[fmela]

Yes, but it's the resolution that would suffer, not necessarily the result. For example, if 65% of the population would vote for candidate 1, an unbiased sample of size 10 would indicate that either 60% or 70% of the population would vote for candidate 1. A sample that is biased could literally tell you anything, regardless of how large it is (in absolute numbers).

[austinjp]

Not every time, surely? A sample is randomly taken, so there will be variation. Even if it's unbiased, your samples will swing between all possible extremes. So you need to take a very large number of small samples.

[learnstats2]

The result of your sample would typically be anything between 30% and 100%.

Whereas, if you instead take a sample of 1000, you typically get results between 61% and 69%.

Source: http://www.wolframalpha.com/input/?i=binomial%2810%2C0.65%29...

You can't take an "unbiased" sample in the sense that you mean here.

There's only one way you can take a completely unbiased sample: if you know exactly how everyone will vote in advance and select them carefully on that basis. But if you already know how everyone will vote in advance, then sampling is a fruitless exercise.