Chapter 15: Properties and paradoxes of common voting rules
Voting can take on many forms. The previous chapter identified the potential for meaningful comparisons when there are only two alternatives but explained how Arrow (and others) proved that any voting rule will fail to satisfy a specific set of minimum conditions when there are more than two alternatives. Thus we can choose only among various flawed voting rules. The purpose of this chapter is to compare some of the most commonly studied voting rules. Throughout this chapter, let m ≥ 2 represent the number of alternatives. Alternatives can represent candidates running for office, nominees for awards, proposed policies, or even host cities for the Olympic Games. The discussion in this chapter will be limited to those situations for which only a single winner is desired. Rules for selecting multiple winners (such as for multiple positions on corporate or local school boards, or in multimember legislative districts) are discussed in Chapter 17. A comparison of simple majority against supermajority rules is presented in detail in Chapter 7 for the limiting case of two alternatives. The purpose of this chapter is to compare a variety of rules when there are multiple alternatives. Unless otherwise specifically noted, the discussion throughout this chapter presumes that all voters behave ‘sincerely’ rather than ‘strategically’. A sincere voter votes strictly in accordance with her preference ordering of the alternatives, without taking into consideration how others may vote. Strategic voting will be briefly discussed toward the end of the chapter.
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