Chapter 6: Majority rule and tournament solutions
Majority rule – the selection of collective outcomes that have majority support – plays a special role in normative and positive theories of social choice. Majority rule works in a straightforward fashion when only two alternatives, call them a and b, are under consideration, for example, an election with just two candidates a and b, or a proposal that can be either accepted (a) or rejected (b). Each voter either prefers a to b or prefers b to a (or possibly is indifferent between them) and votes for his or her preferred alternative (or possibly abstains). When three or more alternatives are under consideration – for example, an election with more than two candidates, or a proposal that can be adopted as is, amended in various ways, or rejected – majority rule as a basis for choice becomes more complicated. In the two-alternative case, majority rule satisfies two distinct principles: the majoritarian principle according to which the alternative with the first-preference support of a majority of voters (sometimes called the strict majority winner) is selected; and the Condorcet principle according to which the alternative that is majority-preferred to every other alternative (commonly called the Condorcet winner) is selected. When there are only two alternatives, these principles are equivalent and, apart from the problems of ties, can always be fulfilled. With more than two alternatives, they are not equivalent and, even apart from the problem of ties, cannot always be fulfilled.
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