Weighted Finite Population Sampling to Maximize Entropy
Attention is drawn to a method of sampling a finite population of N units with unequal probabilities and without replacement. The method was originally proposed by Stern & Cover (1989) as a model for lotteries. The method can be characterized as maximizing entropy given coverage probabilities πi, or equivalently as having the probability of a selected sample proportional to the product of a set of ‘weights’ wi. We show the essential uniqueness of the wi given the πi. We…