Majority rule and utilitarian welfare

We study the welfare properties of majority and supermajority rules when voting is costly and values, costs, and electorate sizes are all random. Unlike previous work, where the electorate size was either fixed or Poisson distributed, and exhibited no limiting dispersion, we allow for general distributions that permit substantial dispersion. We identify conditions on these distributions guaranteeing that a large election under majority rule produces the utilitarian choice with probability one. Absent these conditions, nonutilitarian outcomes are possible, as we demonstrate. We also show that majority rule is the only voting rule with the utilitarian property-strict supermajority rules are not utilitarian.