The effect of social homogeneity on coincidence probabilities for pairwise proportional lottery and simple majority rules

The Condorcet efficiency of Pairwise Proportional Lottery Rules (PPLR) is considered under various assumptions concerning the likelihood that given voters' preference profiles are observed on three alternatives. Representations are developed for the expected Condorcet efficiency under impartial culture, impartial anonymous culture, and a generalization to Pólya-Eggenberger distributions. PPLR is shown to be equivalent to a random selection process in the limit of voters under impartial culture. However, relatively small increases in social homogeneity, as measured by Kendall's Coefficient of Concordance, cause significant increases in the Condorcet efficiency of PPLR.Professor Berg's work was partly supported by the Swedish Research Council for the Humanities and Social Sciences.