Given a set of alternatives, a collective choice rule (function) assigns a subset of alternatives to any given preference profile; the alternative or alternatives that are chosen. Until now we have assumed that the preference profiles of individuals represent their true preferences. This assumption implies that when collective choice rules are applied, individuals who participate in the choice reveal their true preferences. This chapter focuses on the question of whether it is possible to expect true revelation of preferences. In other words, is using the collective choice function an effective way to evoke a sincere report of preferences from the individuals participating in the collective choice? This question is interesting because it raises an additional aspect of collective choice that we have not yet addressed, namely, the strategic or game theoretic aspect. It is possible to consider the collective choice as a strategic game in which a player's set of strategies consists of all possible preference relations. One of the possible strategies of each player is the choice of his true preferences. Therefore, given collective choice rules that determine players' payoff functions, the question is whether the true preference profile is an equilibrium in the collective choice game.

Below we will clarify with the help of examples why the rule of simple majority + chairman, the sequential majority rule, and Borda's rule do not necessarily result in true revelation of preferences.