Attention is drawn to a method of sampling a finite population of N un
its with unequal probabilities and without replacement. The method was
originally proposed by Stern and Cover (1989) as a model for lotterie
s. The method can be characterized as maximizing entropy given coverag
e probabilities pi(i), or equivalently as having the probability of a
selected sample proportional to the product of a set of 'weights' w(i)
. We show the essential uniqueness of the w(i) given the pi(i), and de
scribe practical, geometrically convergent algorithms for computing th
e w(i) from the pi(i). We present two methods for stepwise-selection o
f sampling units, and corresponding schemes for removal of units that
can be used in connection with sample rotation. Inclusion probabilitie
s of any order can be written explicitly in closed form. Second-order
inclusion probabilities pi(ij) satisfy the condition 0 < pi(ij) < pi(i
) pi(j), which guarantees Yates and Grundy's variance estimator to be
unbiased, definable for all samples and always nonnegative for any sam
ple size.