(Many thanks to my political science colleague David Schwab, who made these arguments so clearly in an email that I am very heavily quoting/paraphrasing him here. David, you're a game theory monster.)

The chair of my department sent out an email today suggesting that we check out an "interesting" piece by Nobel Laureate Sebastian Mallaby in the Washington Post. I say "interesting" because it is a direct quote…and because I believe the column might better be described as "retarded."

I am somewhat in disbelief in response to Mallaby's argument. That is, I simply can't believe that he's really this stupid. He's a Nobel Laureate. He brashly, nauseatingly titled the column "A Nobel Laureate's Primary" to remind us all that he's a goddamn Nobel Laureate. They're smart, right? Giving him the benefit of the doubt, we could conclude that he is simply dumbing this topic down for a general newspaper audience. But academics should never, ever do that. Whatever they gain in mainstream notoriety, they will lose to the sharpened claws of their colleagues in the field. Ask James David Barber.

Simply put, Mallaby, a Nobel Laureate in mechanism design (a specialized area of game theory), could show such a complete and appalling lack of understanding of the mechanisms of voting. His proposal is essentially to find a Condorcet winner, which is a concept that any first-year grad student (and many knowledgable laypeople) can explain. Said grad students could easily explain that not every election can or will have a Condorcet winner. Then what, Sebastian?

The heart of his proposal has some appeal to the average reader – let's end up with the candidate who is preferred by the largest number of voters. Let's let voters indicate orders of preference among multiple candidates. Mallaby seems to think he has proposed a system that will do this…and more! It'll help you lose weight, too. It will make you more attractive. Apparently he had his fingers crossed that no one has ever heard of Kenneth Arrow or the General Possibility Theorem, which (again, most undergrads could explain this) proves that, given several generally-accepted criteria for rationality, renders any preference aggregation system involving more than two choices irrational.

I'm not sure Mr. Mallaby proved much aside from the fact that he can wave around an honor he has received like a flag of authenticity while simultaneously giving ample reason to question the Nobel folks' decision. Maybe a fancy title, a "novel" idea, and some big words are enough to create the appearance of authority in the eyes of high school graduates reading the paper during the morning commute, but I wonder why he'd let his academic colleagues see something that shows such an embarassing lack of understanding in his field of "expertise."

(Thanks again, Dave! You explained it a lot better than I could have.)

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  1. mike Says:

    Don't know the social choice that well, but I'll give this a shot. What's wrong with his argument? General Possibility arguments about irrationality apply for all types of election voting (doesn't it?), so it seems unfair to pin that on him.

    All he is saying is that voter preferences can't be aggregated by a transitive utility function that ranks independent of other's actions. This seems very true in primaries.

    Let's say I prefer Kucinich over Obama over Hillary. However Kucinich is losing badly and Hillary is doing well. So I switch my vote to Obama, since I hate Hillary. If, hypothetically, Hillary dropped out for no reason, I'd vote for Kucinich again. This is horribly, disturbingly, deeply irrational – { C => A > B && \C => B > A } – and Kenneth Arrow would no doubt deny my right to vote. I think it may describe how a lot of people vote though, and I wouldn't feel bad for acting that way.

    As far as I know, most of the voters rank their opinions in classical social choice theory in a vacuum – they look into the preferences in their hearts, rank, cast their ballots, without any concern for anyone else or the outcome of the election itself (that may be horribly unfair of a characterization of Social Choice – is it?).

    All Mallaby is saying is that my vote may be conditional on what I think other people's votes are and not just on my preferences – in the same way my auction bid is conditional on what I think others are pay, not just my valuation – and this game theoretics causes informational asymmetries, something mechanism design can work with using auction theory – it can actually get an idea of how much I prefer something.

    For a primary it makes perfect sense to get to rank. For a general election, with 2 candidates, less so.

    Wouldn't a Condorcet winner not exist in the same sense that a general election could end in a tie?

    Of course this treats the political even less like a polis and even more like a commodities market, but he is the one quoting economists.

  2. Ed Says:

    Also not my area of perfect expertise. But I'll give it a shot too.

    First of all, he's not entirely clear about how he's proposing a Borda Count (point value for 1st-2nd-3rd etc) or an Instant Runoff style system of indicating preference on ballots. I am assuming, based on context clues from his description, that he's talking about a Borda Count.

    It is not at all unlikely or rare for a Borda Count to produce no Condorcet winner, especially with many candidates running. Obama-Clinton-Edwards may be a convenient example, but in real life….how many Richardson and Kucinich fans are out there? Lots, I'm guessing, who would never vote for them in the current system. Add them into the count and while it's certainly not LIKELY (i.e., > 50% probability) that there will be no Condorcet winner, it's more than a realisitic possibility. Forgive this crude example, but Major League Baseball awards its MVP trophy based on Borda Count rules, the NCAA uses it to rank college football teams, etc, and those instances often produce victors who are not Condorcet winners.

    Second, he is proposing a Second Price auction (advantage: people bid true valuation) without acknowledging the crucial Nash Equilibrium assumptions that everyone else is going to do the same thing. That NEVER happens in politics. People are always strategically voting ("I like Obama, but can he win the general election?" "Isn't voting Kucinich as my 2nd choice still wasting a vote?"). His system does little, although > nothing, to alleviate this.

    My big problem with the article is that it presents something in an over-simplified manner ("Look, folks, at how much better of a system we could use!") that political scientists have been considering for 75 years….and I think we've covered a lot of the angles on this. It's nowhere near as simple and straightforward as he portrays it, and in practice it would be subject to as much manipulation and strategic voting as any other system. I think it is intellectually dishonest to pitch something like this while only bringing up the ideal, best-case scenario of how it would work – minus the dozen assumptions that economists/game theorists understand are part of the bargain.

    It reminds me of the old joke about the economists stranded on the desert island with canned food but no tools, and their solution is to assume a can opener.

  3. David Says:

    Some thoughts on mike's comments:

    1. Yes, Arrow's Theorem applies to all mechanism's of preference aggregation involving more than two choices. In the article, Mallaby specifically mentions his method is Pareto superior to existing methods, without mentioning that this superiority only comes at the cost of violating other well-established criterion of rationality. He's technically right, but he's not telling you the whole story.

    2. The lack of a Condorcet winner, if not common, is much more likely than an election resulting in a tie. For 3 alternatives and any national electorate a Condorcet winner will fail to exist 8.8% of the time (Liberalism Against Populism, Riker 1982 p. 122). Also, Condorcet winners are not always the same as Borda winners; that is, a Borda count will not always pick the Condorcet winner.

    3. Social choice theory indeed assumes preferences are exogenous. Certainly, the formation of preferences depends on our relationships with others (ie there is a social basis for preference formation). However, when the ballot is cast everyone votes alone. Thus while preferences may be socially conditioned, the votes they lead to are appropriately analyzed according to the atomism of social choice theory.

    4. Although there is some talk of strategic voting in the social choice literature, any real exploration of how I condition my vote based on your vote will rely on non-cooperative game theory. Given the size of the electorate, it is unlikely anyone will arrive at an analytically tractable model without relying on simplifications about individual strategic capacity which, quite frankly, render the model useless. Then there is the problem of applying game theoretic solution concepts like the Nash Equilibrium to voting. Even simple discrete voting games (games where players choose an option A, B, C rather than a spot in policy space) have multiple equilibria, some of which are extremely implausable (yet equilibria nevertheless). So as a predictor of voting behavior, the Nash Equilibrium solution concept leaves much to be desired.

  4. j meezy Says:

    You want to see a ridiculous Nobel laureate? Kary Mullis.

    A selected excerpt:
    "During a symposium held for centenarian Albert Hofmann, Hofmann revealed that he was told by Nobel-prize-winning chemist Kary Mullis that LSD had helped him develop the polymerase chain reaction that helps amplify specific DNA sequences."

    Also, his biography on the nobel website is a quite entertaining read.

  5. Mike Says:

    Again, way out of my element, so I'll ask a rookie question: I'll try looking it up later, but what does it mean for there to be no Condorcet winner? I've seen where the three voters with the three perferences get a circular structural going, but that seems unlikely with lots of voters. When you say 8% ends without a winner, is that a perference rationality condition? Or that we physically can't point to a winner?

    Ed your sporting metaphor is a great example – I do think there is information in seeing what people's 2nd 3rd … perferences are independently, but methods used for them may just make the actual results more cloudly and seemingly less fair.

    I agree that adding strategic behavior would make nightmarish non-closed form solution models (do they Monte Carlo voting models?). However for primaries I do think it is an important part of the story (if not the model). Every news story or opinion column about Hillary's or Huckabee's "electability" is asking you to make your vote more endogenous. Especially when the candidates are similiar enough (Democrats) or each representing a different impulse (Republicans). That situation can complicate transitivity, which makes the consumer and game theory that underlines this more difficult to apply.

    And Game Theory (and in it's own way, consumer theory under uncertainity) can't deal with the notion that there is a "certainity" over which I won't want to risk ANY outcome that risks that certainity. (This is my personal beef with those theories – the old "If someone buys insurance and plays blackjack they should implode" argument). It's very difficult to rationally model "I prefer Kuncinich over Obama, but I prefer _any_ Democrat winning over any Republican, so I'll vote Obama." The fact that 1…5 < 6 shouldn't reorder the ordering of 6…10. But it can.

    And if you are dropping a good economist joke (which it is), I'll drop a good one on poly sci. From Leo Strauss, not really a joke: "The same science – scientific method – which produced the H-bomb must also be able to prevent the use of the H-bomb. The science which produced the H-bomb, physics; the science dealing with the use of the H-bomb, political science."