Flaws in Dasgupta and Maskin's Scientific American article

Unfortunately, Dasgupta and Maskin's article in Scientific American was flawed and misleading.

P.Dasgupta & E.Maskin: The fairest vote of all, Scientific American 290,3 (March 2004) 92-97.

What voting system are they talking about? First of all, Dasgupta & Maskin do not actually specify the voting system they are pushing (!?!), but I believe that they meant Black's system, which dates to the 1950s or earlier.

Strategic voting – ignored without a trace: Dasgupta & Maskin completely ignored the massive effects of voters who vote "strategically" instead of honestly in an attempt to "game the system." For example, in the 2000 election, approximately 90% of the voters who liked Nader best, instead chose to dishonestly vote (as they were urged in hundreds of editorials) for somebody else, e.g. Gore, for strategic reasons ("don't waste your vote"). It is an easy theorem that with strategic voters who employ the strategy: "determine the two frontrunners (based on pre-election polls); then vote one top and the other bottom," the winner in an N-candidate Black-Dasgupta-Maskin election will be the same as the winner in a plain-plurality election! This theorem destroys Dasgupta & Maskin's claim that Black's system is "superior" to plain plurality. This theorem also holds for the IRV system (which Dasgupta & Maskin also mention but do not describe) and is an equally severe indictment of IRV.

What if voters are honest? Dasgupta & Maskin also disserved us by propagating the myth that the "true majority winner" (if one exists) always is the best. Counterexample: Suppose candidate Hitler, if elected, will award 51% of the voters 1 dollar worth of societal benefit but kill the other 49%. Meanwhile candidate Gandhi won't kill anybody and will award 1000 dollars to the 49%. Everybody knows this and everybody acts (i.e. votes) for their own benefit solely. While Hitler will be the "true majority winner," Gandhi is better for society as a whole. Range voting with honest voters would allow the election of Gandhi in this situation, but no other competing system would.

What about voting paradoxes and pathologies? Such as the fact that in Black's system, casting an honest vote can cause the election result (from your point of view) to worsen versus if you had not voted at all? (And in this respect, D&M's Black system actually is worse than plurality voting, albeit there are plenty of reasons to vote strategically even with plurality.) D&M leave that unmentioned as though it did not exist.

What about Bayesian regret as an objective yardstick of voting system quality? Dasgupta & Maskin completely ignored the entire BR concept as though it never existed. However, my 1999-2000 computerized study (paper #56 here, which included both Range Voting, D&M's favored Black system, and IRV, and many other systems too as "contenders") found that Range Voting was superior to all other systems compared there, for either "honest," "strategic," or "ignorant" voters (various ignorance levels) in all of 720 different probabilistic scenarios.

What the devil did Dasgupta and Maskin actually accomplish, anyhow? They wrote a more formal paper titled On the Robustness of Majority Rule and Unanimity Rule. This paper still has not been published in any journal as of March 2008, i.e. exactly 4 years after their Scientific American popular article about it, but they made the 2007 revision available electronically, and that is what you get by clicking the link. This paper claimed to prove a new theorem, which was basically the same as Duncan Black's single-peakedness theorem from 1948, but made to hold under more general conditions than Black had. Precisely what those new improved conditions were, was not easy to elucidate by reading D&M.

So what was Black's theorem, and does it matter in the real world? Black's theorem was that in "one dimensional politics" where all candidates are located on a line and voter quality-ratings of those candidates are single peaked (i.e. rising, then peaking, then falling) functions of location on that line, then, with honest rank-order ballots, a "Condorcet winner" will always exist, i.e. preference cycles are impossible. That theorem's validity is due to the fact that, if 3 candidates A,B,C occur in that order along the 1-dimensional line, then (in Black's model) no voter can regard B as worse than both A and C. Here are three reasons Black's assumptions differ from reality:

  1. Real voters are strategic. A voter may well decide to exaggerate the badness of B, dishonestly ranking him "worst", for strategic reasons ("don't want to waste my vote"). In other words, D&M's assumption of voter honesty is wrong in real life.
  2. Real voters can and should rank B as worse than both A and C. For example, suppose the most important issue is whether to invade and conquer an enemy country that is threatening to kill us all by next week, or to make a peace treaty with them. Well, I would prefer my leader to do one or do the other, but definitely do it fast. I would not want my leader to take the middle course and do neither. More prosaically, on page 94 Dasgupta & Maskin state that their singlepeakedness "simplifying" assumption leads them to regard it as "impossible" that a voter in the 2000 USA presidential election could have had the preference orders Gore>Nader>Bush>Buchanan or Gore>Nader>Buchanan>Bush. In other words, Black's "single peakedness" assumption can just be wrong in real life.
  3. Real voters are not 1-dimensional. For example, consider the Gore-Bush-Nader 2000 election.
So Black's theorem (and presumably also Dasgupta and Maskin's improved version of it) is a perfectly fine theorem in a mathematical world, but in the real world, it is not necessarily applicable.

Suppose I don't buy your criticisms of D&M and I like their 1-dimensional singlepeakedness assumptions just fine? And/or I like their desire for a Condorcet winner just fine? Then what? Then you still should probably prefer Range Voting over D&M's Black-system. Even when Range Voting takes on Dasgupta & Maskin battling in a world in which their assumptions are perfectly satisfied, Range Voting wins and Black's system loses. What do I mean by that? Well,

In summary, while most or all of these errors and omissions might have been excusable in a specialized publication with limited scope, Dasgupta and Maskin chose to make big utterly-unjustified claims in their title (few regard Black as even one of the better Condorcet systems), chose to publish in an ultra-high readership magazine, and exuded an aura of apparent scholarship and authority due to Maskin being a professor at Princeton's Institute for Advanced Study ("president of the Econometric Society") and Dasgupta being a knighted professor at Cambridge. But their article was so badly written that it did not even clearly explain the voting system they were pushing, and was organized around two "proofs by example" (the first-listed logically vacuous proof technique on this list). All that combined, seems to me to render the above sins inexcusable.

You can also see our criticism of a lecture Maskin gave in January 2008.

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