Abstract
A survey of work is presented that is related to the relationship between measures of social homogeneity and probability that a Pairwise Majority Rule Winner (PMRW), or Condorcet Winner, exists. Little evidence has been reported to support the notion of a strong relationship between these two factors. Exact probability representations are derived to show that it is possible to find a parameter that is directly observable from voter profiles that can be systematically changed, so that an expected decrease in social homogeneity will lead to a counterintuitive increase in the expected probability that a PMRW exists. Using a different observable profile parameter that reflects a rough measure of the proximity of profiles to completely single-peaked preferences adds a sufficient degree of consistency among voters' preferences to produce the expected outcome.
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