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...