A comparative analysis of measures of social homogeneity

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.