Fat Steve's Blatherings

Saturday, October 23, 2004

Presidential Polls: a meta-analysis

      Opinion polls are a probability and game.  If a poll says that Candidate X is favored by 52% of voters, with a margin of error of 4%, then it usually means that the polling organization figured a standard deviation of 2%, assuming the distribution of voters "normal." (See here for a definition of normal distribution, here for information on opinion polls, and here for margin of error).  When we consult a z-table, we find the probability is .5, even odds, that Candidate X has a support of 52% or better, only .69 that Candidate X has support of 51% or better, and .84 that his 50% or more.  In other words, Candidate X is very likely the winner.

      Now, basic probability says if it several results are independent of each other (such as the probability of flipping coins or rolling dice), then the probability of all of them happening is the probability of both of them multiplied together.  So the probability of a lot of opinion polls being wrong is the probability of each being wrong, all multiplied together.

      Over at Real Clear Politics, there is a daily listing of the lastest poll data.  They show results for three way tracking polls (Bush/Kerry/Nader), two way tracking polls (Bush/Kerry only), and the Iowa electronic market poll.  Also, Real Clear Politics averages the daily results of all three candidate polls, and has a chart of them.  All tell the same story: since the end of August, Bush is almost always ahead in every poll, and Tied is ahead in more polls than Kerry.

      With any given poll, it's less than even that the person in the second place is ahead.  With all the polls, the probability that the candidate in second is ahead is product of them all.  With four to sixpolls daily showing Bush ahead, the probability that Kerry is ahead is substantially less than 1 in 32, or about 3%.  So as the polls stand now, it is almost certain that Bush will take a popular majority.

      Of course, what really counts is the electoral college.  Since Sept. 21st, Bush has always been ahead in Real Clear Politics's electoral count too.  And despite myths, the undecideds usually break towards the incumbent in a presidential race.

      Put it all together and it means that unless the MSM/Kerry campaign combine manages to pull a very damaging October Surprise, Bush has a lock.



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