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A pairwise probability approach to the likelihood of the paradox of voting
Author(s) -
Weisberg Herbert F.,
Niemi Richard G.
Publication year - 1973
Publication title -
behavioral science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 45
eISSN - 1099-1743
pISSN - 0005-7940
DOI - 10.1002/bs.3830180204
Subject(s) - pairwise comparison , transitive relation , voting , preference , mathematics , mathematical economics , probability measure , limiting , econometrics , statistics , combinatorics , mechanical engineering , politics , political science , law , engineering
The paradox of voting (transitive individual preferences resulting in intransitive group preferences) is concealed by typical voting rules even when it exists. Consequently, researchers have developed theoretical solutions for the likelihood of the paradox which are based on the probability of individual preference orders. Here we develop a pairwise probability approach which depends only on the probability that one alternative is preferred to another; the likelihood of individual preference orders need not be specified. The results make the probability model more meaningful by establishing broad conditions under which the probability of the paradox is limited rather than varying between zero to one as in the unrestricted case. In addition, the maximum limiting probability of the paradox is shown to be smallest in the neutral case when all pairwise probabilities equal. 5.