Protecting minorities through the average voting rules

Properties of an average voting rule - the outcome being some weighted average of votes – are investigated, with particular attention to its ability to protect minorities. The unique average voting outcome is characterized with a median formula which depends on the voters’ preferred allocations and some parameters constructed from the voters’ weights. We provide necessary and sufficient conditions for the average outcome to be above the majority outcome. A minority is said to be protected by a switch in voting rule if the voting outcome becomes closer to the median bliss point of the minority. A sufficient condition for minority protection is that, either the minority’s weight is sufficiently large or the majority outcome is too unfavorable to the minority. Applications to the composition of public goods and to public expenditures level are considered. We end by exploring the combined use of average and majority voting in a two-stage procedure for determining both the level and the composition of public expenditures.