|
|
Kenneth May's theorem is an important contribution to the social choice theory. It states that since group choice must depend only upon individual preferences concerning the alternatives in a set, a pattern of group choice may be built up if we know the group preference for each pair of alternatives.
Definition
Simple majority voting is an example of a social choice rule: a mapping that associates a list of individual preferences with a resulting outcome. Formally speaking, simple majority voting assigns +1 if only if
- N+1(d1, d2, ..., dn) > ½[N+1(d1, d2, ..., dn) + N−1(d1, d2, .., dn)].
Or in more normal words: the winning choice is the one whose number of votes is greater than half of the numbers of individuals who aren’t indifferent between the two choices. This is in contrast with absolute majority voting, where the winner is the option who gets more than half of the votes. Or formally speaking, absolute majority voting assigns +1 if and only if
- N+1(d1, d2, .., dn) > n/2.
The difference is clarified by means of the following example. Suppose D = (+1, +1, +1, 0, 0, −1, -−1), the distribution of votes. Applying simple majority voting yields +1 as the winning option, applying absolute majority voting gives 0, indifference between the options.
See also
External links
May’s Theorem with an Infinite Population (http://troi.cc.rochester.edu/~markfey/papers/May.pdf) Logrolling, May’s theorem and Bureaucracy (http://www.econ.au.dk/fag/7200/e03/materialer/Logrolling.pdf)