Equilibrium and Welfare of Two-Parameter Scoring Rules

We study a cardinal model of voting with three alternatives where voters' von Neumann Morgenstern utilities are private information. We consider voting protocols given by two-parameter scoring rules, as introduced by Myerson (2002). For these voting rules, we characterize symmetric Bayes Nash equilibria, and compare these equilibria according to the level of voter welfare they generate. Numerical welfare comparisons suggest that an optimal two-parameter scoring rule reduces significantly welfare losses relative to other, more common, voting rules such as the plurality rule, approval voting, and the Borda Count. Furthermore, an optimal two-parameter scoring rule appears to involve an extremely small welfare loss relative to second best voting rules