This paper has examined the relationship between social homogeneity measured by σ(p) = p12 + ... + p62 and the likelihood of Condorcet's paradox. Attention was restricted to three-candidate elections. It was shown first that the most general restriction on p vectors that produces a definite inverse relationship between σ(p) and the limit-in-voters probability P∞(p) of Condorcet's paradox is the dual culture restriction. We then deleted this restriction to allow any p vector and considered the relationship between σ(p) and the paradox probability when Abrams' positioning effect was removed by averaging the Pn(p) values all over rearrangements of the components of p. The resultant averaged probability of Condorcet's paradox with n voters was denoted as Qn(p). Theorem 1 showed that there are p vectors for all odd n ≥ 3 which deny a definite inverse relationship between Qn(p) and σ(p). However, Theorem 2 verified for n = 3 that the intervals of possible Qn(p) values for fixed values of σ(p) decrease as σ(p) increases. It was shown also that the latter relationship does not hold for large n although there is a partial tendency for Qn(p) to decrease as σ(p) increases for large n.