5 - Model Extensions: Varying Size of the Minority, the Free-Rider Problem, and Social Welfare

Summary

In this chapter I explore three extensions to the mathematical model presented in Chapter 4. First, I show that the results do not depend upon the balance of minority to majority assumed in Chapter 4. Instead, at any ratio of majority to minority size, candidates might side with an intense minority over a less-intense majority. Candidates do not, however, side with any intense minority, siding only with those of a sufficient combination of size and intensity. Second, I consider the free-rider problem in large electorates. I discuss a modification to the mathematical model where increasing the size of the electorate does not prevent some voters from choosing to incur costly political action. Finally, I consider the social welfare implications of intensity theory showing that utilitarian welfare can sometimes be higher with frustrated majorities and costly political action than under simple majority rule.