| Half a century ago, Kenneth Arrow proved a theorem that straddles the boundary between political science and math, which has become known as Arrow’s Legislative Paradox. Using the theorem in a sloppy and imprecise metaphor, I try to illuminate our stalemate over Michigan Democratic participation in the 2008 presidential selection process. |
| Grebner :: Maybe there was never any way out of the January 15 swamp. |
| To summarize and simplify: Arrow proved that it’s absolutely impossible to find a method of summing the preferences of a group of three or more people in a context where the preferences are non-scalar, without creating either unfairness or arbitrariness. That is, unless there is a single dimension (say, higher taxes <—-> lower taxes), every possible method of voting under certain conditions will encounter deadlocks whose only solutions will be either unfair or depend on random chance. Arrow proved that no technical solution – preferential voting, super-majorities, reliance on seniority, or anything else – can evade this paradox.
The simplest example is the classic three-people-buying-one-pie problem. One likes Apple, is okay with Blueberry, and hates Cherry. (“ABC” – get it?) The second orders her preferences BCA, and the third CAB. ABC says, “Let’s order Apple”, but there’s a 2/3 majority to change to Cherry. And 2/3 to change to Blueberry. Then 2/3 to revert to Apple. It’s completely circular and perfectly symmetric. Any method that avoids this problem (say, in case of deadlocks, ABC is allowed to make the choice) will break down under a different set of circumstances. Every reliable “solution” involves reducing the electorate to fewer than three voters (say, by weighting ABC’s vote to exceed the other two so she always wins), or forcing the choices to become scalar (by imposing rules that exclude certain orderings of preference), or introducing randomness (flipping a coin in the event of deadlock). Wikipedia has a good explanation. I’m not sure the formal requirements of Arrow’s theorem are met, by the angry and confused squabbling over Michigan’s participation in the Democratic nomination process this year, so this is more an illustration than a rigorous application of his proof. There are more than three positions involved, but that only makes the situation more intractable. Even if everybody were perfectly reasonable – and they aren’t – there’s no fair method of solving the mess, because there are multiple “majorities” that want inconsistent things. Let’s define three “tendencies” 1) “Anti-Iowa.” These people think the most important objective is to break the primacy of Iowa and New Hampshire, and bring effective suffrage to the other 48 states. This group is headed by Debbie Dingell and Carl Levin. 2) “Anti-Farce.” For them, the most important objective is to have a real vote, not just a choice between Hillary and Uncommitted, with no delegates at stake anyway. Most posts on ML seem to be in this camp. 3) “Anti-Caucus.” Most party activists aren’t sympathetic to this view, but most voters are. They distrust small-turnout, private, party-run caucuses, and want an ordinary election. The fact that the 2004 Caucus attracted 160,000 people, while the 1992 primary drew nearly 600,000 even though the nomination was already settled, illustrates the appeal of government-run elections. Now the problem is that EACH of these tendencies has overwhelming support, when tested against its opposite, just as each of the pies had a 2/3 vote. Almost everybody in Michigan agrees that we have to break the grip of Iowa and New Hampshire on the nomination process, and most of us are willing to support actions that challenge or even violate theDNC’s rules, if that’s what is needed. But we disagree among ourselves whether it’s so important that we’re willing to lose all voice in the 2008 process to press the point. At the same time, I don’t think anybody thinks the current arrangement is ideal, or even acceptable. If we all had votes on the Democratic State Central Committee, it would be easy to pass a resolution abandoning the January 15 primary for February 9 caucuses – but we don’t have such a voice, and it may be too late anyway. Finally, the great majority of Democrats would have opted for a meaningful primary over a caucus, even if that meant conforming to DNC rules. But of course, that would mean leaving Iowa and New Hampshire enthroned, which is unacceptable to most of us. . . . Even if we were all perfectly sincere and reasonable, and had well-written and accepted rules – not one of which predicates is true – this would be an intractable mess. If the issue were simply “A” or “B”, it’s not hard for any political system to choose. But once a third choice is introduced, each person has to make both a first choice, a second, and a third. If different groups make different rankings, there may be no way out, except something that leaves a large majority angry and alienated. One “solution” is to abandon democracy and turn the decision over to a dictator, which in this case would be Mark Brewer, or more precisely, the cabal that pulls his strings. They’ve made their decisions, and nobody’s happy with it. Arrow tells us there may never have been any way to fix it that would make most of us any happier. |