Does majoritarian approval matter in selecting a social choice rule? An exploratory panel study

Abstract

This study is an attempt to empirically detect the public opinion concerning majoritarian approval axiom. A social choice rule respects majoritarian approval iff it chooses only those alternatives which are regarded by a majority of “voters” to be among the “better half” of the candidates available. We focus on three social choice rules, the Majoritarian Compromise, Borda’s Rule and Condorcet’s Method, among which the Majoritarian Compromise is the only social choice rule always respecting majoritarian approval. We confronted each of our 288 subjects with four hypothetical preference profiles of a hypothetical electorate over some abstract set of four alternatives. At each hypothetical preference profile, two representing the preferences of five and two other of seven voters, the subject was asked to indicate, from an impartial viewpoint, which of the four alternatives should be chosen whose preference profile was presented, which if that is unavailable, then which if both of the above are unavailable, and finally which alternative should be avoided especially. In each of these profiles there is a Majoritarian Compromise-winner, a Borda-winner and a Condorcet-winner, and the Majoritarian Compromise-winner is always distinct from both the Borda-winner and the Condorcet-winner, while the Borda- and Condorcet-winners sometimes coincide. If the Borda- and Condorcet-winners coincide then there are two dummy candidates, otherwise only one, and dummies coincide with neither of the Majoritarian Compromise-, Borda- or Condorcet-winner. We presented our subjects with various types of hypothetical preference profiles, some where Borda respecting majoritarian approval, some where it failed to do so, then again for Condorcet, some profiles it respected majoritarian approval and some where it did not. The main thing we wanted to see was whether subjects’ support for Borda and Condorcet was higher when this social choice rule respected majoritarian approval than it did not. Our unambiguous overall empirical finding is that our subjects’ support for Borda and Condorcet was significantly stronger as they respect majoritarian approval.