Abstract
This paper studies a general class of social choice problems in which agents’ payoff functions (or types) are privately observable random variables, and monetary transfers are not available. We consider cardinal social choice functions which may respond to agents’ preference intensities as well as preference rankings. We show that a social choice function is ex ante Pareto efficient and Bayesian incentive compatible if and only if it is dictatorial. The result holds for arbitrary numbers of agents and alternatives, and under a fairly weak assumption on the joint distribution of types, which allows for arbitrary correlations and asymmetries.
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Notes
A restricted version of Theorem 1 for the case with two alternatives has appeared as Proposition 3 in the working-paper version of Kikuchi and Koriyama (2023), available at https://arxiv.org/abs/2206.09574.
Part of Mas-Colell et al. (1995, Proposition 16.E.2) says that if \(Y\subset \mathbb {R}^k\) is a convex set and if an element \(y^*\in Y\) is in the Pareto frontier of Y, then there is a vector \(\mu =(\mu _i)_{i=1}^k\) with \(\mu _i\ge 0\) for all \(i=1,\cdots ,k\) and \(\mu \ne 0\) such that \(y^*\) is a solution of the maximization problem \(\max _{y\in Y}\mu \cdot y\).
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We are thankful to Matías Núñez for the fruitful discussions and useful comments. We are also grateful to two anonymous reviewers and the Associate Editor for their thoughtful and insightful comments. Financial support by Investissements d’Avenir, ANR-11-IDEX-0003/Labex Ecodec/ANR-11-LABX-0047 and PHC Sakura program, project number 45153XK, is gratefully acknowledged.
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Kikuchi, K., Koriyama, Y. A general impossibility theorem on Pareto efficiency and Bayesian incentive compatibility. Soc Choice Welf (2024). https://doi.org/10.1007/s00355-024-01515-4
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DOI: https://doi.org/10.1007/s00355-024-01515-4