Optimal Voting Rules under Participation Constraints

We study the design of voting rules for international unions when countries’ participation is voluntary. While efficiency recommends weighting countries proportionally to their stakes, we show that accounting for participation constraints entails overweighting some countries, those for which the incentive to participate is the lowest. When decisions are not enforceable, cooperation requires the satisfaction of more stringent constraints, that may be mitigated by granting a veto power to some countries. The model has important implications for the problem of apportionment, the allocation of voting weights to countries of differing populations, where it provides a rationale for setting a minimum representation for small countries.