The zany Iowa allocation

Really, this is unjustifiable. I used to believe the Democratic Party actually used “proportional representation” for its presidential nominating delegate allocation. But this is not even close.

“Realigned vote” is the shares after participants in candidate-supporting groups that were below 15% in any given precinct shift to their second choice. This is the only good part of the whole process. The “realignment advantage” is just an indicator of how much a candidate gains (or loses) at that stage: the realigned vote share divided by the initial vote share.

How you get from there to the final delegate allocation is clearly some sort of black magic. It goes by way of this weird phantom called “state delegate equivalents”.

And somehow out comes an allocation in which a candidate who started off in second place, even after realignment, not only comes in first in delegates but somehow is over-represented to about the same degree as the first place party in your average FPTP election. (Delegate advantage is the delegate share divided by the realigned vote share.)

This is not proportional representation. Whatever it is, it is no way to run a presidential nominating process.

And I have not even mention the great app failure, or the possibility that some precinct-level allocations were just calculated wrong. (See spreadsheet of errors.)

Sources for data: NYT, WaPo, IDP.

See also a breakdown of available delegates by county and precinct. (The IDP link above has it even more detailed.)

Ireland 2020

Ireland holds its general election on 8 February. I wish I could offer a good preview. But no time. However, given how much many of us enjoy elections under single transferable vote, it seems like the community might want to gather and do some fruitful plantings. So here’s the place for it.

One thing of note I am aware of is polling showing Sinn Féin doing well, possibly enough to break into the top two. In first preferences, that is. Given STV, of course, an important consideration will be if it picks up transfers (or where, if anywhere, its supporters go in districts where they have votes that don’t elect one of their own).

Apparently this is the first time Ireland has voted on a Saturday. Naturally, I am not a fan of that idea. (The link is to Charles Richardson’s blog, The World is Not Enough, which I just discovered thanks to a comment on another thread here by Tom.)

Some thoughts on Peru’s midterm election

After the Constitutional Tribunal ruled them legal, Peru held extraordinary legislative elections on 26 January. President Vizcarra dissolved Congress on the grounds that Congress had voted no-confidence in his cabinet (although not directly) twice. This was the first use of this provision since Peru’s 1992 constitution was promulgated, and as such it was the first time when legislative and presidential elections were not held concurrently.

However, the election did not merely lack a presidential contest. Almost uniquely, President Vizcarra, despite having been elected as part of former President Pedro Pablo Kuczynski’s party (previously Peruanos por el Kambio, now Contigo), chose not to endorse any party for the elections, merely advising voters to inform themselves. This reluctance was seemingly not due to any concern that Vizcarra’s endorsement would be a weakness for any party: at the time of the election, his approval rating stood at 58%.

Peru’s unicameral Congress is elected using open party-list proportional representation in 26 regions, with a 5% threshold applied at the nationwide level. The average district magnitude of 5 makes this a relatively moderate form of proportional representation, which explains why Keiko Fujimori’s Fuerza Popular was able to win a comfortable majority of 56% of the seats in Congress at the 2016 election despite only winning 36% of the vote.

The results of this election, however, were extraordinarily fragmented. The largest party, Accion Popular, got only 10% of the vote, and nine parties made it above the 5% threshold to enter Congress. More than a quarter of votes went to parties below the threshold, and in four provinces the leading party will receive no representation in Congress.

I will leave it to Peruvian experts, which I most certainly am not, to discuss what this result means for Vizcarra’s ability to pass his agenda. However, the results are interesting for other reasons.

Since the promulgation of the 1992 Constitution, Peru’s party system has remained quite stable (at least in terms of numbers, the identity of the parties has changed quite a lot). It has also remained quite close to the number of parties that the Seat Product Model (Shugart and Taagepera, 2017) would predict.

These elections are thus extremely unusual, and are perhaps indicative of the high importance of presidential elections and presidential endorsements in imposing structure on legislative elections in presidential countries. A fact particularly suggestive of this is the disastrous result for the two leading parties in 2016, both of which were affiliated to presidential candidates. Keiko Fujimori’s Fuerza Popular fell from 36% of the vote and 78 seats to 7% and 15 seats, while Peruvanos por el Kambio/Contigo fell from 16% and 18 seats to 1% and no seats.

Thuringia: Leader of smallest party in state parliament elected premier, with AfD support

This is a strange development, and one to keep a concerned eye on. The German state of Thuringia, which held an election October, 2019, will now have a premier from the Free Democrats (FDP), who barely cleared the 5% threshold in the election. The FDP candidate for state premier, Thomas Kemmerich, was elected by one vote over the incumbent, Bodo Ramelow, of the Left Party. With the help of the Alternative for Germany (AfD), an extreme right party, Kemmerich defeated Ramelow in a third round of voting, 45-44.

The two largest parties in the state parliament since the 2019 election are the two most extreme parties in the German party system–The Left with 29 seats, and the AfD with 22. The Christian Democrats (CDU) came third with 21, then 8 for the Social Democrats (8), and 5 each for Greens and FDP (who really did just scrape over with 5.0%). The outgoing government was Linke-SPD-Green. But they fell to 42 seats out of the 90, compared to 46 in 2014. The 2014 outcome was also a little unusual–a three-party coalition excluding the largest party (CDU, which had 34, with Left second on 28). But not as unusual as whatever government Kemmerich will put together now.

I don’t know how common a government led by the sixth largest party in parliament is, but I am guessing pretty uncommon. (Answer in comments!) Kemmerich says he will not bring the AfD into a coalition, but he now owes his position to them. What does this mean for the cordon sanitaire the establishment parties (and the Left, which really can’t be called “establishment”) have been maintaining against the far right?

UPDATE: The premier-elect has resigned, and early elections will be proposed. A decision on early elections requires a vote in the state parliament. In fact, it requires a two-thirds majority, and at this point the state’s CDU leadership has been opposed to returning to the electorate.

Why so much “high policy” in the LDP?

I am close(-ish) to finishing up a book on Party Personnel, coauthored with Matthew Bergman, Cory Struthers, Ellis Krauss, and Robert Pekkanen. The short version of what the book is about: How does the electoral system (and electoral reform) shape how parties deploy their “personnel” (i.e. elected legislators) to legislative committees to allow them to engage in activities that support the party organizational goal of seat-maximization?

(Quick note: While the book is coauthored, I should make clear that this post is just my musing about a puzzle, and not a piece of the book. Nor do my coauthors bear any responsibility for what I am writing here, or conclusions I attempt to draw.)

The outcome variable of interest in the Party Personnel project is the “type” of committee assignment a legislator receives–high policy, public goods, or distributive. This typology first appeared in Pekkanen, Nyblade, and Krauss (2006). In most of the countries covered in the book, a party typically has 50%-60% of its legislators sitting on high policy in any given term of parliament (not necessarily all at once, as members may be rotated). But, in Japan, the Liberal Democratic Party often has 75% or more on high policy, and in some years over 90%!

What explains the unusually high rate of high policy committee assignments in the LDP? I do not think we currently have a good explanation. We have floated some in internal discussions (mostly internal to my own brain), but as I will show in this post, they are not adequate. Before we get into trying to answer the question posed in bold at the start of this paragraph, let’s establish which committees are classified as high policy. These are committees charged with involvement in policies that are about the management of the economy and other matters of state–this is the sense in which they are “high”. Examples are finance, economy, budget, justice, defense, and foreign affairs.

Japan underwent a major electoral reform prior to the 1996 election. The old system was single non-transferable vote (SNTV). The post-reform system is mixed-member majoritarian (MMM). If we look only at averages by electoral-system era, it looks like a case of electoral reform resulting in a large increase in the percentage of LDP members of the House of Representatives obtaining high policy (HP) committee assignments:

SNTV era: 73% of legislators on HP.

MMM era: 86% of legislators on HP.

The difference in means when comparing eras is statistically significant. So, it is the electoral reform, right? (Never mind that even 73% pre-reform would be high, compared to other cases.) Is there a reason why MMM would lead a party to want to emphasize the experience of its caucus in HP more than would be the case under SNTV? Amy Catalinac‘s book, Electoral Reform and National Security in Japan (2016), suggests a reason why the answer might be yes. She analyzes individual candidates’ campaign manifestoes and finds that they are more likely to mention defense under MMM than they were under SNTV. The reason she gives is that members’ having a reputation for high policy areas like defense and foreign affairs was not useful under SNTV, when they were overwhelmingly concerned with “pork” for which they could get individual credit. By contrast, under MMM, each member is the sole standard-bearer in a single-seat district (and is often also running on a closed party list), and thus the pork incentive is greatly diminished. As national security is a key component of high policy, a similar effect might also account for the higher rate of HP committee assignments after electoral reform. That is, HP committees are assigned to LDP legislators at a greater rate under MMM because the party as a whole has a stronger interest in appearing credible on high-policy issues, including national security. This is one plausible explanation of the changes in era averages. For reasons I will turn to later, I am not satisfied with this attempt to explain the patterns in committee assignment.

An initial idea I had was that perhaps the high rate of HP, post-reform, is a legacy of a high rate under SNTV, and will be seen to have declined under MMM. In other words, this is a totally competing explanation to the one that could be derived from a logic similar to that of Catalinac. I would expect more delegation to the cabinet under MMM, in the sense of its being more Westminster-like than under SNTV. (This is a point that Catalinac explicitly argues, in justifying her disagreement with some Japan specialists who, upon the electoral reform, thought pork would remain just as important, only district-focused rather than more narrowly focused as under SNTV.) The problem with expecting a shift towards more HP committee membership under a supposedly more Westminster-like system, or just generally a more policy-centric system, is that it does not comport well with our comparative evidence.

We know that in two Westminster systems covered in the book, Britain and pre-reform New Zealand, the rate of HP committee membership is not especially high (30% in UK Conservatives, 33.5% in Labour; NZ National 54%, Labour 68%). All of these percentages are lower–most are much lower–than the MMM-era mean for the LDP. Nor is it high in Germany (near 60% in both major parties) or post-reform NZ (46% National, 57% Labour), our two MMP cases. These are all systems in which we expect party policy reputation to matter more than individual reputation. So, if Japan moves from SNTV, with its strong focus on the individual, to MMM, with greater focus on the party as a “team” seeking to take on (or hold on to) governing, why would HP be high under MMM?

With this as a puzzle, it seemed likely it might have been just a legacy of pre-reform SNTV. Perhaps, under SNTV, there actually is a logic to getting nearly everyone on HP because your electoral system makes everyone need to have a unique personal reputation. While this does, as noted, run up against the problem that the HP percentage is higher post-reform, it is worth entertaining why its being high under SNTV might not itself be inconsistent with the incentives of the system.

Why might HP for almost everyone be a strategy compliant with SNTV? Maybe the former SNTV system led the party to want most of its members to gain experience in high-policy areas because each member needs to be “his own party”. (Under SNTV, especially, LDP legislators have been overwhelmingly male.) This possible explanation seems at first to be in tension with common expectations that members under SNTV have to differentiate themselves, such as by credit-claiming for pork. Because votes are not pooled (or transferred) among co-partisans, the party needs a way to divide the vote efficiently in order to maximize seats. The literature on vote-division emphasizes how members need to be distinct from one another, so why have almost everyone on high policy?

Actually, this piece of the larger puzzle turns out not to be such a puzzle at all, even though it initially struck me as odd. Even if all legislators (2 or 3) from a given district are on HP, they can still differentiate by being on different HP committees (one on budget, one on defense, for example). Thus having many members on HP and having them develop their own personal reputations are not in any way contradictory. However, differentiating on sub-categories within HP may still not be as beneficial to claiming credit for things uniquely attributable to a specific politician as are pork-related benefits. A common expectation in the vote-division literature (including a key point of Catalinac’s thesis) is that pork is more useful for vote-division than high policy.

Even if we accept that HP is likely suboptimal for vote-division purposes, having everyone on HP does not preclude legislators also being on more specifically district-focused committees in the areas of public goods (e.g., health or education) or distributive (e.g., construction, agriculture, or transport). In fact, the LDP also has an unusually high rate (relative to other parties among the book’s cases) of category overlap. The average member is on about 1.6 of our three categories, unlike in most other countries where the figure is in the range of 1.2 to 1.4. In other words, by our categories, it is members in other countries that are the specialized ones. In the LDP, they are not; they are actually closer to being generalists, at least in this sense.

Having assignments in multiple categories allows each legislator to build a personal portfolio, almost like a micro-party, in which they are involved in some HP task and also frequently a task in either public goods or distributive during the same term. This kind of portfolio could be very useful for building the personal electoral coalition each individual needs to ensure election under an electoral system that pits members of the same party against each other in multi-seat districts, with no party-level vote-pooling. In other words, SNTV.

If the building of a personal portfolio, including but not limited to HP, due to SNTV incentives were the explanation, we should see a decline after the change to MMM. In the graph below, we will see that we do! So that is good. However, we still face the problem that it should not be higher on average during the era of MMM (so far) than it was during the era of SNTV. Yet that is precisely what we saw in the era averages shown above. Now, let’s disaggregate this thing called an electoral-system era. The graph shows the percentage on HP in each election from 1980 through 2009. The vertical line demarcates the eras, marking the first election under MMM.

The decline under MMM is certainly consistent with the notion that HP is less important to the individual legislator over time, given an electoral system that has eliminated intraparty competition in multi-seat districts. Additionally, the 1990 and 1993 elections show exceptionally high levels of personal portfolios including HP at the end of the SNTV era. Yet look how low the rate is before 1990. Thus, while we might be able to say that adaptation to MMM is leading to an expected decline in HP service after 1996 (albeit perhaps too slowly by 2009), we obviously should not conclude that it started so high because of SNTV! It was low under SNTV… until it was high. It then peaked in the first MMM election, before beginning a decline.

So what changed to lead the LDP suddenly to want nearly everyone to have high policy in their portfolio in 1990 and 1993? This–finally–is the question I am crowd-sourcing. The context of the 1990 election is one in which the LDP had just lost its majority in the second chamber (the House of Councillors). There was also a divisive debate at the time on enacting a national consumption tax, around the same time that real estate and stock market valuations were unsustainably high (leading to a subsequent period of economic stagnation). Also in 1993, due to splits over various issues including electoral reform, the LDP actually failed to win a parliamentary majority and found itself temporarily in opposition. How these would explain a surge in HP is not clear to me. So I am not proposing an explanation, but that is the context and perhaps points towards an explanation.

The pattern is similar if we look at category overlap. Again, this simply measures how many categories–out of high policy, public goods, and distributive–a member sits on. So, ignoring anyone who is on no committees in these categories (and I am ignoring such rare birds here), it can range from 1 to 3. The next graph shows this averaged across LDP legislators by election year. Again, the vertical line marks 1996, the first election under MMM. As we see, it is only 1990, 1993, and 1996 when the average number of committee categories per legislator approaches or exceeds 2.0. While lower in the other seven election, it is still above 1.5 in all elections except the three earliest SNTV elections in the sample (1980 through 1986) and then again in 2003 and 2009 of the MMM era. In the five just mentioned, it is between 1.3 and 1.4.

The pattern is again consistent with the LDP deciding for some reason before the 1990 committee allocations that it needed each member to have both high policy and at least one committee assignment from another category. After 1996, this category overlap becomes markedly less common (but still is higher than in most other parties we cover in the book).

A final graph breaks the HP category down and shows three of the main committees within it.

It is clear that the pattern of surging HP membership in 1990 is largely about the budget committee. More than half the party’s legislators sat on this committee in the legislatures elected in 1990, 1993, and 1996. The other two included here (economy and defense) show smaller bumps as well, just not rising as high. This again would be potentially consistent with my proposed explanation that “everyone needs a diverse portfolio under SNTV”, provided we can add a condition as to why this need is only actually realized at the end of the SNTV period and not the entire era. So, the electoral system explanation needs to be augmented by some political factor, like fracturing of the party and greater pressure from the opposition.

It is further worth noting that of all “high policy” committees, it is budget and economy that would have the greatest “pork” potential. While I would not want to reclassify committees dealing with such clearly aggregate national matters to the distributive category–they are clearly “high” topics–they do allow for opportunities to claim credit. Did the LDP simply need this even more in the 1990s than in the 1980s? The patterns certainly suggest they need it less under MMM, at least after the first MMM election of 1996. The patterns also show that defense committee assignments very quickly went back down in the 2000s after their peak with the first MMM election. So, while they may continue to talk about national security in the individual campaign manifestoes (per Catalinac), few LDP members by 2009 are sitting on committees where they can actually be involved in such policy discussions.

This has been a long post. Thank you to anyone who made it this far! I hope someone has some suggestions for why these patterns are seen in the data. The book does not look at time factors in committee assignments, except for pre-reform and post-reform eras where there has been a change of electoral system (Japan and New Zealand, among our cases). However, any attempt to explain the anomalously high averages in high policy assignment and committee-category overlap in Japan has to grapple with the fact that there is a within-era variance in the LDP that is quite stark. It is not just a story about two different electoral systems, nor is it something immutable about the LDP.

Australian fires

I have a lot of readers and regular commenters in Australia. I actually don’t know where most of them live. I just wanted to take a moment to say that I hope you are all safe. Being a Californian, I know that, even if you do not live in direct harm’s way, the smoke and the accompanying weather can make life difficult during these emergencies. Be safe, and be well.

Spain coalition agreement and possible electoral reform

The Spanish Socialist Party (PSOE) and Unidas Podemos (UP) have publicized an agreement on a program of coalition government. It is an ambitious “Progressive Coalition.” It is a minority coalition: out of the 350 seats, the PSOE won 120 and the UP 26, so together they have 41.7% of the seats, 30 seats short of a majority. Other agreements with regional parties for parliamentary support may be forthcoming; in fact an accord with the Basque Nationalist Party (PNV, with 7 seats) has already been published.

The PSOE-UP agreement has one provision of special interest to F&V: Section 5.7 concerns electoral reform, and states the parties will work to find “a consensus that would permit reforming the electoral formula to improve the proportionality of the system.”

Electoral reform is, of course, generally difficult. That the current system is relatively disproportional for an electoral system we would clearly classify as “proportional representation” (PR) is well established. The modest level of proportionality is due to the use of many districts, resulting in a mean magnitude around 7, and the D’Hondt formula. There is also substantial malapportionment. Consider the following advantage ratios (%seats/%votes) for several key parties; a value greater than one indicates the party is over-represented. These are from the most recent (“2019b“) election.

PP 1.22

PSOE 1.22

UP 0.78

C’s 0.42

Vox 0.98

ERC 1.03

JxCat 1.04

EAJ/PNV 1.10

The last three are among the larger regional parties. It is noteworthy that they are not significantly over-represented, despite the regionalized nature of the PR system.   On the other hand, both “large” parties are quite over-represented, while the new government’s junior partner is quite severely under-represented (not as bad as Ciudadanos, however). Some very small regional parties are significantly over-represented. For instance, Sum Navarre has an advantage ratio of 1.43. (It helps to win all of your votes in one rather low-magnitude (5) district in which you had the local plurality of votes.)

I have no information on what reforms the parties may have in mind. However, some combination of the following might be possible:

1. Readjusting magnitudes (long overdue!);

2. Small compensation tier;

3. Shift to (Modified?) Ste.-Laguë.

An interesting feature of the agreement with the PNV is its sixth provision, which states that the new government will make good on policy deals previously struck with the Partido Popular (PP), when it was in government. A PP minority government was replaced by a PSOE minority in a constructive vote of no confidence in June, 2018, which the PNV supported. This new agreement follows the second general election since that parliamentary vote.

Thanks to Bonnie Field (on Twitter) for the links to the two accords.


UPDATE:  There is now a further agreement, this one with the Republican Left of Catalunya (ERC). It is an agreement to abstain. I am not sure how common inter-party agreements over abstention on government formation are, but here we have one.

Field has a good rundown of where things standas of 3 January, the day before the parliamentary debates being.

Lithuania threshold reduction

The Lithuanian parliament has passed an amendment to the country’s electoral law. If it secures final passage, as expected, the threshold for party-list seats will be reduced from 5% to 4% for parties running alone and from 7% to 5% for electoral coalitions.

A proposal to reduce the assembly size from 141 to 121 was defeated in a referendum in May.

(Source: Linas Eriksonas, 2019)

Note that Lithuania has a mixed-member majoritarian (MMM) system: 70 of 141 legislators are elected in single-seat districts, the rest by list PR (nationwide, non-compensatory). The legal threshold affects only the list component.

Canada and UK 2019: District level fragmentation

With two of the big Westminster parliamentary democracies having had general elections in 2019, we have a good opportunity to assess the state of district-level competition in FPTP electoral systems.

(Caution: Deep nerd’s dive here!)

Before we turn to the district level, a short overview of what is expected at the national level is in order.

As noted previously, Canada’s election produced a nationwide seat balance that was extremely close to what we expect from the Seat Product Model (SPM), yet the nationwide votes were exceedingly fragmented (and, anomalously, the largest seat-winning party was second in votes). The UK election, on the other hand, was significantly less fragmented in the parliamentary outcome than we expect from the SPM, even if it was in key respects a “typical” FPTP outcome in terms of manufacturing a majority for a party with less than a majority of the vote.

In general, over decades, Canada tends to conform well to the SPM expectation for the shape of its parliamentary party system, whereas the UK is a more challenging case from the SPM’s perspective.

The SPM states that the effective number of seat-winning parties (NS) should be the seat product, raise to the power, 1/6. The seat product is the assembly size, times the mean district magnitude. The SPM predictions for NS explain around 60% of the variance in actual outcomes for elections around the world under a wide variety of electoral systems. SPM predictions for other output quantities also explain in the neighborhood of 60%. So the SPM is both successful at explaining the real world of seat and vote fragmentation, and leaves plenty of room for country-specific or election-specific “other factors” (i.e., the other 40%). The SPM is based on deductive logic, starting from the minimum and maximum possible outcomes for a given number of seats at stake (in a district or an assembly). The logic is spelled out in Votes from Seats.

In the case of a FPTP system, the SPM makes the bold claim that we can understand the shape of a party system by knowing only the assembly size. That is because with district magnitude, M=1, the seat product is fully described by the country’s total number of seats, S, which is also the number of districts in which the voting is carried out. Thus we expect NS=S1/6. Let’s call this “Equation 1.”

For Canada’s current assembly size (338), this means NS=2.64, as an average expectation. Actual elections have tended to come pretty close–again, on average. Of course, individual elections might vary in one direction or the other. (The assembly size was also formerly smaller, but in recent times, not by enough to concern ourselves too much for purposes of this analysis.) For the UK, the corresponding expectation would be 2.94 based on a seat product of 650.

The actual Canadian election of 2019 resulted in NS=2.79; for the UK it was 2.39. Thus for Canada, we have a result very close to the expectation (ratio of actual to expected is 1.0578). For the UK, the actual result was quite short (ratio of 0.8913). As I said, the UK is a challenging, even aberrant, case– at least at the national level.

What about the district level? A national outcome is obviously somehow an aggregation of all those separate district-level outcomes. The SPM, however, sees it differently. It says that the districts are just arenas in which the nationwide election plays out. That is, we have a logical grounding that says, given a national electoral system with some seat product, we know what the nationwide party system should look like. From that we can further deduce what the average district should look like, given that each district is “embedded” in the very same national electoral system. (The logic behind this is spelled out in Votes from Seats, Chapter 10).

The crazy claim of the SPM, district-level extension, is that under FPTP, assembly size alone shapes the effective number of votes-earning parties in the average district (N’V, where the prime mark reminds us that we are talking about the district-level quantity rather than the nationwide one). (Note that for FPTP, it must be the case that N’S=1, always and in every district).

The formula for expected N’V under FPTP is: N’V=1.59S1/12 (Equation 2). It has a strictly logical basis, but I am not going to take the space to spell it out here; I will come back to that “1.59” below, however. It is verified empirically on a wide set of elections, including those from large-assembly FPTP cases like Canada, India, and the UK. So what I want to do now is see how the elections of 2019 in Canada and UK compare to this expectation. (Some day I will do this for India’s 2019 election, too.)

If the effective number of seat-winning parties at the national level (NS) is off, relative to the SPM, then it should be expected that the average district-level effective number of vote-earning parties (N’V) would be off as well. They are, after all, derived from the same underlying factor–the number of single-seat districts, i.e., the assembly size (S). We already know that NS was close to expectation in Canada, but well off in the UK in 2019. So how about the districts? In addition to checking this against the expectation from S alone, we can also check one other way: from actual national NS. We can derive an expected connection of N’V to NS via basic algebra. We just substitute the value from one equation into the other (using Equations 1 and 2). If we have NS=S1/6 then it must be that S= NS6. So we can substitute:

N’V=1.59(NS6)1/12= 1.59√NS (Equation 3).

In a forthcoming book chapter, Cory L. Struthers and I show that this works not only algebraically, but also empirically. We also suggest a logical foundation to it, which would require further analysis before we would know if it is really on target. The short version suggested by the equation is that the voting in any given district tends to be some function of (1) the basic tendency of M=1 to yield two-candidate competition (yes, Duverger!) in isolation and (2) the extra-district viability of competing parties due to the district’s not being isolated, but rather embedded in the national system. The 1.59, which we already saw in Equation 2, is just 22/3; it is the expected N’V if there were exactly two vote-earning parties, because it is already established–by Taagepera (2007)–that the effective number tends to be the actual number, raised to the power, two thirds. And the square root of NS suggests that parties that win some share of seats (i.e., can contribute more or less to the value of NS) tend to attract votes even though they may have no chance of winning in any given district. By having some tendency to attract votes based on their overall parliamentary representation, they contribute to N’V because voters tend to vote based on the national (expected, given it is the same election) outcome rather than what is going on in their district (about which they may have poor information or simply not actually care about). If the parliamentary party system were fully replicated in each district, the exponent on NS would be 1. If it were not replicated at all, the exponent would be zero. On average, and in absence of any other information, it can be expected to be 0.5, i.e., the square root.

How does this hold up in the two elections we are looking at in 2019? Spoiler alert: quite well in the UK, and quite badly in Canada. Here are graphs, which are kernel density plots (basically, smoothed histograms). These plots show how actual districts in each election were distributed across the range of observed values of N’V, which in both elections ranged from around 1.35 to just short of 4.5. The curve peaks near the median, and I have marked the arithmetic mean with a thin gray line. The line of most interest, given the question of how the actual parliamentary outcome played out in each district is the long-dash line–the expected value of N’V based on actual NS. This corresponds to Equation 3. I also show the expectation based solely on assembly size (light dashed line); we already have no reason to expect this to be close in the UK, but maybe it would be in Canada, given that the actual nationwide NS was close to the SPM expectation, based on S (Equation 2).

Here is the UK, then Canada, 2019.

What we see here is interesting (OK, to me) and also a little unexpected. It is the UK in which the actual mean N’V is almost the same as the expectation from nationwide NS (i.e., Equation 3). We have actual mean N’V=2.485 compared to expected N’V from actual NS of 2.45; the ratio of actual to expected is 1.014. We can hardly ask for better than that! So, the nationwide party system (as measured by NS) itself may be well off the SPM expectation, but the vote fragmentation of the average district (N’V) closely tracks the logic that seems to stand behind Equation 3. Voters in the UK 2019 election tended to vote in the average district as if parties’ national viability mattered in their choice.

In Canada, on the other hand, even though national NS was very close to SPM expectation, the actual average district’s N’V (2.97) was really nowhere near either the expectation solely from S (the light dashed line, at 2.58) or the expectation from the actual NS (2.66). The average district was just so much more fragmented than it “should be” by either definition of how things ought to be! (The ratio of actual to that expected from Equation 3 is 1.116; the Equation 3 expectation is almost exactly the 25th percentile of the distribution.)

The Canadian outcome looks as if the exponent on actual NS in Equation 3 were around 0.64 instead of 0.5. Why? Who knows, but one implication is that the NDP (the third national party) performed far better in votes than the party’s contribution to NS implies that it should have. Such an overvaluing of a party’s “viability” would result if voters expected the party to do much better in terms of seats than it did. This is probably a good description of what happened, given that pre-election seat extrapolations implied the NDP would win many more seats than it did (and the Liberals fewer). The NDP also underperformed its polling aggregate in votes (while Liberals over-performed), but it held on to many more voters than it “should have” given its final seat-winning ability would imply. That is, the actual result in votes suggests a failure to update fully as the parties’ seat prospects shifted downward at the very end of the campaign. In fact, if we compare the final CBC poll tracker and seat projections to the ultimate result, we find that their actual votes dropped by 13.6% but their seats dropped by 31.7% (percent change, not percentage points!). In other words, this was just an unusually difficult context for voters to calibrate the expectations that Equation 3 implies they tend to make. (I am assuming the polls were “correct” at the time they were produced; however, if we assume they were wrong and the voters believed them anyway, I think the implications would be the same.)

It should be understood that the divergence from expectation is not caused by certain provinces, like Quebec, having a different party system due to a regional party, as some conventional expectations might point towards. While Quebec’s size is sufficient to exert a significant impact on the overall mean, it is not capable of shifting it from an expected 2.6 or 2.7 towards an observed 3.0! In fact, if we drop the Quebec observations, we still have a mean N’V=2.876 for the rest of Canada. The high fragmentation of the average district in the 2019 Canadian election is thus due to a Canada-wide phenomenon of voters voting for smaller parties at a greater rate than their actual viability would suggest they “should”. In other words, voters seem to have acted as if Trudeau’s promise that 2015 would be the last election under FPTP had actually come true! It did not, and the electoral system did its SPM-indued duty as it should, even if the voters were not playing along.

On the other hand, in the UK, voters played along just as they should. Their behavior produced a district-level mean vote fragmentation that logically fits the actual nationwide seat balance resulting from how their votes translated into seats under FPTP. There’s some solace in that, I suppose.

South Korea moving to MMP?

South Korea’s National Assembly appears close to passing an electoral reform bill. It seems that it would change the existing mixed-member majoritarian (MMM) system to mixed-member proportional (MMP).

I always take media reports about important details of electoral systems with caution, but it seems the list seats will be made compensatory: “Under MMP, parliamentary seats are tied to the percentage of voters’ support for political parties.”

The current system (as of 2016) has 47 non-compensatory list seats, in a 300-member assembly.

However, there is a catch. The article says, “The number of PR posts to be allocated under the MMP representation scheme will be capped at 30.” Yet there are to remain 47 list seats; how are the other 17 allocated? To the largest party, or based on vote shares without taking district wins into account (as under MMM)? I wish it were clear, as such details would make quite a difference.

Regardless, proportionality will be quite limited.

An earlier provision of the reform bill that would have provided for 75 list seats was turned down.

Maybe we can call the new system MMp. Maybe.

Thanks to FairVote Vancouver and Kharis Templeman for the tip.

Democratic primary: Don’t understate Biden’s dominance

The fragmentation of the US Democratic Party’s field of presidential pre-candidates exaggerates the weakness–real though it is–of the clear front-runner, Joe Biden.

Taking two poll trackers, Economist and FiveThirtyEight, here are those polling at five percent or more:

Pre-candidate Economist FiveThirtyEight
Biden 26 27.3
Sanders 17 17.8
Warren 16 14.7
Buttigieg 8 8.0
Bloomberg 7 5.0
(Sub-)total 74 72.8

It is noteworthy that even with so many candidates and different methodologies, the two trackers agree on the order. The only really substantial difference between them is in the estimate for Bloomberg. Not shown here, the two trackers also agree in the order of the next three: Yang, Klobuchar, and Booker. After that they diverge on the farther trailing candidates. (Economist has both Gabbard and Steyer at 1% but lists her ahead of him; perhaps we could say they agree on the order of the top ten.)

In the Economist tracker, the full list of all candidates who are given a vote percentage includes five listed as “<1%” (trailing two estimated at 1%). If we assumed all these five averaged 0.5% (which is probably too high) we still get to only 88.5% as a “total”. So that leaves too much for the thirteen who were running but have dropped out; the tracker does not report a percentage undecided. If we take Biden’s percentage over all those with at least 1%, he is just over 30%. Still pretty weak for a front-runner. But the one in second place, Sanders, would rise only to just under 20%. That’s a large gap.

Applying the same exercise to the FiveThirtyEight percentages–which have six candidates over 1%–we get a “total” of 86.3% and the top two at 31.6% and 20.6%.

The Democratic Party obviously does not use a nationwide two-round majority rule. But if it did, where would a top two 30–20 finish rank? How likely would it be that the second place candidate would win the runoff? I looked at this question in 2016; the graph at that post shows rather few real-world presidential contests with approximately 30–20 for the top two. But if one were to draw a line on the graph marking the region in which the gap is ten percentage points or more, no second-candidate comeback shows up with this large a gap until the leading candidate is around 35% (Austria 2016, the case that prompted the post). That is, even with a first-round candidate as weak as a third of the vote or less, comebacks occur only when the two are rather closer than Biden and Sanders are at this point. And this is, of course, before one even considers ideological placement of the candidates.

What I am getting at, in case it is not obvious, is that it is hard to imagine Biden not being the winner were there a hypothetical direct two-round primary–and even if the field stayed this fragmented up till the first round (which is itself unlikely). Perhaps Warren’s chances increase slightly if this nationwide primary were run under the alternative vote. She might pick up enough from eliminated candidates to surpass Sanders in the final two when calculated this way. It still seems a stretch that she could end up with a majority after reallocation of preferences.

Now, let’s try a different hypothetical. The primary actually uses proportional representation to allocate delegates. Sort of. There is a 15% threshold, and the rules consist of a mix of statewide delegate allocation and allocation in congressional districts using varying district magnitude. If it were a single-shot affair rather than sequential across states and regions, only three candidates look like they would get any delegates (generously granting Warren what she needs to get over 15% in the FiveThirtyEight tracker or allowing for regional variance even if she stayed at 14.7%). In this scenario, Biden has 44% or 45% of the above-threshold vote. That might just be enough to win a majority of elected delegates or close to it, given a medium district magnitude on average. It would certainly put him close.

(There are 3,836 “pledged” delegates; 435 congressional districts plus separate statewide districts for the states that have more than one congressional district, DC, and various territories means ~480 districts, so an average magnitude of about 8.)

None of this is to say Biden can’t be caught by someone. And in the real and strange world, Iowa and then New Hampshire get to go before anyone else. According to FiveThirtyEight, Biden is in a tight three-way fight in their Iowa estimate, with Buttigieg still clinging to a slight lead over Biden and then Sanders (19.7–19.1–18.3), with Warren at just 13.4%. The New Hampshire estimate is similar, only with Sanders the one clinging to a narrow lead over Biden and Buttigieg (18.0–17.3–15.6) and Warren at 13.9%. (Gasp–the fifth place candidate is Tulsi Gabbard, on 4.9%.)

The odd (I am being kind) procedure the party uses in the real world could still produce a surprise, if Biden fails to get a plurality in either Iowa or New Hampshire, and if the pre-candidate (or two or more) beating him were to surge nationally afterwards. It looks unlikely to me. I think Biden has it, barring an occurrence of something even stranger than the method by which the party selects its nominee.

Votes, seats, and exit polls: UK 2019 edition

Two political scientists, Pippa Norris and Patrick Dunleavy, have accused the BBC and others of “systemic media bias” on the recent UK election night for not emphasizing the voting outcome and instead focusing on the seats. Their claims appear at the LSE blog. Of course, I am very much inclined to agree that votes and seats both matter–I’ve (co-) written two books that have both words, votes and seats, in their titles, after all! Thus I largely agree with Norris and Dunleavy’s bigger point that media coverage in majoritarian electoral systems tends to exaggerate the notion that a party that wins the seat outcome has a “mandate”. As I said in my own election post-mortem, the “mandate” claim is a stretch, at best, and very much depends on how the electoral system manufactures majorities–not only for Conservatives overall but also for the SNP among Westminster constituencies within Scotland.

Nonetheless, the claims in the LSE blog piece are somewhat hard to swallow. The main argument is that at 10:00 p.m., when polls closed, only the seats were mentioned. The votes did not come till 5:00 a.m., they claim. Anthony B. Masters has already shown that is not actually true, in a really excellent rebuttal. I won’t repeat Masters many points regarding misleading evidence that the LSE blog authors present to make their case.

The deeper issue here is that the exit poll is bound to be more accurate for seats–the initial projection almost nailed the result for the UK as a whole–than for votes. The voting estimates are subject to more error, because of uncertainty about turnout. Moreover, seats are the currency of power. Votes are relevant as a “currency of legitimacy” (as Jonathan Hopkin put it on Twitter), which is important for the subsequent narratives and intraparty soul-searching for the losers. That is, however, very much the kind of stuff that can only happen once the full results are known (not that it stops the media talking heads from engaging in speculation all night long). Basically, it is just very odd to slam as “biased” the media for reporting what was proven to be an actually accurate projection of the one thing the poll was designed to do and that matters most on election night–who won the most seats, was it a majority, and if so, how big?

Besides, as Masters notes in his rebuttal, it is not even true that votes were not being reported all night long. They simply are subject to more revisions as the picture gets clearer because, as noted above, the vote estimate is subject to more error.

Finally, I’d note that it could be much worse. In US elections, the topic of votes hardly comes up in the media, particularly for congressional elections. Even if you stayed up till 5:00 a.m. on election night (not that I ever have), you would not hear what percentage of the House votes each party had.

Reminder from UK 2019 result: Electoral systems matter

Keep this in mind about the UK result. The Conservatives won less than 44% of the vote. Polling has consistently shown that if there were another referendum on Brexit, a majority would vote for Remain. But the Conservatives won 56% of the seats, so Johnson is banging on about his great “mandate” to “get Brexit done”.

You see, electoral systems matter.

Even if you add in the Brexit Party votes (which got no seats), the combined votes cast for parties still advocating outright for leaving the EU do not reach a majority. In fact, it barely breaks 45%.

Meanwhile, the SNP has won 81% of the Scottish seats, with 45% of the votes cast in Scotland. And their leader, Nicola Sturgeon, is going on and on about the mandate for Scotland to decide on independence. It’s a fishy claim.

Which party gained the most in votes, relative to the last general election? That would be the Liberal Democrats. But the party suffered a net loss of one seat (and its leader was defeated).

The first-past-the-post (FPTP) electoral system makes a country seem more divided than it is, and often leads to policy outcomes a majority of voters actually oppose.

FPTP certainly is not very representative. But it can produce a decisive government, and Boris Johnson now looks like he could take his place among the significant Prime Ministers in the country’s recent history.

At least this result means my old lectures about British majoritarianism do not to be heavily caveated as they’ve been for the past several years.

Election days and early voting

Sometimes an orchard is all laid out in neat rows, and then “volunteers” pop up in unexpected places. (For those not familiar with the gardening use of that term, a volunteer is a plant that grows where the gardener did not intend. It is a nicer term than “weed” and does not connote anything undesirable.) This happens in the virtual orchard from time to time.

Case in point: There is a fun and interesting discussion of election days and early voting sprouting and even thriving productively over in the row originally planned for Australian Senate reform. Many readers might find it interesting, so I am calling it out with this link to where it starts. By this point, if you have something to contribute, you might as well add it there, and so I will not have comments open on this guide to unexpected virtual-orchard plantings.

Ecuador list-type change

Ecuador will travel a somewhat rare path in electoral reform: Abandoning a highly candidate-centered system in favor of a highly party-centered one.

In recent elections, Ecuador has used a free list system, in which voters could cast up to M votes (where M is the number of seats in the district) for candidates on one or more different party lists. Any vote for a candidate also counted as a vote for the list for purposes of inter-list allocation. Broadly speaking, a form of the “panachage” systems used in Luxembourg and Switzerland, as well as in recent years El Salvador.

A newly passed reform will switch Ecuador’s list type to closed-list PR.

It is unusual for countries to make a move like this. Japan moved from SNTV to MMM in its first-chamber elections, so that is another example of abolishing intra-party choice. But MMM is still quite candidate-centered, given single-seat districts. (In addition, the optional procedure in the Japanese variant for ranking lists based on district-level performance also preserves a candidate-centered feature, even though candidates on the list do not compete directly with one another for votes.) Colombia moved from de-facto SNTV to a list system, with parties having the option to present either an open or closed list. But I doubt anyone has moved from free list to closed list before. Even a move from open to closed lists must be very rare.

At the same time, Ecuador’s inter-list allocation will move from D’Hondt to “Webster” (Ste.-Laguë).

Even if you do not read Spanish, the linked news item is worth a visit, as it shows a simulation of how the party seat totals would have been different at the last election had Webster already been in place.

I have one concern with the change, if the video also at the linked item accurately portrays what the new ballot will look like. Voters might still tend to mark candidate images in different lists, as the ballot depicted is almost identical. That would make it impossible to tell which one list the voter would favor. But maybe this is not what the ballot really will look like. One must hope not.

Thanks to John Polga for the tip.