritarian (MMM), sometimes called a “parallel” system, and was indeed highly disadvantageous to small parties, by design. So much so, that its effective magnitude is probably best considered somewhat less than one. That is, despite a component of seats that are themselves allocated proportionally, its effect on the party system would be more like that of a multi-seat plurality system than like FPTP, let alone MMP.

It may be that the current system is indeed already MMP, based on what was enacted in 2016. So I am not saying that the statement about the new system being a “throwback” must be the true one, rather than the one about it being MMP.

The only clear statement in the WaPo article about a change from the status quo is that it will “give voters two separate ballots instead of the single one used in the 2019 election.” This is not a variable that divides MMP from MMM, but rather one that can take either value (one vote or two) within either type.

Thailand has changed its electoral system so many times that I can’t keep track. But it would not seem too much to ask of journalists reporting on electoral system changes to have a basic grasp of the topic so as to avoid making contradictory statements like the ones quoted above.

In my earlier preview of September elections, I noted that the surge in polls for the Conservatives in the Canadian election might lead to the NDP losing votes. It is possible this is happening now.

In recent days, the Liberals have returned to a narrow lead in votes and strengthened their existing seat lead, according to the CBC poll tracker. At the same time, there is a notable dip in NDP votes and seats.

We need to be careful about inferring individual change from aggregate trends. But the most likely cause of what the poll tracker and its seat estimator are picking up is softer NDP voters worried about a Conservative plurality.

Note that this would be strategic voting, but not based on district-level expected outcomes (“coordination”), rather on national-level expectations. “All politics is national”, as Taagepera and I put it in the title of our chapter (10) on predicting district patterns from the Seat Product Model in Votes from Seats.

Here are screen shots from the poll tracker on the morning of 12 Sept.

Votes:

Estimated seats:

The challenge for voters who prefer the NDP over Liberals but are motivated more by stopping the Conservatives is that some of them may be in districts where the Conservatives wouldn’t have won anyway. But some of these voters may help the Liberals win a majority of seats—the poll tracker shows this outcome back within its 95% confidence interval. Yet the sort of voter I am describing wound surely prefer a Liberal minority with a strong NDP third-party caucus.

Getting just the right amount of strategic voting is hard when seats are determined one-by-one, but voters key mostly in national expectations. Yet this is exactly the best available information, which voters tend to employ in choosing voting strategy, according not only to the Seat Product Model, but also Richard Johnston’s The Canadian Party System.

It appears the Liberals have regained their stalled momentum and thus Justin Trudeau just might get what he was seeking after all. On the other hand, a short-term trend need not continue, and at the moment the most likely result still seems to be a Liberal plurality of seats.

Yes, this is how coalitions work. Sometimes politicians give you quotes that are just golden, in how they show real-world recognition of the political-science understanding of political processes.

We are in continuous dialogue with everyone — the left-wingers from Meretz and Labor, and the right-wingers from New Hope — so that all can have wins to show their voters.

The quotation is from Idit Silman, the Coalition Chair for the current Israeli government. “So that all can have wins for their voters” is just what I was getting at in explaining why I think the government will be able to pass its budget and accompanying package of policy reforms. Each party has an interest in the government surviving, and for that, each party must have some policy outputs it can credit-claim for. Ensuring this can happen is precisely the job of the chair of the coalition.

The TOI article in which the quote appears also details the misogyny she is putting up with from the opposition. The Netanyahu sycophants in Likud, and its “religious” party allies really show their true values, and how bereft they are of ideas for governance.

It won’t be quite like September, 2005, back when the virtual orchard was just a sapling, but somewhat like that September sixteen years ago featured several interesting elections, this month also looks great for election watchers.

In September, 2005, we had elections in three major examples of mixed-member systems: Japan, New Zealand, and Germany. (As I look back, I see I wrote several times about Afghanistan’s election that month; I am guessing there will no longer be a need for new Afghanistan elections plantings. I also see lost of posts about a hurricane disaster in New Orleans. Some things do recur, though fortunately in this case not on as horrific a scale, though bad enough.)

In September, 2021, we have the California recall. I don’t have anything at the moment to say about that beyond what I’ve already said. We have Germany, again, with its general election on 26 Sept. And we have Canada, on 20 Sept. There are also various other elections this month, but these are the two I will focus on here.

The German election for this September has been known about for a long time, as it is occurring on schedule (unlike the one in 2005). The Canadian one, on the other hand, is a snap election as one would not have been due till 2023. Both of these elections are going to become case studies in how campaigns really can matter.

For months it has seemed certain that in Germany, the ruling Christian Democratic/Christian Social “Union” bloc (CDU/CSU) would again come out on top, with the Greens in second place and a likely new coalition partner. Then a funny thing happened: the Social Democratic Party (SPD), for years seemingly finished as a major party, started to surge and seemingly now has pulled ahead of the CDU/CSU. The range of coalition possibilities is suddenly rather large, with some novel possibilities in the cards.

The election is also notable compared to past German elections in that the incumbent Chancellor (prime minister), Angela Merkel (CDU) is not a candidate to remain head of government. In fact, it seems likely that the campaign has caused voters to reckon with the with the less than inspiring leadership of the party’s chosen successor to Merkel (Armin Laschet), to feel less than sure they are ready to make the Greens potentially the largest or even second largest party, and to have turned to the SPD and its new leader, Olaf Scholz as the potential safe pair of hands to lead the government. These three parties seem certain to be the big three, but with the largest still below 25% in polls, it will probably take three parties to forge a majority coalition (taking the Union as one for purposes of government-formation, even though it is actually two parties). Unless all three govern together, or the current no-so-grand coalition clears a majority fo seats and continues in power, only with the SPD on top, it is going to take some combination involving the Free Democrats (FDP) to have a majority coalition. The post-election bargaining will be interesting (FDP with either Greens or SPD is not “natural”), and thus the election will really matter for which combines are possible and how much bargaining power each party has.

In Canada, the Liberal Party of incumbent Prime Minister Justin Trudeau looked safe to be not only the largest party, but also to win a majority of parliamentary seats. In fact, given that the election timing was the government’s choice, that is precisely why it is happening–to convert a minority Liberal government into a majority Liberal government. Then Trudeau called the election and a funny thing happened: his party started sinking in the polls and the Conservatives appear to have caught up. In votes, that is.

As in 2019, the Conservatives could lead in votes and still come second in seats. The Conservatives probably need to win the votes by more than a couple percentage points to have a reasonably good chance at a plurality of seats, due to their inefficient vote distribution across the country. A majority Conservative government probably requires that party to keep adding support at a rapid pace, and that may be happening. Yet if that continues, some voters would probably dessert the New Democratic Party (NDP), currently running at around 20%, in favor of the Liberals. Given the FPTP electoral system, of course, such NDP desertion for the Liberals would not be guaranteed to help the latter at the aggregate seat-winning level, although it probably would do so. (Canada’s Green Party, meanwhile, is in a shambles, largely because its black, female, Jewish leader was not sufficiently anti-Israel for others in the party.) One thing seems safe to say at this point: A Liberal majority has become rather unlikely.

That’s the funny thing about campaigns. Sometimes they actually matter.

I’ve complained many times about the MLB playoff system. In fact, when I was looking back on September, 2005 (while drafting the previous entry on this month’s elections) I happened upon my plea for MLB to develop an anti-mediocrity provision, on account of the Padres leading their division in late August, and thus looking assured of a postseason berth, despite being under .500. The Padres did end that season over .500, barely, at 82-80. This was the seventh best record in the National League that year, yet they ended up coasting in to the playoff with a five game lead in their division, while the Phillies (88-74), and Marlins and Mets (both 83-79) sat out. (The Astros were the single Wild Card included in the postseason at the time, at 89-73, being in the same division with the Cards who went 100-62). Every team in the NL East was at .500 or better.

Here we are in 2021, with another absurdity of the playoff format on display as we enter the final weeks of the season. There is no sub-.500 team threatening to make the playoff, fortunately. However, there is a problem potentially even worse: The team with the second best record in the NL could end up playing only one playoff game despite a THIRTEEN AND A HALF GAME lead over the team it would face in the single Wild Card Game. Meanwhile, a team with the fifth best record (currently the Braves, leading the NL East) goes straight to a Division Series.

As I write this, an important regular-season showdown series is about to begin, between the old rivals, the Dodgers and Giants. This will be exciting! The two are currently tied for best record, at 85-49. If there is one good thing we can say about the current playoff format, it is that it certainly matters which of these teams wins the division, and hence goes straight to a Division Series, while the other faces a single-elimination game against the second Wild Card.

Therein lies precisely the problem. It would be a travesty if the team with the second best record happened to lose that one game and be out. You just should not set up a baseball postseason so that one game, rather than a series, can end the post-season of one of your top two teams. Yet at the moment, the second Wild Card slot is held by a team (the Reds) that is 13.5 games behind the Dodgers/Giants. The Padres, who not too many weeks ago seemed a shoo-in for this slot, are another half game back, in a fight not only with the Reds but also with the Phillies (2.5 out in the WC as well as just 2 out in the NL East) and Cards.

It seems that even with two wild cards, there is still a need for an anti-mediocrity provision. I’d say the fundamental problem–now as it was in 2005–is with the privilege in the postseason seeding given to division winners. I understand the value MLB places on having regional representation (kind of like I understand that in electoral systems!), but there needs to be more privilege to the overall national result (again, as in my electoral-system preferences!). I have had a proposal over the years, although it was for four teams per league advancing, not the current five. Surely institutional designers could come up with a better system than one that pits a team that might be just behind–or even tied for–the best record against a mediocre team in a single-game playoff, while still giving an appropriate benefit for being the best regular-season team.

I am always interested in fruit-variety stories. Many famous varieties of fruit were discovered quite by chance, or were deemed lost and then recovered. It seems the boysenberry has an interesting origin story. While I knew it was Knott’s Berry Farm, in Buena Park, California, near where I grew up, that had popularized this variety of berry, until reading a history of Knott’s, I did not know this part of the story:

Amid the Great Depression, Walter [Knott] was making a name for himself with his berries, and in 1932 a man named George M. Darrow heard about a superior berry that was said to be created by a “Mr. Boysen.” Darrow figured Walter would know this Mr. Boysen due to their mutual interest in berries, however Walter admitted he did not, but suggested they look up Boysen in the phonebook. This led them to Rudolph Boysen in Anaheim. Boysen admitted to experimenting with berries, but left them behind on his previous property. Together the three men found Boysen’s long-forgotten berry plant in a ditch covered in weeds and without berries. Boysen said the plant was a cross between a red raspberry, blackberry, and loganberry. After securing permission from the new owners, Walter took cuttings back to Buena Park to plant and cultivate. One year later Walter had a welcome surprise — massive berries! In 1934, Walter had enough cuttings and berries to introduce the new boysenberry as a commercial product…

While I am on the nostalgia trip about Knott’s and the theme park that grew up around the original berry farm and its fried chicken restaurant, I want to quote this passage from the history, as well:

The Knott family struggled through the Great Depression, but in 1934 Cordelia [Knott, wife of Walter] had an idea that would change everything. On a June evening, Cordelia made eight fried chicken dinners for her Tea Room guests. Served alongside salad with rhubarb, biscuits, vegetables, mashed potatoes with gravy, and berry pie on the family’s wedding china, the dinner cost 65 cents. Walter recalled the moment was “the turning point in our economic life.” It was really the turning point that would transform a farm into a theme park.

Word spread of this delicious fried chicken and soon people were flocking to the little farm and Tea Room in Buena Park. The small dining room originally sat 20, and in 1935 they expanded it to 40, only to have to expand it again the following year to accommodate 70. Cordelia’s little Tea Room had become a full-fledged restaurant and when they expanded to seat 350 they figured people would no longer have to wait, but they did!

Indeed, I was there many times with my mother, and we almost always had to wait. This would have been in the 1970s. In addition to that memory, I also can recall back to before there was a fence and required admission fee, before 1968. My mom and aunt would go out do whatever the sisters liked to do, and leave me with Uncle Bob. He often took me to Knott’s and we would just walk around–maybe taking in a few rides or other attractions (for which individual tickets were sold) and certainly riding the train–and mostly just sitting on a bench and watching the goings on. Uncle Bob was always one to strike up conversations with strangers about… whatever.

Fun times. I do not think I have been to Knott’s since the 1980s. But I understand the berry pies and chicken dinners are still going strong.

The title above must seem like a trick question. The current Israeli coalition government consists of eight parties–or perhaps more accurately, seven parties that have cabinet ministers plus a formally committed support party. It bridges left and right, and includes a party of the Arab minority (the support party, without which the parties around the cabinet table lack a majority). So that would seem to fit the definition of a “consensus” government pretty well, per definitions like that of Lijphart.

On the other hand, it has just about the narrowest majority possible (61 seats, or on a good day 62, out of 120). The concept of consensus democracy, per Lijphart, is that governance encompass as wide a range of representatives of social and political groups as possible. This new Israeli government is thus both “broad” and “narrow” at the same time!

We might expect a government that has such a diverse mix of parties and a narrow parliamentary basis to be very cautious. Any bold move could cause it to break apart; in fact, in its first big legislative test it failed to pass anything and allowed a policy reversion point surely not preferred by any member party to stand. It has had other policy failures as well. Yet, as it develops the most important measure it will deal with in its first year, the state budget, it is so far looking surprisingly bold. The headline of an article by Haviv Rettig Gur from 28 July makes the point succinctly: “New budget bill shows coalition launching sweeping reforms despite fragility.” Another from 8 August states the government “aims to transform Israel.”

The measures being incorporated into the budget include reforms to the state’s relationship with it Arab citizens, competition in the kosher-supervision process, a reduction in trade protection, liberalization of the agricultural sector, easing rules concerning electric vehicles, making the banking system more competitive, and a “regulatory revolution.” As Gur explains in the 28 July article, these measures are in the so-called Arrangements Bill, a required companion to the spending bill that delineates structural and policy reforms needed to make the numbers in the more narrowly defined budget bill work.

The idea of sweeping reforms and transformative policy seems more in keeping with majoritarian models of government, which typically are on the classic Westminster model. In such a system, a bare parliamentary majority–albeit one normally not based on a popular vote majority– is able to push through its perceived “mandate” for policy change against an opposition that can complain but not block. Of course, this model assumes–by common definition–a single party controlling the parliamentary majority. How can a fragile multiparty coalition, which does not even include the largest single party, be bold like this?

The answer is certainly not because there is not resistance. Interest groups that benefit from the status quo have ramped up a campaign against reforms, and surely some of the reforms will be phased in, watered down, or dropped before the budget finally passes. Indeed, Gur notes:

These reforms share one characteristic: All have been advocated for many years, but could not advance due to resistance from industry groups, government agencies or various political factions. Haredi parties stood in the way of taxing sugary drinks and plasticware, while farmers’ and manufacturers’ lobbies resisted the agriculture and import reforms.

He further suggests that the unwillingness to advance reforms under previous Likud-led governments was grounded in a basic feature of those governments: they were built around a single relatively dominant party with a dominant leader.

The past 12 years of Benjamin Netanyahu’s rule were marked by tight control over the cabinet and the coalition. New initiatives and controversial reforms were reined in; fewer initiatives meant fewer destabilizing fights. Stability was paramount, so nothing that could cause dissension within the coalition was allowed to advance. No one even contemplated reforms to the state religious bureaucracies as long as Haredi parties were in the coalition. Wherever possible, domestic policy was farmed out to relevant interest groups.

I agree with this interpretation, and it is indeed probably what we would expect from coalitions comprised of one “large” party that is actually so small as to have held, on several occasions, only around half of the needed 61 seats, plus a smattering of small and often sectoral parties. But shouldn’t a government with no big party at all, like the current one, be even more fragile and stymied by the need to avoid defections?

Maybe not. As Gur says, “It’s a government keenly aware that any of its member factions could topple it at any moment. It is in that sense a more egalitarian cabinet than any in Israel’s history.” I think this is accurate, but I’d go a step farther. It is a government that consists of several parties that have not been in a governing majority for many years (like Meretz, or ever, like Ra’am), or were formed explicitly to get Netanyahu out of power (New Hope), or who currently exercise senior ministerial positions such as they they previously were able to hold only in a subordinate position to Netanyahu (thinking here of Yisrael Beiteinu, recent past incarnations of Labor, as well as the government’s two core power-sharing/alternating partners, Yesh Atid and Yamina). Benny Gantz’s Blue & White probably straddles a couple of those categories–formed initially to get Netanyahu out of power, and then accepting a decidedly subordinate role to him in the previous “alternating” government.

That is, this government came together around a new cleavage–opposition to the previous Prime Minister, not a specific policy or ideological cleavage. Each party in the government has reasons to prefer making this work to the alternative, which might very well be a new Netanyahu-led coalition that some of these parties would have to join for it to have a majority. No one in the new majority wants that–at least for now. And most of these governing parties might lose seats if there were a new election before the government they were in could show any progress on which to run.

The situation just described is strikingly like a majoritarian pattern of government. For at least the current moment, these parties need a record of joint achievement to run on (albeit still as separate parties) in the next election. They are thus collectively accountable in a way that more resembles a single-party majority than it resembles many past Israeli governments of one relatively large party buttressed by a bunch of small ones.

The Israeli government change earlier this year shows that accountability–the usual selling point of two-party dominant majoritarian systems–can be achieved even under conditions of party-system fragmentation. The government was made possible only because a new party, Gideon Saar’s New Hope, offered an alternative option for voters on the right that Yamina (the party of new PM Naftali Bennet) was able to go along with, and in fact end up (co-)leading. Only via those mechanisms was it possible to produce alternation in government. And now because the parties all need to work together to deliver for their own distinct interest-group and ideological constituencies it needs to push a bold reform agenda on which to be accountable at the next election. I think the point holds even if we assume that these parties will never seek a renewed collective mandate at election time, to be reelected as a government. I assume they will not do that, unless perhaps if Netanyahu is still leading Likud at the next election and none of these parties prefer working with him again. But in the meantime, they are kind of stuck with one another, and need to show results.

This moment in Israeli politics is thus quite majoritarian, despite all the parties that must forge a consensus to keep their government together. I am using the term, majoritarian, in a way that is more consistent with how some recent literature has used it, which is somewhat different from Lijphart’s sense. For Lijphart, part of the definition of majoritarianism is “single-party, bare majority” governments. However, more recent works suggest that we can conceptualize majoritarianism as parties that collectively reflect a majority of voters and can pass policy with a bare majority of parliament sufficing. Some significant works I am thinking of that have made key contributions to this conception of majoritarianism include McGann, Latner and McGann, Ganghof, and Li. This conception is in contrast to the core notion of the consensus pattern of democracy, which implies super-majorities, either due to institutional requirements (like strong bicameralism or an entrenched constitution that must be amended to carry out significant policy change) or due to oversized coalitions (those that contain more parties than needed to comprise a majority). Basically, what has happened here should become the new textbook definition of how PR-parliamentarism should work: creating the opportunity for one majority to be replaced by another majority, when a new salient cleavage emerges, but for the new majority to consist of multiple parties given that proportional representation normally does not allow for the majority to consist of a single party.

So, yes, the current Israeli government is quite majoritarian, despite the need for a consensus across a diverse range of parties in order to govern. If it pulls off the reforms in its proposed budget, it will have performed quite like a classic case of alternation in power in a Westminster-type system, only with its set of policies actually grounded in the votes of a majority of the electorate and not merely a majority in parliament. The path to such policy success will not be smooth. For instance, a group of 11 members of Knesset, from Blue & White and Labor, are threatening to block the arrangements bill over opposition to the agricultural liberalization. Expect more of this as the process plays out. It does not necessarily undermine my conclusion on the majoritarian nature of this coalition. Even single-party majority governments often have to negotiate with blocks of their own members who object to government policy changes. The difference is that in a multiparty government, these disagreements are more likely to be public, precisely because each party generally needs to claim credit as a separate party at the next election. However, if my core claim about this government is correct–that they have a collective need to hang together to produce anything to run on, given they lack good exit options for now–then they should still pull off a significant part of their transformative policy agenda (see the bill on military draft of Haredim for one other case to watch). And that is a key aspect of the majoritarian pattern of parliamentary governance, whether conceived of single-party, bare-majority cabinet (per Lijphart’s ideal type and the Westminster model) or as bare-majority coalition of parties representing a mix of policy positions in juxtaposition to an alternative majority (per McGann, Latner, Li, and Ganghof).

Very pleased with this article by Geoffrey Skelley at FiveThirtyEight: “How The House Got Stuck at 435 Seats.” The author interviewed me for the piece, and references my work and that of coauthors, including Rein Taagepera, the discoverer of the cube root law of assembly size.

There is also a good visualization tool for how each state would be over- or under-represented with various House sizes.

I remember back at the time of the 2003 California gubernatorial recall election, one of my laments was that, with so many candidates on the replacement portion of the ballot, not one of them was a secessionist/sovereigntist. Well, this time, no such lament!

I recently learned that there is a sovereigntist candidate this time. His name is Michael Loebs, who in his day job is a lecturer in political science at San Francisco State University. He is running with the California National Party, which has styled itself on the model of the Scottish National Party. (Because the state restricts what party names can appear on the ballot even though party affiliations are self-declared by candidates, he appears as an “independent.”)

I am not posting this to have a conversation about whether California should have an active movement for (peaceful) separation, although I have felt such leanings myself for about as long as I have been politically aware. Nor do I use this space to endorse candidates. I am simply happy that, if we have to have this trainwreck of a recall/replacement election, at least we finally have a sovereigntist candidate in the mix.

Of course, I will vote NO on the recall regardless of how I vote on the replacement question. In fact, you can call NO on the recall an endorsement!