Tag Archives: voting

Are Alabama’s House seats gerrymandered?

This map has a lot of people saying so:


Here’s what I think:  Alabama’s House maps might well be gerrymandered, but the Moore-Jones numbers aren’t very strong evidence.

First of all, about that weirdly shaped District 7 where so many Democrats live.  That’s a majority-minority district.  The Voting Rights Act requires the creation of some such districts, and that provision has increased the representation of racial minorities in Congress.  But most people agree they hurt Democrats overall.  You might be able to draw a district map for Alabama, Republican though it is, with two districts where Democrats have a chance instead of one.  But you’d also increase the likelihood of Alabama sending an all-white delegation.

Alabama, without District 7, is about 78% white, and white people in Alabama are about 85% Republican.  It’s not gerrymandering that Dems don’t have a chance in those six districts under normal conditions; it would happen just about any way you drew the maps.

But the Moore-Jones election was anything but normal conditions!  Did the party draw a map designed to withstand a historic Democratic turnout wave?

I doubt it.  Suppose you wanted to draw a map that would keep your big House majority even if just over half of Alabamian voters chose the Democrat.  You’ve got no chance in AL-7, and in the other 6 districts combined, the Republican is winning by 10 points.  Well, the last thing you’d do is draw an ultra-Republican district like AL-4; that makes the other districts way too close.  You’d take some of those wards and move them over to shore up AL-5, which Moore won by less than half a percent.  You might also try to concentrate the more Democratic parts of AL-1 and AL-2 into one, creating a district you might lose in a wave but leaving the rest of the state so solidly Republican that even an election more disastrous than this one for Republicans would leave five seats in GOP hands.

Outside district 7, Alabama is a very Republican state, even when offered the weakest Republican candidate in recent memory.  That’s the simplest explanation for why Moore finished ahead in districts 1-6, and it’s the one I favor.

Update:  Some people have communicated to me that in their view district 7 is more majority-minority than the Voting Rights Act requires, and that the district was drawn this way on purpose in order to increase Republican margin in the other 6 districts.



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“Worst of the worst maps”: a factual mistake in Gill v. Whitford

The oral arguments in Gill v. Whitford, the Wisconsin gerrymandering case, are now a month behind us.  But there’s a factual error in the state’s case, and I don’t want to let it be forgotten.  Thanks to Mira Bernstein for pointing this issue out to me.

Misha Tseytlin, Wisconsin’s solicitor general, was one of two lawyers arguing that the state’s Republican-drawn legislative boundaries should be allowed to stand.  Tseytlin argued that the metrics that flagged Wisconsin’s maps as drastically skewed in the GOP’s favor were unreliable:

And I think the easiest way to see this is to take a look at a chart that plaintiff’s own expert created, and that’s available on Supplemental Appendix 235. This is plain — plaintiff’s expert studied maps from 30 years, and he identified the 17 worst of the worst maps. What is so striking about that list of 17 is that 10 were neutral draws.  There were court-drawn maps, commission-drawn maps, bipartisan drawn maps, including the immediately prior Wisconsin drawn map.

That’s a strong claim, which jumped out at me when I read the transcripts–10 of the 17 very worst maps, according to the metrics, were drawn by neutral parties!  That really makes it sound like whatever those metrics are measuring, it’s not partisan gerrymandering.

But the claim isn’t true.

(To be clear, I believe Tseytlin made a mistake here, not a deliberate misrepresentation.)

The table he’s referring to is on p.55 of this paper by Simon Jackman, described as follows:

Of these, 17 plans are utterly unambiguous with respect to the sign of the efficiency gap estimates recorded over the life of the plan:

Let me unpack what Jackman’s saying here.  These are the 17 maps where we can be sure the efficiency gap favored the same party, three elections in a row.  You might ask: why wouldn’t we be sure about which side the map favors?  Isn’t the efficiency gap something we can compute precisely?  Not exactly.  The basic efficiency gap formula assumes both parties are running candidates in every district.  If there’s an uncontested race, you have to make your best estimate for what the candidate’s vote shares would have been if there had been candidates of both parties.  So you have an estimate for the efficiency gap, but also some uncertainty.  The more uncontested races, the more uncertain you are about the efficiency gap.

So the maps on this list aren’t the 17 “worst of the worst maps.”  They’re not the ones with the highest efficiency gaps, not the ones most badly gerrymandered by any measure.  They’re the ones in states with so few uncontested races that we can be essentially certain the efficiency gap favored the same party three years running.

Tseytlin’s argument is supposed to make you think that big efficiency gaps are as likely to come from neutral maps as partisan ones.  But that’s not true.  Maps drawn by Democratic legislatures have average efficiency gap favoring Democrats; those by GOP on average favor the GOP; neutral maps are in between, and have smaller efficiency gaps overall.

That’s from p.35 of another Jackman paper.  Note the big change after 2010.  It wasn’t always the case that partisan legislators automatically thumbed the scales strongly in their favor when drawing the maps.  But these days, it kind of is.  Is that because partisanship is worse now?  Or because cheaper, faster computation makes it easier for one-party legislatures to do what they always would have done, if they could?  I can’t say for sure.

Efficiency gap isn’t a perfect measure, and neither side in this case is arguing it should be the single or final arbiter of unconstitutional gerrymandering.  But the idea that efficiency gap flags neutral maps as often as partisan maps is just wrong, and it shouldn’t have been part of the state’s argument before the court.

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Is Arrow’s Theorem interesting?

Suppose a group of people has to make a choice from a set S of options.  Each member of the group ranks the options in S from best to worst.  A “voting system” is a mechanism for aggregating these rankings into a single ranking, meant to represent the preferences of the group as a whole.

There are certain natural features you’d like a voting system to have.  For instance, you might want it to be “monotone” — if a voter who likes option A better than B switches those two in her ranking, that shouldn’t improve A’s overall position or worsen B’s.

Kenneth Arrow wrote down a modest list of axioms, including monotonicity, that seem like pretty non-negotiable features you’d want a voting system to have.  Then he proved that no voting system satisfies all the axioms when S consists of more than two options.

Why wouldn’t that be interesting?

Well, here are some axioms that are not on Arrow’s list:

  • Anonymity (the overall outcome is invariant under permutation of voters)
  • Neutrality (the overall outcome is invariant under permutation of options)

Surely you don’t really want to consider a voting system that doesn’t meet these requirements.  But if you add these two requirements, the resulting special case of Arrow’s theorem was proved more than 150 years earlier, by Condorcet!  Namely:  it is not hard to check that when |S| = 2, the only anonymous, neutral, Arrovian voting system is majority rule.  Add to that Arrow’s axiom of  “independence of irrelevant alternatives” and you get

(*) if a majority of the population ranks A above B, then A must finish above B in the final ranking.

But what Condorcet observed is the following discomfiting phenomenon:  suppose there are three options, and suppose that the rankings in the population are equally divided between A>B>C, C>A>B, and B>C>A.  Then a majority ranks A over B, a majority ranks B over C, and a majority ranks C over A.  This contradicts (*).

Given this, my question is:  why is Arrow’s theorem considered such a big deal in the theory of social choice?  Suppose it were false, and there were a non-anonymous or non-neutral voting mechanism that satisfied Arrow’s other axioms; would there be any serious argument that such a voting system should be adopted?

Thanks to Greg Kuperberg for some helpful explanation about this stuff on Google+.  Relevant reading:  Ben Webster says Arrow’s Theorem is a scam, but not for the reasons discussed in this post.

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Absentee ballot non-hijinx in the Wisconsin recalls

I’m in the Atlantic today talking about the charges that GOP-linked groups sent Democratic voters absentee ballot applications with the wrong due date, in order to trick them into missing the election.  It can’t be denied there’s been a lot of sleaze and bad acting in this election, but I think this one was an honest mistake.  The anti-Fred Clark ad Wisconsin Family Action is running, on the other hand, is vile.


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Condorcet was an interesting dude

I knew about him only in relation with the voting paradox.  But he also wrote The Future Progress of the Human Mind (1795), a utopian tract featuring surprsingly modern stuff like this:

No one has ever believed that the human mind could exhaust all the facts of nature, all the refinements of measuring and analyzing these facts, the inter relationship of objects, and all the possible combinations of ideas….

But because, as the number of facts known increases, man learns to classify them, to reduce them to more general terms; because the instruments and the methods of observation and exact measurement are at the same time reaching a new precision; . . . the truths whose discovery has cost the most effort, which at first could be grasped only by men capable of profound thought, are soon carried further and proved by methods that are no longer beyond the reach of ordinary intelligence. If the methods that lead to new combinations are exhausted, if their application to problems not yet solved requires labors that exceed the time or the capacity of scholars, soon more general methods, simpler means, come to open a new avenue for genius….

The organic perfectibility or degeneration of races in plants and animals may be regarded as one of the general laws of nature.

This law extends to the human species; and certainly no one will doubt that progress in medical conservation [of life], in the use of healthier food and housing, a way of living that would develop strength through exercise without impairing it by excess, and finally the destruction of the two most active causes of degradation-misery and too great wealth-will prolong the extent of life and assure people more constant health as well as a more robust constitution. We feel that the progress of preventive medicine as a preservative, made more effective by the progress of reason and social order, will eventually banish communicable or contagious illnesses and those diseases in general that originate in climate, food, and the nature of work. It would not be difficult to prove that this hope should extend to almost all other diseases, whose more remote causes will eventually be recognized. Would it be absurd now to suppose that the improvement of the human race should be regarded as capable of unlimited progress? That a time will come when death would result only from extraordinary accidents or the more and more gradual wearing out of vitality, and that, finally, the duration of the average interval between birth and wearing out has itself no specific limit whatsoever? No doubt man will not become immortal, but cannot the span constantly increase between the moment he begins to live and the time when naturally, without illness or accident, he finds life a burden?

Read a longer excerpt here.

The voting paradoxes are found in Condorcet’s 1785 treatise Essay on the Application of Analysis to the Probability of Majority Decisions. But the main body of the book isn’t about voting paradoxes; it’s an attempt to provide mathematical backing for democratic theory.  Condorcet argued that the probability of the majority holding the wrong position was much smaller than the chance that the minority would be in the wrong.  So democracy is justified not only on principle, but because it is more likely to yield true beliefs on the part of the government.  I learned this, and other interesting facts, from Trevor Pateman’s article “Majoritarianism,” which presents Condorcet as a kind of quantitative version of Rousseau.  

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