Uttar Pradesh, 2017

Election results have been released for the state assembly of Uttar Pradesh, India’s largest state. It was a big win for the federal ruling party, the BJP. The seat tally shows 312 for the BJP, with the second highest being the Samajwadi Party (SP) at 47. The SP, the ruling party since 2012, was in a pre-election coalition with the Indian National Congress (INC), which won just 7 seats. The Bahujan Samaj Party (BSP), which has been a significant party in the state in the past, won 19 seats.

Unlike 2012, when the SP majority in the assembly was achieved on not even 30% of the vote, this year’s BJP victory was a big win in votes, too. Not a majority, but a decisive plurality, at 39.7% of the vote. The SP-INC combine had 28.0% and the BSP 22.2%.

Note that the BJP managed a three-fourths majority (77.4%) of the 403 seats on not even 40% of the vote. The advantage ratio (%seats/%votes) was 1.95. That must be one of the biggest manufactured majorities under FPTP anywhere, at least in a large assembly.

Several other states have had recent elections as well. The news was better for the struggling INC in some, including Punjab, Goa, and Manipur, though its pluralities in these are short of majority status. The Aam Aadmi Party (which governs Delhi, but has had minimal success elsewhere) managed a distant second place in Punjab. See the results at the second link in this entry.

Republicans will likely keep their House majority – even if Clinton wins by a landslide – and it’s because of gerrymandering.

By Michael Latner

While the presidential race has tightened, the possibility of Donald Trump being defeated by a wide margin has some Republicans worried about their odds of retaining control of Congress. However, only a handful of Republican-controlled districts are vulnerable. Speaker Paul Ryan’s job security and continuing GOP control of the House is almost assured, even if Democrats win a majority of the national Congressional vote. How is it that the chamber supposedly responsive to “The People Alone” can be so insulated from popular sentiment? It is well known that the Republican Party has a competitive advantage in the House because they win more seats by narrow margins, and thus have more efficiently distributed voters. What is poorly understood is how the current level of observed bias favoring the GOP was the result of political choices made by those drawing district boundaries.

This is a controversial claim, one that is commonly challenged. However, in Gerrymandering in America: The House of Representatives, the Supreme Court, and the Future of Popular Sovereignty, a new book co-authored by Anthony J. McGann, Charles Anthony Smith, Alex Keena and myself, we test several alternative explanations of partisan bias and show that, contrary to much professional wisdom, the bias that insulates the GOP House Majority is not a “natural” result of demographic sorting or the creation of “majority-minority” districts in compliance with the Voting Rights Act of 1965. It is the result of unrestrained partisan gerrymandering that occurred after the 2010 Census, and in the wake of the Supreme Court’s 2004 decision in Vieth v Jubelirer, which removed legal disincentives for parties to maximize partisan advantage in the redistricting process.

Partisan bias tripled after congressional redistricting

We measure partisan bias using the symmetry standard, which asks: What if the two parties both received the same share of the vote under a given statewide districting plan? Would they get the same share of seats? If not, which party would have an advantage?

We calculate seats/votes functions on the assumption of uniform partisan swing – if a party gains 5% nationally, it gains 5% in every district, give or take an allowance for local factors (simulated through random effects that reduce our estimates of bias). Linear regressions provide an estimate of what level of support the Democrats expect to win in each district if they win 50% of the national vote, given the national level of support for the party in actual elections, and we generate a thousand simulated elections with hypothetical vote swings and different random local effects for each district, to create our seats/votes functions.

Figure 1: Seats/Votes function for Congress 2002-2010
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Figure 2: Seats/Votes function for Congress 2012
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Figures 1 and 2 show the seats/votes functions under the 2002-2010 Congressional districts, and the 2012 post-redistricting districts, respectively. We observe a 3.4% asymmetry in favor of Republicans under the older districts. This is still statistically significant, but it is only about a third of the 9.39% asymmetry we observe in 2012. Graphically, the seats/votes function in Figure 1 comes far closer to the 50%votes/50%seats point. The bias at 50% of the vote is less than 2% under the older state districting plans, compared to 5% in 2012. That is, if the two parties win an equal number of votes, the Republicans will win 55% of House seats. Furthermore, the Democrats would have to win about 55% of the vote to have a 50/50 chance of winning control of the House in 2016. Thus it is not impossible that the Democrats will regain control of the House, but it would take a performance similar to or better than 2008, when multiple factors were favorably aligned for the Democrats.

Increased bias did not result from “The Big Sort” 

Perhaps the most popular explanation for increased partisan bias comes from the “Big Sort” hypothesis, which holds that liberals and conservatives have migrated to areas dominated by people with similar views. Specifically, because Democrats tend to be highly concentrated in urban areas, it is argued, Democratic candidates tend to win urban districts by large margins and “waste” their votes, leaving the Republicans to win more districts by lower margins.

The question we need to consider is whether the concentration of Democratic voters has changed relative to that of Republican voters since the previous districts were in place. In particular, if it is the case that urban concentration causes partisan bias, then we would expect to find relative Democratic concentration increasing in those states where partisan bias increases. In order to address this question, we measure the concentration of Democratic voters relative to that of Republicans with the Pearson moment coefficient of skewness, using county-level data from the 2004 and 2012 presidential elections. As shown in Table 1, in most states the level of skewness toward the Democrats actually decreased in 2012.

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In twenty-seven out of the thirty-eight states with at least three districts, the relative concentration of Democratic voters compared to Republican voters declines. Moreover, in those states where partisan bias increased between the 2000 and 2010 districting rounds, those with an increase in skewness are outnumbered by those where there was no increase in skewness, by more than two to one. We also find that there was reduced skewness in most of the states where there was statistically significant partisan bias in 2012.

Of course, we should not conclude that geographical concentration does not make it easier to produce partisan bias. North Carolina was able to produce a highly biased plan without the benefit of a skewed distribution of counties, but to achieve this, the state Generally Assembly had to draw some extremely oddly shaped districts. While the urban concentration of Democratic voters makes producing districting plans biased toward the Republicans slightly easier, it makes producing pro-Democratic gerrymanders very hard. In Illinois, the Democratic-controlled state legislature drew some extremely non-compact districts but still only managed to produce a plan that was approximately unbiased between the parties.

Increasing racial diversity does not require partisan bias

Another “natural” explanation for partisan bias, one that is especially popular among Southern GOP legislators, is that that it is impossible to draw districts that are unbiased while at the same time providing minority representation in compliance with the Voting Rights Act of 1965. The need to draw more majority-minority districts, it is argued, disadvantages the Democrats because it forces the inefficient concentration of overwhelmingly Democratic minority voters.

There are four states with four or more majority-minority districts – California, Texas, Florida, and New York – and they account for more than 60% of the total number of majority-minority districts. Of these, Texas and Florida have statistically significant partisan bias, but California, Illinois, and New York do not, so the need to draw majority-minority districts does not make it impossible to draw unbiased districting plans. Yet many of the states that saw partisan bias increase do have majority-minority districts – or rather a single majority-minority district in most cases. It is possible that packing more minority voters into existing majority-minority districts creates partisan bias.

To test this possibility, we subtract the average percentage of African-Americans and Latinos in districts where those races made up a majority of the population in the 110th Congressional districts from the 113th Congress averages. Figures 3 and 4 display the results for these states. For majority-Latino districts, we find no evidence that states with increased Latino density have more biased redistricting plans.

Figure 3: Majority-Latino District Density Change and Symmetry Change
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Figure 4: Majority-Black District Density Change and Symmetry Change
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By contrast, states with increased majority-Black densities have clearly adopted more biased districting plans. Among the states with substantial reductions in partisan symmetry, only Louisiana (−1.9 %), Ohio (−1.0 %), and Pennsylvania (−0.9 %) had lower average percentages of African Americans in their majority-minority districts after redistricting. The three states with the largest increases in majority-Black district density, Tennessee (5.2 %), North Carolina (2.4 %), and Virginia (2.2 %), include some of the most biased plans in the country. This is not in any way required by the Voting Rights Act – indeed, it reduces the influence of African-American voters by using their votes inefficiently. However, it is consistent with a policy of state legislatures seeking partisan advantage by packing African-American voters, who overwhelmingly vote for the Democratic Party, into districts where the Democratic margin will be far higher than necessary.

Demography is not destiny

The bias we observe is not the inevitable effect of factors such as the urban concentration of Democratic voters or the need to draw majority-minority districts. It is for the most part possible to draw unbiased districting plans in spite of these constraints. Thus if state districting authorities draw districts that give a strong advantage to one party, this is a choice they have made – it was not forced on them by geography. The high level of partisan bias protecting GOP House control can only be explained in political terms. As we show in our book, Pro-Republican bias increased almost exclusively in states where the GOP controlled the districting process.

One of the immediate consequences of unrestrained partisan gerrymandering is that, short of a landslide Democratic victory resembling 2008, the Republicans are very likely to retain control of the House. But one of the more profound consequences is that redistricting has upended one of the bedrock constitutional principles, popular sovereignty. Without an intervention by the courts, political parties are free to manipulate House elections to their advantage without consequence.

 

“Votes that count” in different electoral systems

Throughout the discussion on electoral-system reform in Canada, I have seen various social-media posts that purport to compare the percentage of votes that “count” in Canada vs. in existing PR systems. Typically, these posts will cite a figure of 50% of votes counting in Canada and 95% or more in PR countries.

The numbers seemed fishy to me. I do not doubt that votes are substantially more likely to “count” towards election of a representative under PR than under FPTP or other majoritarian systems. But the 95% figure seemed too high.

As I happen to have a dataset of district-level electoral results in many countries at my disposal, it was not too hard to subject the claim to a test. The harder part is knowing how to operationalize “count”. I chose two methods, based on my understanding of the complaint that reform advocates have against FPTP. The problem, it will be seen, as I suspect both methods are being used by these advocates, but different methods for different systems.

The first method is the one that I believe they are applying to Canada, which is: “did my vote contribute to the election of someone in my district?” Guess what–when your district elects one, for many voters the answer is “no”. (And this may be sufficient reason to want to ditch the system!) The second method is one that I suspect the authors of these posts apply when looking at PR systems: “Did the party I voted for win representation?” That is, I suspect a district-level standard is being applied to FPTP, but a national-level one to PR countries. My calculations seem to bear that out.

If we use the first method–district-level count of votes for parties (or candidates) that did not win in the district, we almost nail the 50% figure for the most recent Canadian election for which I have data. In 2011, I get 50.4% of votes across the country “counting” in the sense that they were cast for the winner in the voter’s district.

Across the 25 FPTP elections for which I have complete data, the average figure is 55.8%. The lowest figures are around 47% in several UK and Indian elections, with the highest being 62% or more in the US and Barbados. (What do these latter two countries have in common? Very few votes going to parties other than the top two.)

I then apply that same standard to PR systems. A pause is needed here. Canada is very highly unlikely to adopt nationwide PR, either with a single national district (which I think we can say is politically and constitutionally impossible) or with districts but also nationwide compensation (as in Germany or Denmark, among others). Thus I consider the relevant metric to be those PR systems that employ districts, plural, and no nationwide compensation.

Using the same standard–votes “count” when cast for a party that wins a seat in the district–the mean for (districted) PR systems is 87.2%. That figure is a lot higher than 50%, I will grant. It is also a good deal lower than 95%.

If we look at nationwide (single-district) PR, guess what? 96.5%! A few specific elections come in at 99%, such as the Netherlands, 2002, and Israel, 1951. (Most Israeli and Dutch elections are over 97%, but Netherlands, 1952, was at a paltry 94.7%.) That’s great! However, most PR advocates, unless they are real purists (and not at all realists) do not advocate the adoption of the Dutch or Israeli type of PR.

What about the second standard? Under this one, your vote “counts” if it was cast for a party that won representation somewhere (at least one seat), even if it did not win in your district. As I noted above, I suspect this is the standard being applied, at least implicitly, to the PR countries in the social-media posts I have seen.

By this standard, districted PR systems’ average percentage of votes that count rises to 93.7%. We are almost to 95%! For nationwide PR, it obviously does not change (there’s only one district). What about for FPTP? 97.1%. Canada, 2011, comes in at 99.1%.

I do not actually know if a Canadian voter feels “represented” if she voted NDP but the NDP candidate in her district lost. I suspect many do feel so represented, or else the NDP would not get more than trivial vote shares in districts where it has no chance of winning. Yet it does. Greens can also get votes near or above their nationwide percentage even in many districts that are totally hopeless for them. Perhaps they feel represented by Elizabeth May (the one Green MP) even if they reside in a different district or province. Not as well represented as if their own MP was Green, presumably, but my point is that voters probably tend to think of national party systems when voting, even in districted systems. Yes, even in systems in which districts have one seat apiece.

There may be many reasons to prefer PR over FPTP. I can think of quite a few myself. But the idea of a vote “counting” towards representation may not be one of the more meaningful criteria to use. Or, if it is used, it might be OK not to exaggerate. The difference between 50% (Canada, 2011) and 87% (mean for districted PR) is impressive enough, using the first (district-based) criterion. We don’t need to pretend that twice as many votes “count” under PR as under FPTP. 1.74 times as many is still a lot more!

Does AV mean higher or lower effective number of parties?

There may be a conventional wisdom among people who study comparative electoral systems that the Alternative Vote (also known as Instant Runoff or Majority Preferential) tends to suppress the effective number of parties, compared to plurality (First Past the Post, or FPTP). Or maybe it is just me, but I will admit to having such a notion. After all, Australia is a pretty strict two-party system, isn’t it?

The correct way to approach the question of whether AV means a higher or lower effective number of parties (N) than FPTP is to ask: What we should expect N to be, given the country’s seat product?

As explained by Taagepera (2007) and further elaborated and tested by Li and Shugart (2016), the seat product is a country’s mean district magnitude (M), times its assembly size (S). The Seat Product Model says that the effective number of seat-winning parties (Ns) tends to be the sixth root of this product: Ns=(MS)1/6.

The model is logical, not a mere product of empirical regression work, although regression tests confirm it almost precisely (Li and Shugart, 2016).

When all districts elect just one member, thus M=1, the Seat Product is just the assembly size, S. Hence we take the sixth root of S to get an expectation for Ns. What if we do this for Australia’s House of Representatives? We get an expectation of 2.31.

The actual Ns for Australia’s elections since 1984, the year S was increased from 125 to 148 (subsequently it has increased to 150, a minor change) is… 2.53. However, I believe that figure (I am using Gallagher’s Election Indices) treats the Coalition parties as one in elections before 2010.

In the two most recent elections, Ns has been 2.92 and 3.23. The notes to Gallagher’s Election Indices indicate that for these elections the Liberal Party, the Nationals, and the Liberal National Party of Queensland are treated as separate parties. In my opinion they should be so treated, although I suppose one could have a debate about that.

The actual mean is thus above the expectation for a hypothetical FPTP of the same size assembly. If we use the figure of 2.53, it is obviously not much higher than 2.31 (the ratio is 1.10). However, if we consider the value, at least in recent elections, to be around 3.0, it is about 1.30 times the expectation value.

Contrast this with the UK, where elections of the same period (1987-2010) have a mean Ns=2.30. This is just what we expect for FPTP, right? Not much over 2.0. Not so fast! The UK has a huge assembly, and with S=650 (aprpox., as it varies over the period), we should expect Ns=2.94. The UK actually has one of the more under-fragmented assemblies, according to the Seat Product Model, with this recent-period average being only 78% of expectation.

So how about Canada, where AV is one of the potential reforms being considered? Over a similar period (1984-2011) we get Ns=2.63. With S around 300 during this time, we should get Ns=2.59. So Canada pretty much nails the expectation of the model.

So, should we expect Ns to go down if Canada were to adopt AV, as (what I characterized as) the conventional wisdom would have it? Or should we expect it to go up?

I would not be inclined to say ‘down’. I will just leave it at that for now.

The new UK constituencies

For the next (expected 2020) UK election, the assembly size will be reduced from 650 to 600, and the balance in the number of constituencies across the UK’s component units (including English regions) will be shifted. Ron Johnston, at the LSE blog, has a rundown of the changes.

Imagine the research-design opportunities for analyzing personal-vote behavior:

Some current MPs will see their current seat dismembered, and may worry whether they will be selected for another; David Cameron has promised all current Conservative MPs that they will have a seat to fight in 2020, but it may well be very different from the one they currently represent. And so much change will break the bonds between MPs and both their constituents and their party organisations – some of them of long standing – that will have to be rebuilt before the 2020 contest. Many MPs may spend a lot of time building support in their new constituencies rather than serving their existing ones – let alone debating and decision-making in Westminster.

The partisan effects also could be substantial: “The Conservative lead over Labour will probably be widened with the new seats,” says Johnston. However, the extent of this impact is unclear as, given the LibDem collapse and the rise of UKIP and Greens in 2015, “there are fewer marginal seats than at any time since 1945.” Conservatives, especially, have many very safe seats. Still their path to a majority in the House of Commons looks better for 2020 under the constituency revisions than was the case in 2015, when the manufacturing of their majority by the FPTP system was a close call.

 

 

Alberta election follow-up

The ThreeHundredEight blog has a follow-up on the recent Alberta election. Key point of interest:

The idea that the PCs and Wildrose share the same voter pool is simply wrong. The right wasn’t divided. Rather, the anti-PC vote was divided between the New Democrats and Wildrose.

I suspect this is a more general phenomenon: when it appears that some party won due to divisions in its main opponent’s base, things are quite likely not as they appear.

UK 2015 and Duverger’s Law

Before the election, I said that it was premature to declare Duverger’s Law dead. With an apparent late swing, relative to what opinion polls were showing, in English votes from Labour and especially from Liberal Democrat to Conservative, I am going to say that my “prediction” was not the worst one on this election!

The swing from Labour might be interpreted as nationally focused voting–“which government would I prefer?”. English voters certainly seem to have recoiled from the idea of a Labour government dependent upon keeping the Scottish National Party content. The swing from Liberal Democrats was far greater than had been anticipated, and looks like the district-level “psychological effect” working as anticipated. The party generally benefits more than others from incumbency, given its incumbents’ reputations as good constituency MPs. In this sense, the Lib Dems could be thought of as the party that made FPTP “work”–it is supposed to be a system in which local representation matters, after all. In this election, however, it seems the LibDems suffered major desertion even in districts where they were up against Conservatives. (Defection to Labour from Lib Dem was widely expected, ever since they entered the coalition in 2010.)

In making the case for Duverger’s Law not being dead yet–even if it has been on life support in the UK for some time–I suggested that this election would be more “top two” than the last one, at least in England. That looks like a good call. The following table shows the percentage of votes and seats for Conservative + Labour in 2010 and 2015 in the UK as a whole, and in England.

UK UK England England
votes seats votes seats
2010 65.1 86.8 67.7 91.7
2015 67.3 86.7 72.6 98.5

Even with Scotland included, there was a slight increase in the top-two percentage, back up over two thirds (which is still low for a “classic” FPTP system!). In England alone, it was more dramatic, and the collapse of the Lib Dems, plus the failure of either UKIP or the Greens to win more than a seat apiece despite major growth in votes, sure is noticeable in the top-two seat percentage. The UKIP vote in England was 14.1% in this election, compared to 3.5% in 2010. The Greens won 4.2%, up from 1.0%. The mechanical effect is especially alive and kicking!

The increase of these two small parties’ votes obviously cuts against the notion of a Duverger’s Law rebound. Yet in spite of their increases, we still see an almost five percentage-point increase in the Labour + Conservative percentage, thanks to the major third party having collapsed to fourth place: the Lib Dems, in England, fell from 24.2% to 8.2%! Their seats–still England only here–fell from 43 to 6 (57 to 8 in the UK as a whole).

So, yes, overall a more Duvergerian result. But let’s not overstate it. UK-wide, the effective number of vote-earning parties (NV) went to 3.93. That is by far the highest it has been in the entire post-WWII era. The next highest were 3.71 (2010) and 3.60 (2005). So the trend as of 2015 remains upward, and fairly substantially so. The effective number of seat-winning parties (NS), on the other hand, did decline, although only a little bit: to 2.53 from 2.57. As I pointed out in the previous post, based on Taagepera’s Seat Product, the UK’s large assembly should lead us to expect NS=2.9. So it is still much more a “two-and-a-half” party system than expected–even with the massive SNP win (56 of Scotland’s 59 seats).

Speaking of the Scottish result, that near sweep certainly is a gift from the electoral system. The SNP’s 94.9% of the seats in Scotland comes on almost exactly half the votes. By contrast, the formerly dominant party in Scotland, Labour, in 2010 had 69.4% of the seats on 42.0% of the votes. In 2010, the SNP was a distant second in votes (19.9%) and an even more distant third in seats (6), compared to the Lib Dems (11 seats on 18.9%). What a difference a 30 percentage point swing can make under FPTP!

It is also noteworthy that the SNP received 1,454,436 votes in the parliamentary election. The YES side in the independence referendum last September obtained 1,617,989. Given the turnout differences, the YES vote was 44.7%, so just over five percentages point less than the SNP obtained in this week’s election. (In the last Scottish Parliament elections the SNP had 902,915 votes, which was 45.4%.)

Finally, below is a table of NS, NV, and the gap between them since 1945. The final column is an “expected NV” derived from NS, based on another (as yet unpublished) Taagepera formula that I will put below the table. The noteworthy thing is that we could expect the NV– NS gap to be around .4, given the actual  NS, values in UK elections. In most elections since the resurgence of the Liberals (in votes) in 1974 it has been above that. The gap has been more than 1 in each election since 1997, but surged all the way to 1.4 in 2015. This is extraordinarily high; in fact, I record a gap that high in only 31 of 517 parliamentary elections worldwide (details in the first comment below).

The 2015 result thus appears to confirm that there is demand for more party representation than the electoral system can deliver, but due to what we might call the “Duvergerian rebound”, I have to agree with Alan Renwick that the probability of electoral-system reform has gone down, rather than up, as appeared at least somewhat likely (despite many obstacles) if the result had been as anticipated in pre-election forecasts.

year Ns Nv Nv-Ns ‘Expected Nv’ from Ns
1945 2.12 2.58 0.46 2.56
1950 2.08 2.44 0.36 2.52
1951 2.05 2.13 0.08 2.49
1955 2.02 2.16 0.14 2.47
1959 1.99 2.28 0.29 2.44
1964 2.06 2.52 0.46 2.50
1966 2.02 2.42 0.4 2.47
1970 2.07 2.46 0.39 2.51
1974a 2.26 3.15 0.89 2.68
1974b 2.25 3.13 0.88 2.67
1979 2.15 2.87 0.72 2.58
1983 2.09 2.83 0.74 2.53
1987 2.17 2.85 0.68 2.60
1992 2.27 3.03 0.76 2.69
1997 2.12 3.23 1.11 2.56
2001 2.17 3.33 1.16 2.60
2005 2.46 3.6 1.14 2.87
2010 2.57 3.71 1.14 2.97
2015 2.53 3.93 1.4 2.93
mean 2.18 2.88 0.69 2.61
mean, 1983- 2.30 3.31 1.02 2.72
mean, 2005- 2.52 3.75 1.23 2.92

‘Expected Nv’ here is NV=(NS3/2 +1)2/3.

Trust me, it works amazingly well across hundreds of elections under different electoral systems. To see the derivation, you will have to wait for some forthcoming Shugart-Taagepera work!