We provide a survey of the literature on ranking sets of objects. The interpretations of those set ranking include those employed in the theory of choice under complete uncertianty, rankings of opportunity sets, set rankings that appear in matching theory, and the structure of assemly proferences.

We study social choice functions for societies confronting alternatives which can be described as vectors in a Euclidean space, and where all voters have preferences on these alternatives which are saturated at an ideal point and satisfy an appropriate restriction of single-peakedness.

We model the decision problems faced by the members of societies whose new members are determined by vote. We adopt a number of simplifying assumptions. In spite of these simplifications, we show that interesting strategic behavior is implied by the dynamic structure of the problem: the vote for...