Once upon a time (up to 1925 or about), there was "representative sampling" meaning, "creating a representation of the population in the sample" i.e. quotas, The caricature is that to obtain the so-called representation, you *have to* get those 5 middle-age out-of-work with post-secondary education living in towns of less than 20000 people, otherwise ou don't have the "true" representation. With Neyman's theory on disproportional allocation to stratified random samples, "representative sampling" sort of faded away, at least among (mathematical) statisticians dealing with survey sampling. In the recent years, the only times I've heard/read "representative sampling" were with reference to "the ability to obtain unbiased estimates from the sample"; if memory serves, it was so defined by C.E.SÃ¤rndal during a conference. I have searched in more than 20 textbooks, never coming up with any satisfying "modern" definition of "representative sampling". Basically, (mathematical) statisticians have dropped the notion altogether. When I hear it, I'll question the speaker (if I can) as to what he/she actually means, and it more or less boils down to unbiasedness.