Social choice in large populations with single-peaked preferences - Martin Hellwig (Max Planck Institute for Research on Collective Goods, 2021)
An anonymous social choice function for a large atomless population maps cross-section distributions of preferences into outcomes. Because any one individual is too insignificant to affect these distributions, every anonymous social choice function is individually strategy- proof. However, not every anonymous social choice function is group strategy-proof. If the set of outcomes is linearly ordered and participants have single-peaked preferences, an anonymous social choice function is group strategy-proof if and only if it can be implemented by a mechanism involving binary votes between neighbouring outcomes with nondecreasing thresholds for "moving higher up". Such a mechanism can be interpreted as a version of Moulin's (1980) generalized median-voter mechanism for a large population.
hdl:21.11116/0000-0009-5984-E
Keywords: D60; D70; D82; H41; 330; Social choice; large populations; strategy proofness; group strategy proofness; single-peaked preferences