  When can a majority of voters find common ground, that is, a position they
all agree upon? How does the shape of the political spectrum influence the
outcome? When mathematical objects have a social interpretation, the associated
theorems have social applications. In this article we give examples of
situations where sets model preferences and develop extensions of classical
theorems about convex sets, such as Helly's theorem, that can be used in the
analysis of voting in "agreeable" societies.
