Yes but we basically decide who those people vote for.

 

n8kwx called that one right on the money.

 

More than 77% of political surveys use sample size less than 1368.
(I made that up -- take with a grain of salt and a grin. But I think it's not very far off.)

Seriously, there are several good articles on wikipedia about polling and statistical sampling. http://en.wikipedia.org/wiki/Samplin...29#Sample_size
http://en.wikipedia.org/wiki/Sample_size
http://en.wikipedia.org/wiki/Central_limit_theorem

A larger sample size gives a smaller margin-of-error, assuming that you do the appropriate things to obtain a random sample of the population. But the sample that is large enough to get a margin-of-error of only a few percent is surprisingly small when you are asking a simple yes/no question.

The advantage to using a small sample is, of course, the cost. Political polls cost serious money. Pollsters get serious bucks for each person that they get to answer the questions, so large samples are very expensive. They have statistics consultants to figure out how large a sample they need, based on the type of questions being asked and the desired margin of error. Then, they have more consultants to help them get a representative sample of the population.