CONDORCET WINNERS AND THE PARADOX OF VOTING - PROBABILITY-CALCULATIONS FOR WEAK PREFERENCE ORDERS

That individual preferences may be aggregated into a meaningful collec tive decision using the Condorcet criterion of majority choice is one of the central tenets of democracy. But that individual preferences ma y not yield majority winners is one of the classic findings of the soc ial choice literature. Given, this problem, social choice theorists ha ve attempted to estimate the probability of Condorcet winners, given c ertain empirical or theoretical conditions. We shall estimate the prob abilities of Condorcet winners and intransitive aggregate orders for v arious numbers of individuals with strong or weak preference orders ac ross various numbers of alternatives. We find, using computer simulati on, a stark contrast between these estimates assuming strong individua l preferences and the estimates allowing for individuals' indifference between pairs of alternatives. In contrast to earlier work, which dep ends on the strong-preference assumption, we suggest that the problem is most acute for small committee decision making and least acute for mass elections with few alternatives.