What is the US Presidential election about? Well, one possible answer is that it is about which of George W. Bush and John Kerry would make the best President of the United States. Now there’s certainly room for disagreement about the relevant qualities to be best President, but much of the media and blogospheric discourse is couched in such a way as to appear to be discussing a matter of fact: best translates as “most competent”, “wisest” etc. I’m going to assume — for the purposes of this post alone and contrary to my saner instincts — that a matter of fact is indeed involved. Given that simplifying assumption, the matter of determining who would be the best President by a democratic vote is something we might justify by invoking Condorcet ’s jury theorem. According to the jury theorem (which I cite in Zev Trachtenberg’s formulation [1])
bq. the probability that majority is correct ( _Pm_ ) is given by the formula
v h-k/(v h-k+e h-k ), where number of voters = n = h+k , where _h_ is the number of voters in the majority, _v_ is the probability that each voter will give the correct answer, and _e_ is the probability that each voter will give the wrong answer.
This has the remarkable consquence that just in case we expect each voter’s competence slighly to exceed the tossing of a fair coin (say we expect each voter to be right 50.1 per cent of the time), and just in case we can interpret “each voter” to mean “the average voter”, then with an electorate of, say, 100 million, the probability of a majority getting the result right approaches one. Of course, there’s a flip side to this: if the each voter has a < .5 probability of getting the right result, the majority will almost certainly be wrong!
So what should we think, _ex ante_ , about the competence of the average American voter? The votemaster at the excellent electoral-vote.com opines:
bq. Are the voters stupid? It is not considered politically correct to point out that an awful lot of voters don’t have a clue what they are talking about. A recent poll from Middle Tennessee State University sheds some light on the subject. For example, when asked which candidate wants to roll back the tax cuts for people making over $200,000 a year, a quarter thought it was Bush and a quarter didn’t know. And it goes down hill from there. When asked which candidate supports specific positions on various issues, the results were no better than chance. While this poll was in Tennessee, I strongly suspect a similar poll in other states would get similar results. I find it dismaying that many people will vote for Bush because they want to tax the rich (which he opposes) or vote for Kerry because they want school vouchers for religious schools (which he opposes).
(Lest Carol Gould or her apologists think that this post reflects the anti-Americanism of a sneering Brit, let me say (a) I’m quoting an American and (b) that I’m far from convinced that citizens of the UK would fare much better than the people of Tennessee were _their_ competence to be evaluated in a similar poll.) [2]
fn1. Trachtenberg, _Making Citizens_ p. 281 n. 6
fn2. A commenter to a recent post of mine asked, sarcastically, whether the I thought flipping a coin would have been superior to having the Supreme Court decide on the outcome in 2000. Actually, I do think flipping a coin would have been a better method then. Whether it would be a better method than having the US electorate decide is questionable, although _if_ voter-competence is such that individuals are more likely to get the wrong answer than the right one, it would yield a better chance of choosing the best President. Observant and thoughtful readers will also notice that, since Al Gore won a majority of the popular vote in 2000, I ought to believe that either Bush was the right answer then or that average voter competence has declined below the .5 level in the past four years….or perhaps I should believe that voter competence then as now exceeds .5 and that Kerry will inevitably triumph, or …..you do the permutations.