A number of societal factors have been found to have an impact on the probability that a PMRW exists. The factor that has been most thoroughly examined in this context is the degree of coherence or consistency of voters’ preferences, as measured according to some definition of social homogeneity. Numerous studies have sought to find general relationships between these measures of social homogeneity and the probability that a PMRW exists. Some theoretical studies have successfully shown that such relationships can exist on an expected value basis, without measuring the overall strength of the relationships. Strong evidence has also been provided to indicate that simple measures of social homogeneity are very ineffective at showing such a relationship at all. In particular, the connection between some of these measures of social homogeneity and the probability that a PMRW exists is found to be reversed, based on whether the number of voters is restricted to be odd or even. If such a general relationship is to be found with a significant degree of strength, the measure of homogeneity has to be based on an understanding of the mechanism by which voters preferences are formed. The proximity of the voters’ preferences to single-peaked preferences is an example of such a measure of social homogeneity.
Other significant societal factors that have an impact on the probability that a PMRW exists include: the propensity of voters to abstain from the election, the degree of voter indifference between candidates, the propensity of voters to have intransitive preferences, and the presence of uncertainty regarding the exact position that candidates represent on issues.