Voting in Agreeable Societies

When is agreement possible? An important aspect of group decision-making is the question of how a group makes a choice when individual preferences may differ. Clearly, when making a single group choice, people cannot all have their “ideal” preferences, i.e, the options that they most desire, if those ideal preferences are different. However, for the sake of agreement, people may be willing to accept as a group choice an option that is merely “close” to their ideal preferences. Voting is a situation in which people may behave in this way. The usual starting model is a one-dimensional political spectrum, with conservative positions on the right and liberal positions on the left, as in Figure 1. We call each position on the spectrum a platform that a candidate or voter may choose to adopt. While a voter may represent her ideal platform by some point x on this line, she might be willing to vote for a candidate who is positioned at some point “close enough” to x, i.e., in an interval about x.