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.