In other news, does anyone else remember the Isaac Asimov short story about the one voter? The premise is that polling had got so accurate and so refined that, rather than fund an actual election, people just accepted the final poll results as a perfect prediction of what the result would have been - and then, with polling techniques being able to get more and more accurate results from fewer and fewer people, the system reached its logical conclusion with a single person taking a computer-administered survey, from which the election results that would have happened are extrapolated...
Did he really write something like this? I can't see Asimov writing something that couldn't be backed by some type of scientific theory. Extrapolating based on one voter isn't accurate regardless of the theory
(now, I'm off to Google to find it)
Edit: The story is "Franchise" and is similar to what the OP suggested, but I don't think it indicates any type of statistical relevance to the one-person polling. It appears that it is a computer that ultimately makes the decision using input from the one "voter".