Abstract
Social homogeneity refers to the degree to which the preferences of individuals in a society tend to be alike. A number of studies have been conducted to determine whether or not a relationship exists between various measures of social homogeneity and the probability that a Condorcet winner exists. In this study, it is shown that a strong general relationship of this type does not exist for measures of social homogeneity which account only for the proportions of individuals with various preference rankings. That is, for measures which account for these proportions but not for the preference rankings to which they are assigned.
Profile specific measures of homogeneity do account for the preference rankings to which the proportions of voters are assigned. A much stronger relationship exists between profile specific measures of homogeneity and the probability that a Condorcet winner exists than for non-profile specific measures. In particular, Kendall's Coefficient of Condordance is shown to dominate twenty other measures of social homogeneity in terms of the strength of its relationship to the probability that a Condorcet winner exists.
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References
R. Abrams, The voter's paradox and the homogeneity of individual preference orders, Public Choice 26 (1976) 19–27.
F. DeMeyer and C.R. Plott, The probability of a cyclical majority, Econometrica 38 (1970) 345–354.
P.C. Fishburn, Voter concordance, simple majority, and group decision methods, Behavioral Science 18 (1973) 364–376.
P.C. Fishburn and W.V. Gehrlein, Social homogeneity and Condorcet's paradox, Public Choice 35 (1978) 403–420.
M. Garman and M. Kamien, The paradox of voting: probability calculations, Behavioral Science, 13 (1968) 306–316.
W.V. Gehrlein and P.C. Fishburn, The probability of the paradox of voting: a computable solution, Journal of Economic Theory 13 (1976a) 14–25.
W.V. Gherlein and P.C. Fishburn, Condorcet's paradox and anonymous preference profiles, Public Choice 26 (1976b) 1–18.
W.V. Gehrlein and P.C. Fishburn, Proportions of profiles with a majority candidate, Computers and Mathematics With Applications, 5 (1979) 117–124.
D. Jamison and E. Luce, Social homogeneity and the problem of intransitive majority rule, Journal of Economic Theory 5 (1972) 79–87.
M.G. Kendall and B.B. Smith, The problem of m rankings, Annals of Mathematical Statistics 10 (1939) 275–287.
K. Kuga and H. Nagatani, Voter antagonism and the paradox of voting, Econometrica 42 (1974) 1045–1067.
R.M. May, Some mathematical results on the paradox of voting, Behavioral Science 16 (1971) 143–151.
R.G. Niemi, Majority decision making with partial unidimensionality, American Political Science Review 63 (1969) 488–497.
R.G. Niemi and H.F. Weisberg, A mathematical solution to the probability of the paradox of voting, Behavioral Science 13 (1968) 317–323.
K.E. Sevick, Exact preobabilities of the voter's paradox through seven issues and seven judges, U. of Chicago, Institute for Computer Research Quarterly Report 22 (1969), Section III-B.
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Gehrlein, W.V. A comparative analysis of measures of social homogeneity. Qual Quant 21, 219–231 (1987). https://doi.org/10.1007/BF00134521
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DOI: https://doi.org/10.1007/BF00134521