> Is there a statistical definition of "representative sampling?" That > is, is there a way to show that a sampling strategy will yield > (within some tolerance) a sample that is "representative" of the > population? [...]
As pointed out elsewhere in this thread, "representative" isn't a technical term, so it doesn't have a technical definition. That said, I think we can agree that what we want is for parameters and what-not estimated from a sample be not too different from the results we would get if we had the entire population available to us. In this sense, clearly some sampling schemes are more "representative" than others.
Other posters have mentioned random and stratified-random sampling. Parameters estimated from a stratified sample generally have less variance, so it's reasonable to say such a sample is "more representative".
However, there is at least one class of interesting problems for which deterministic sampling can yield better results than either random or stratified-random sampling. This is the class of problems of estimating an integral over some space, and for these problems sampling sequences can be constructed (so-called "low-discrepency sequences") which yield results with less variance than strictly random sampling.
So for some spatial sampling problems, there are good deterministic sampling algorithms. I don't know whether one could construct a "low-discrepency" method for sampling categorical data, but it seems possible, at least.