Majority rule

Voting on alternate proposals so that the one with the greatest number of supporters is the one adopted.

Majority voting is perhaps the most common rule for making collective decisions. A long time ago, this rule was found to have serious deficiencies, in addition to the fact that it may allow a majority to suppress a minority. In some situations it may pay off to vote strategically (i.e. by not voting for the preferred alternative), or to manipulate the order in which different alternatives are voted upon. Voting between pairs of alternatives sometimes fails to produce a clear result in a group. A majority may thus prefer alternative a to alternative b whereas a (second) majority prefers b to c; meanwhile, a (third) majority prefers c to a. In the wake of this kind of "intransitivity", the decision rule cannot select an alternative that is unambiguously best for any majority. In collaboration with Prasanta Pattanaik, the Nobel Prize winner Amartya Sen has specified the general conditions that eliminate intransitivities of majority rule.