What makes surveys precise?

You may have seen polls published in newspapers or magazines which make a claim about precision. For example, they may say:

"The sample size was 1020; for a sample of this size the maximum margin of error is about 3%."

Have you ever wondered what this means? It is referring to the precision of an estimate—the percentage currently saying they'll vote ALP, for example. This might be, say, 43%. The error claim is that we're pretty sure the true value in the population is 43 ±3%, or somewhere between 40% and 46%.

It may seem strange, but the accuracy of this estimate hardly depends at all on the size of the population. It depends only on the size of the sample. Polls of similar size and with similar precision are carried out in the USA, which has a voting population many times that of Australia.