Poll statistics

Recently Terry Tao posted an interesting article at his blog that discusses some mathematics behind poll statistics. He proved (under some technical assumptions) that in a poll if p is the actual percentage of the whole population who vote yes and q is the percentage of people in a sample of the population who vote yes, then the probability that p and q differs by less than is at least



where n is the number of people in the sample. One of the key facts here is that the probability can be bounded by the absolute size of the sample (rather than the relative size with respect to the total population). Here's his original article:

http://terrytao.wordpress.com/2008/10/10/small-samples-and-the-margin-of-error/