In 1936 an American magazine ran what was, at the time, the largest opinion poll ever attempted. It sent out millions of ballots and received more than two million replies, which is an extraordinary number even now. On that basis it announced confidently that the challenger would win the presidential election.
He lost, and he lost by an enormous margin. The magazine's reputation never recovered.
The reason was not the size of the sample. It was where the names had come from. The magazine had built its list from telephone directories, car registrations and its own subscribers — and in 1936, in the middle of a depression, owning a telephone or a car meant something about your income. The two million people who replied were a real and enormous group. They were simply not the electorate.
There was a second problem underneath the first. Ballots were posted out, and the people who took the trouble to fill one in and post it back were not a random half of those who received one. Choosing to reply is itself a choice.
In the same year a young researcher named Gallup predicted the result correctly, using a sample a small fraction of the size, chosen to reflect the country rather than to be as large as possible.
The lesson has been taught in every statistics course since, in one sentence: a biased sample does not become less biased by getting bigger. It only becomes more convincing.