THE PARADOX OF VOTING: SOME PROBABILISTIC RESULTS.
JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF STATISTICS
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The paradox of voting was discovered by Condorcet in the 18th century and has intrigued mathematicians, economists, and political scientists since then. Briefly, the paradox is that group decision processes which involve majority rule can lead to cycles circular preferences. Because it calls into question democratic methods of group decision making and also has relevance to the construction of a social welfare function, the paradox of voting is an important problem in the behavioral sciences. Recent work on the paradox of voting has involved calculating the probability that a majority rule decision process cannot arrive at a preferred alternative in a situation where k alternatives are being considered by a randomly selected group of m2n1 members. It is assumed that the preference ordering of each individual in the group can be any one of the rk factorial possible preference orderings rankings of the k alternatives -- the probability that the individual has ranking R sub alpha being p sub alpha, p sub alpha or 0, Summation alpha 1 tor of p sub alpha 1, alpha 1, 2, ..., r. This paper is concerned with approximations to the probability of the paradox of voting in the case where the p sub alphas can take on any value, and where m is large. Author