Regarding the Minnesota recount, reader RC points out: “By any meaningful scientific standard of measurement, the vote in Minnesota is a tie, and the recount process is just a mechanism for adjudicating a tie rather than a way of determining overall voter preference.” If RC is correct, this gives a different way to think about the recount than what partisans are saying.
Let’s think about what’s happening. Approximately 2,000,000 people voted for Coleman and Franken combined. Their supporters were as close to equal in number as one can imagine. We often speak of polls being an imperfect sampling of the likely-voter pool. But what about the pool of actual votes cast? In some sense, is that also a sampling of likely voters?
First, the math. The right tool for thinking about this is the statistics of the binomial distribution, which describes the distribution of all possible outcomes in a two-choice situation with fixed probability p. For N two-outcome trials (i.e. N votes cast), the average outcome is N*p and the standard deviation is sqrt[N*p*(1-p)].
Now think about a model in which each voter simply flips a coin to decide who to vote for. In this case p=0.5. For 2,000,000 votes, the average number of people voting for Franken (or Coleman) is 1,000,000 – with a standard deviation of 707. Therefore a random-choice situation would generate margins that typically deviate by much more than the margins that have been reported. By this criterion, the election is indistinguishable from a tie.
But this isn’t quite right. When asked, most voters declare themselves to be decided. Is there still variability in the outcome? Indeed yes. People who are sure that they will vote may not always get to voting stations. Imagine that each major candidate has 1,050,000 supporters. Further imagine that those supporters have only a 95% chance of actually voting – because of work, health, weather, whatever. In this case, the standard deviation is still 223 votes. The popular vote margin between Coleman and Franken would have a standard deviation of sqrt(2) times this: 316 votes, larger than any recent reported margin. So the current situation is, by any statistically reasonable standard, a perfect tie.
What should we think of the fights, ballot challenges, and uproar on both sides? RC put it so well that I will simply paraphrase.
I think elections are best understood as a compromise between several different goals:
1) A tool to measure voter preferences accurately,
2) A fair method of choosing between alternatives, and
3) A ceremony celebrating our commitment to democracy.
But this [last goal] fails if the system is not perceived as fair.
So, balancing all these things, along with considerations of speed, cost, and efficiency, we try to make a system of clear, transparent rules, agreed upon in advance, understanding that the results can never be perfect, and then let the mechanism play out, accepting the final result (where rules for challenges are also part of the mechanism). When the results are closer than any reasonable estimate of experimental error, I think we should just accept hand recounts as a kind of coin flipping, with the added advantage of being able to detect whether there were systematic errors biasing the system.
I advocate just sitting back with the popcorn and enjoying the show at this point.
Well said. Pass the popcorn.