Selecting a Social Choice Rule — An Exploratory Panel Study

Abstract

This study is an attempt to empirically understand public preferences concerning social choice rules. We focus on four social choice rules: Plurality, Plurality with a Runoff, the Majoritarian Compromise and Borda’s Rule. We confront our subjects with hypothetical preference profiles of a hypothetical electorate over some abstract set of four alternatives at which the four social choice rules all disagree, and we ask each subject which alternative should be chosen for the society whose preference profile is shown. We report responses obtained from three studies with disjoint groups of 288, 36 and 24 subjects, resp., who were confronted with three or four preference profiles each. The responses in each study show a very clear support for the Majoritarian Compromise and Borda’s Rule, while generally disfavoring Plurality and Plurality with a Runoff.

More specifically, the profiles of total orders over four alternatives which separate all four of our social choice rules, i.e. render distinct and singleton values for each, require a minimum of seven voters, and we used only such profiles. In fact, there are just three “root” profiles of this (minimal) type, the entire population of separating total order profiles of seven voters over four alternatives being generated by these three simply by renaming (permuting) alternatives and/or voters.

Our empirical findings aggregated over the three studies we conducted with a total of 348 subjects are quite consistent from one study to another, the Majoritarian Compromise winner being chosen at 43.1% of the profiles, the Borda winner at 42.6%, the Plurality winner at 12% and the Plurality with a Runoff winner at 2.3% of the profiles.

As an inevitable consequence of our economizing on the size of our profiles, however, there was always exactly one alternative which was no voter’s worst, thus constituting the Social Compromise winner, and this alternative always coincided with the Borda winner for the profiles used. To resolve the consequent ambiguity in cases where the coincident Social Compromise and Borda winner was chosen, we consulted the explanation given by subjects for their choices, and we found that in 58.3% of these cases it was chosen because it was the Social Compromise winner and only in 22% because it maximized the Borda score. This observation would tilt our overall results, if anything, in favor of the Majoritarian Compromise (and the Social Compromise), against Borda’s Rule.

Semih Koray and Rosemarie Nagel gave us important critiques concerning the randomness of the preference profiles we used. Todd Davies and Rosemarie Nagel helped in planning a series of related studies (yet to be carried out) in a possibly cross-cultural, comparative framework. The study was refined thanks to a discussion with Vernon Smith. Fuad Aleskerov critically read and commented on parts of the study. We thank Hakan Inal and Rahmi İlkιlιç for their assistance in applying our questionnaires and in recording the subjects’ responses. We used software composed by Hakan Inal to obtain our root profiles. We acknowledge the financial support of the Boğaziçi University Research Fund. We are thankful for the support of the Turkish Academy of Sciences.