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.

Each solution concept on a class of normal form games with a given outcome space can be regarded as a social choice correspondence. Here we present a general method of constructing compound solution concepts out of given ones by means of games of pretension.