Legal Commentary

The crocuses are out, the birds are singing, the weather is sunny but not humid: Spring is in the air, so a young man's thought's naturally turn to...public choice theory.

Sitting in the Columbia Law School lobby with Matt Stephenson and Sascha Volokh at the 18th ALEA conference this weekend, I asked my perennial Arrovian question. Viz: As a normative matter, how is a cycling situation different from a simple tie in the legislature?

With a 50-50 tie in a 100-person legislature, no one argues that the notion of collective opinion is incoherent. Instead, we'd just say that the collectivity is indifferent between the two options. Both are just equally valued points on the collective indifference curve, right? One must resolve the impasse (say, with a coin toss), but the existence of the tie does not say anything normatively interesting about the nature of collective rationality.

How is a cycling situation normatively different from such a tie? Suppose preferences are so aligned that three equal-sized groups each have different 1st, 2nd, and 3rd choices over a menu of three choices. No Condorcet winner, in that any choice can win in a pairwise comparison with one of the other choices.

How exactly is this more normatively troubling than a two-way tie? Sascha volunteered (I think) that the normal voting rules seem to produce a majority-approved winner in such a case, whereas the public choice function of majority rule does not produce such a winner with a straight tie between two options.

But what rides on this illusion of an apparent majority, if the legislators themselves are not taken in by the illusion and realize that each of the three options is equally the will of the majority? If such a legislature picks a cycle-breaking procedure that gives each of the three factions equal weight, then no one's been "manipulated," right?

Suppose, for instance, they decide that the Speaker of the House will decide the issue when preferences are in the cycling mode and that each of the three factions (call them Shi'ite, Sunni, and Kurd) will take turns serving as Speaker. Why is such a procedure not perfectly analogous to a coin toss to resolve a 2-way impasse? And why is this structure-induced equilibrium not itself a reflection of popular (meta-)will?