Poison Arrow

Today Steven Den Beste, interesting as always, cites Ken Arrow’s result that “all electoral systems are flawed in one way or another.” This is true, as far as it goes, but inexact. More precisely, Arrow proved that no electoral system can, in every case, so long as more than two choices are involved, accurately reflect the subjective preferences of the electorate. Still more precisely, he proved that no election can meet all of a fairly long list of plausible-sounding “fairness conditions.” Den Beste confuses two kinds of failure when he writes:

The same thing goes for electoral systems. No matter which you consider, it is always possible to construct a scenario where it fails and clearly gets the wrong answer. Arrow proved it. What you do, instead, is to try to make sure that failures are rare, and the consequences of them are not serious. Ideally you’d like to engineer the electoral system in such a way that structurally it is resistant to critical failures, but that may not be possible and it may be necessary to get above the level of signal processing and start applying semantic filtration.

In the case of the American electoral system, the founders decided that there were certain specific issues which were much too important to risk. The consequences of failure in these areas was perceived to be so great that even if the chance of failure was low, it had to be prevented. So they passed the Bill of Rights.

Arrow’s result assumes mob rule, electoral preference, to be the desideratum: he addresses himself to means, not ends. The Founders had larger considerations. They designed the Bill of Rights to protect certain liberties against mob rule. If the American electorate votes to repeal, say, freedom of assembly, this is a catastrophe, but not a “failure” by Arrow’s lights. I agree with Den Beste about “the wisdom of the Founders to put certain decisions beyond the reach of the normal electoral process” and I share his preference for “a system with a high degree of noise rejection,” but these questions have nothing to do with group decision theory. Suppose it were possible to design a “perfect” election, in the Arrovian sense. Wouldn’t the Bill of Rights still be an excellent idea?