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?
Posted by Rick Hills on May 19, 2008 at 11:24 AM
Comments
Yes, I think that the presumed gullibility of lawmakers is precisely the distinction between a two-way tie and a three-way cycle. But the presumption that lawmakers are too dumb to understand the effects of agenda-setting rules is, well, so presumptuous that only an academic could believe it.
Lawmakers are masters of process: That’s why everyone in the House wants a seat on the Rules Committee and why every rules resolution defining the order, number, and nature of every amendment for any important bill is carefully vetted by the Speaker and Minority Leader.
Of course, the procedural rules themselves might cycle. But note that (a) no amendments are allowed for rules resolutions and (b) the permanent rules defining House procedure — germaneness, the “two-degree” rule, the “five-minute” rule for debating amendments, and so forth — have been in force for decades, if not centuries. Hard to imagine that these devices can be used manipulatively only by the party in power.
Posted by: Rick Hills | May 20, 2008 7:29:24 PM
Interesting question, but, in partial defense of Sasha’s intuition, cycling appears to conflate first and second-order decision-making procedures. In the case of the majoritarian tie, the normal voting rule does not produce a decision. At that point, some second-order decision procedure must be selected to determine an outcome. (It might be a coin toss, but there may be reasons to select other second-order procedures, including deference to another decision-maker.) In the cycling example, a decision is reached without having to reflect on the need for a second-order procedure. As you say, there is an induced equilibrium. But having pointed out the indeterminacy across preferences, it might be rational to select some other decision procedure to resolve the indeterminacy, as you would to reach a decision in the case of a tie (supposing a tie is not a viable option). In short, the tie forces you to deliberate about second-order decision-making. If cycling isn’t troublesome, then, it’s because of your stipulation that the legislators are aware of it and approve cycling mechanisms to resolve cases of rational indeterminacy.
Posted by: Micah Schwartzman | May 20, 2008 6:05:16 PM