Many Profiles; Many New Paradoxes
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I now turn from the single profile consequences of election outcomes to describe the fascinating properties of voting theory involving several profiles. A natural example is the electoral fable controversy about the Dean’s Council caused by combining the two profiles — one for each subcommittee. Beyond constructing amusing “paradoxes,” the importance of multiprofile issues is, for instance, to understand what can happen if a voter votes strategically, or if he doesn’t vote. (The voter’s options are to vote sincerely, strategically, or abstain; each option defines a different profile.) Other multiprofile issues include a concern about the consequences should more voters vote. What happens if voters change preferences? Can forming a coalition cause problems? In fact, as I show, important theorems in social choice theory, such as the Arrow Impossibility Theorem, are based on the properties a procedure must exhibit with changes in profiles.
KeywordsRelative Ranking Condorcet Winner Plurality Vote Weak Consistency House Size
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