For an n-member body making dichotomous decisions, decision rules can be formulated as simple games. Of all possible decision rules, majority rule maximizes the average reponsiveness of the body to individual preferences. It is the unique decision rule which does this when n is odd, but not when n is even. Other conditions limit the choice of decision rules when n is even.
Suppose that an n-member body must collectively decide whether to accept or reject each of a series of proposals. We might, for instance, think of a society which must decide whether to impose or not to impose each of a series of proposed laws. What decision rule would be best for that body to adopt? To answer this question, we must make precise what we mean by a decision rule, and we must specify the criteria by which we propose to judge a decision rule best.
We should first note that we are dealing only with dichotomous choices: to accept or to reject. Hence we avoid the difficulties surrounding the Arrow Impossibility Theorem, which become relevant as soon as a decision is required among three or more alternatives. 1 Although decisions among many alternatives are very important, many societies and legislatures operate under 'parliamentary procedures' which have the effect of reducing multi-choice decisions to a sequence of dichotomous decisions, at which point our question of how best to make dichotomous decisions becomes applicable.
Among the decision rules which an n-member body might adopt, majority rule has occupied a special place in political theory. An obvious attractive property of majority rule, at least for democratic theory, is its symmetry: it treats all members of the decision-making body alike. Of course, itt shares this property with other decision rules. One can, for instance, require approval by three-fifths, two-thirds, or all of the members of the body. Alternatively, one can make decisions by a 'two stage plebiscite': partition n = mk voters into m districts, with k voters in each district. Require approval by a majority (say) of the k voters in each of a majority of the m districts. The 'pure delegate' model of representative democracy is essentially such a two stage plebiscite. We think of each district as electing a representative who votes on each issue Theory and Decision 8 (1977) 351-360. All Rights Reserved.