Accession Number : AD0668154

Title :   THE PARADOX OF VOTING: SOME PROBABILISTIC RESULTS.

Descriptive Note : Technical rept.,

Corporate Author : JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF STATISTICS

Personal Author(s) : Gleser,Leon Jay

Report Date : MAR 1968

Pagination or Media Count : 26

Abstract : 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 m=2n+1 members. It is assumed that the preference ordering of each individual in the group can be any one of the r=k 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 alpha's can take on any value, and where m is large. (Author)

Descriptors :   (*POLITICAL SCIENCE, STATISTICAL ANALYSIS), (*GROUP DYNAMICS, DECISION MAKING), BEHAVIOR, PROBABILITY, MATHEMATICAL MODELS, RANDOM VARIABLES, ANALYSIS OF VARIANCE, APPROXIMATION(MATHEMATICS), STATISTICAL DISTRIBUTIONS

Subject Categories : Psychology

Distribution Statement : APPROVED FOR PUBLIC RELEASE