Monday, January 24, 2011
In case you think that presidential polls at this stage mean anything, Le Monde offers a sobering reminder of just how wrong they were 18 months before the last three presidential elections. The problems are numerous: too many candidates, aleatory press coverage, and, perhaps most interesting, misleading comparisons demonstrating Arrow's impossibility theorem at work. All right, so the application of Arrow's theorem isn't rigorous: different polls involve different groups, different questions, and different combinations of candidates. But the principle remains: person A may prefer Valls to Royal to Besancenot in poll X and wind up voting for Sarkozy over Montebourg in round 2 of 2012. Voters are hard pressed to sort out their preferences when there are too many candidates to choose from, and there is no consistent way of aggregating the preferences over the broad field to arrive at a consistent group choice in a binary confrontation. For the same reason, we tend to overinterpret "presidential mandates." The ultimate binary choice required in a presidential system of the French type yields the illusion that "the nation" has made a consistent choice between two competing sets of preferences. But underlying that choice is a chaotic sea of individual preferences that cannot be consistently combined.