Introduction to Part II

Abstract

In this chapter we first recall the Gibbard-Satterthwaite Theorem and review some of its implications. This is done in Section 8.2. The rest of the chapter is devoted to consideration of the problem of preference distortion as a consequence of manipulation of non-dictatorial voting rules. First we observe that the Gibbard-Satterthwaite Theorem does not tell us whether or not the sincere outcome is obtained after manipulation. It may be the case that strategic voting leads to an equilibrium of which the outcome is the sincere outcome. In that case, the result of voting by a secret ballot would be indistinguishable from that of sincere voting. Indeed, in Section 8.3 we define exactly and strongly consistent social choice functions. Such social choice functions have for each profile of (true) preferences a strong (Nash) equilibrium that yields the sincere outcome. This class of social choice functions is the main topic of Chapters 9–11, in which we present several existence and characterization theorems. In particular, in Chapter 11 we extend some of the results of Chapters 9 and 10 to voting games with a continuum of voters.