Chapter 20: Empirical examples of voting paradoxes
Several earlier chapters, especially Chapter 15, identified important properties of voting rules whose violation is sufficiently counter-intuitive that we may call them ‘paradoxes’. These paradoxes are not just mathematical curiosities. Under certain conditions, they may be highly consequential. The purpose of this chapter is to discuss empirical examples of paradoxical situations that have serious political consequences. My review of empirical occurrences of paradoxes begins in section 20.2 with the phenomenon of election inversions. Section 20.3 pertains to the Condorcet properties discussed in Chapters 6, 10, 14, 15 and 16; I first examine the Condorcet paradox – that is, preference profiles that produce pairwise majority rule cycles – and then voting rules that fail to select a Condorcet winner and may even select a Condorcet loser. The next sections investigate the properties of apportionment formulas (briefly discussed in Chapter 17) and IAS failures (discussed in Chapter 15). The final section briefly reviews problems with monotonicity (discussed in Chapter 15) and House size effects in the Electoral College.
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