Depressed, and taking you with me

Hi. I was a bit spent from the whole rant on Israel. The Evian conference alone is depressingness enough for a week. I retreated to econometrics for a nice, morally unambiguous respite, but I'm doing some work which is basically uncharted statistical waters (for me at least), which once again raises questions of meaning and certainty.

Went to Barnes & Noble, and did what I usually do: sit around looking at mindless magazines. Wound up looking at Adbusters, which was a mistake. The magazine is filled with great photos, and I generally agree with the non-consumption thing, which you'd understand if you'd seen my apartment. But most of their content is sort of, well, shrill, and repeats the same sort of thing that nonthinking liberals have been repeating since time immemorial. It complains about the concentration of media power, but offers no solutions. [I even agree with this one, having sketched out an academic paper on the very subject of the optimal number of media outlets (the conclusion: more). I gave it to the Chief Economist of the FCC, who was a Caltech professor, but politics forced him to toe the party line and allow the FCC to allow more mergings. Maybe my paper changed his mind.] Adbusters complains about how antidepressants are brainwashing the populace, and suggests that people who are suicidally unhappy for years on end should maybe just quit their oppresive jobs and get some sun. It complains about Israel in exactly the same fact-free way that all other nonthinking liberals complain about Israel, and says that the Arabs violently resisting, instead of just waiting for their Ghandi, will one day be revered as freedom fighters. Way to make the world a better place, guys.

Anyway, here's one thing that I do know for certain, which I've been meaning to write down properly for a while: democracy is a sham. More generally, the concept of a `will of the people' is a sham.

Condorcet Here's the easy case, a chestnut known as Condorcet's paradox. You've got three voters, choosing among three candidates, and their preferences are as follows:

That is, person one prefers candidate A over candidate B, and prefers candidate B over C; person two prefers B to C to A, and person three perfers C to A to B.

So we need to set up a voting rule. Notice that a simultaneous three-way vote is a deadlock, so instead, we can set up a runoff system, wherein they first vote between A and B, and then run the winner against C. Well, in the A vs B vote, A gets two votes (persons one and three) and B gets one vote (person two), so A runs against C, and C wins. So C is the victor.

Or instead, we can run A vs C first, and then run the winner (in this case, C) against B. The winner will be B.

Or instead, we can run B vs C first, and then run the winner (in this case, B) against A. The winner will be A.

You get the picture: if we decide on an election of the form X vs Y and then the winner runs off against Z, then we can select an X, Y, and Z such that a candidate of our choosing will win. And everybody will think that it's totally democratic.

Arrow This little toy problem generalizes with a vengeance. Let us say you want a rule that will allow multiple people (more than two) to decide among multiple options (more than two), with the following two properties. First, the outcomes must always be transitive, meaning that we can't get these runoff cycles like above: for a given set of options, our runoff rules will select one and only one winner. Second, if candidate X is everybody's unanimous, undisputed favorite, then X will be the winner. Kenneth Arrow showed that there is only one decision rule which satisfies all these constraints: a dictatorship, wherein we pick one person and just go with his/her/its preferences, ignoring everybody else.

Since we don't like dictatorships, this is known as Arrow's Impossibility Theorem, since it establishes that it is impossible to have a collective decision rule which we would ever find palatable. I got to have lunch with Kenneth Arrow a few times a week or two, and he's a pretty cool guy. I asked him whether he prefers `impossibility theorem' or `possibility theorem', and he said that he originally called it the possibility thrm, because his adviser thought it was too pessimistic; but he agreed when the literature called him on it and redubbed it the impossibility theorem. Arrow would have gotten the Nobel prize in political science for this result, excepting only the unfortunate fact that there's no such prize.

But this is a big deal in the political science world, because it very clearly sets the ground rules: there is absolutely no way that you can describe `the collective will' of a group in any more than a simple binary choice (and such choices never really exist in the real world).

Government's decisions are an arbitrary amalgamation of a long series of manipulations of the agenda. If there's a general consensus among the voters that one choice is better than the others, then the agenda-manipulating to favor that choice will be much easier, and much more likely to occur, but for any pet policy a member of the House Ways and Means Committee, there is an agenda that will put any outcome through. This would be true even if everybody thinks it's a crappy policy. [This anything-can-happen fact is commonly referred to as the `McKelvey Chaos Theorem'. Richard McKelvey hated this name, and, also being too modest to use his own name to refer to a theorem, would just call it that result about the indeterminacy of the agenda or some such.]

So, in short: there is no `will of the people'. If we ousted Bush and put in a President who listened to people who aren't the President, there would still be no will of the people. Anything they told you in fourth grade that there is such a thing, and that democracy as exercised in the USA can correctly work out this nonexistent will of the people, is basically false.