Key points are not available for this paper at this time.
Blackwell & Girshick (1954) have shown that simple random sampling is the minimax sampling strategy when the quantity being estimated and the space of possible population values are suitably eymmetric. In this paper, sampling with probabilities proportional to size is shown to be the minimax strategy under fairly strong conditions when the quantity being estimated is not symmetric.
Scott et al. (Fri,) studied this question.