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As the campaign for the U.S. Presidential election gains momentum, we're once again subjected to the irritating spectacle of candidates responding to simple questions with paragraphs of vacuous waffle, and mouthing totally contradictory opinions to different groups. It's tempting, and maybe partially correct, to suspect they're all just slippery and mealy-mouthed weasels. But here's another idea: maybe the way they act has its origins in a deeper problem inherent in the mathematics of democracy and public opinion. There's good reason to believe that a candidate can appeal to more people by holding several contradictory views all at once.
The French philosopher, the Marquis de Condorcet, once proved a truly surprising theorem about public opinion. As individuals, people tend to be logically consistent in their opinions or preferences. If I prefer Obama over Clinton, and Clinton over Romney, then I'll also prefer Obama over Romney. If A outranks B, and B outranks C, then A should outrank C. Most of our thinking conforms to this basic rule of logic, at least most of the time.
But just because individual preferences follow such logic, this doesn't imply that groups do as well. Within a population of people, Condorcet proved, it is entirely possible for a majority to prefer A over B, a majority to prefer B over C, and a majority also to prefer C over A - making a cycle of collective preference, so that's its impossible to say which of A, B or C the people really prefer. (For example, take three voters who, respectively, rank three policy alternatives in the following orders: A > B > C, C > A > B, and B > C > A. It is easy to see that two out of three will prefer A over B, B over C, and yet also C over A.)
Nearly a decade ago, physicist David Meyer of the University of California at San Diego, and political scientist Thad Brown of the University of Missouri, suggested that this peculiar logic of popular opinion might well have something to do with the slippery views of politicians. Think of a candidate who just tries to mouth opinions that match up as closely as possible with the majority view. Quite possibly those opinions will necessarily involve some contradictions and apparently irrational cycles of preference. If so, then candidates and their advisors face a real choice between a strategy that respects ordinary logic, with the candidate promoting the kinds of consistent preferences than an individual might hold, and another in which the candidate abandons the need for consistency and uses more flexible and slippery tactics to appeal to as many voters as possible.
I'm guessing that almost all candidates follow the latter strategy, and those who don't tend to fall out of the polls very quickly. I recall being excited some years ago at the early Presidential candidacy of Governor of Arizona Bruce Babbit, who seemed to speak entirely sensibly about the importance of things like education, public health, investment in the nation's infrastructure, etc. He was so sensible and intelligent that his polling number quickly fell into the single digits and he dropped out of the race in about three weeks.
I suspect that experienced politicians may get drawn into adopting strategic contradictions more or less unconsciously, as they study polls and the results of focus groups and try to say things that put them in touch with the voters. "This," as Meyer and Brown put it, "is why it’s so hard for us as voters to discern exactly for what they stand."
The naive view of political strategy might hold that if most peoples' views fall into three sets, A, B, and C, which you might visualize in some "policy space," then the politician does best by "triangulating" -- setting out a position that falls at the center of those views. This way he or she appeals at least a little to everyone. But if cycles exist among the voting public, then a better bet may be to occupy not one point in policy space, but to spread out over a region and, roughly speaking, be as inconsistent as the voters.
Maybe there's a kind of perverse quantum logic to flip-flopping: just as quantum particles don't exist at any one point, but act as quantum waves and spread out through space, politicians defy the logic of individual thinking, and benefit by having fuzzy and ill-defined views.
Just after I posted this, I remembered another interesting point relevant to this problem of Condorcet cycles in public opinion. The importance of the matter depends, of course, on the actual likelihood that public opinion really does show such cycles. Condorcet proved that it can. But in reality, does this happen very often?
Some physicists, Matteo Marsili and Giacomo Rafaelli, looked into this a few years ago. Their idea was to assume that individuals in a big population rank a series of alternatives, A, B, C, ... and so on in a random order. Each person has his or her own ranking, determined at random. Then they asked -- what is the chance, mathematically, that you'll find cycles in the group preferences when these people vote on the various alternatives in pairs? They vote on A versus B, A versus C, B versus C and so on. How likely is it that their voting shows a cycle? Their results showed that as the number of alternatives gets reasonable large, the chance of not having cycles dwindles rapidly to zero.
So if peoples' preferences were random, cycles are almost a guarantee. Of course, preferences aren't random, but treating them as such is at least crude approximation. And it suggests that the trouble presented by cycles, and the waffling strategies they make effective, may indeed be real.
On caveat, however -- Marsili and Rafaelli also showed that the tendency of people to conform with the views of others may play a powerful role in preventing Condorcet cycles and making the public's collective views more "rational" than they would otherwise be.
Friday, July 27, 2007
One update (below)