In the present chapter we consider the situation wherein a group of voters is collectively trying to choose among several alternatives. When people speak of the area of “social choice,” it is typically this context that they have in mind.
In the case where there are only two alternatives, the standard democratic process is to let each person vote for his or her preferred alternative, with the social choice (the “winner”) being the alternative receiving the most votes. The situation, however, becomes complicated if there are more than two alternatives. In particular, if we proceed exactly as we did above where we had two alternatives, then we are not taking advantage of some individual comparisons among the several alternatives that could be made.