Two simplified proofs for Roberts' theorem

Ron Lavi; Ahuva Mu'Alem; Noam Nisan

doi:10.1007/s00355-008-0331-y

Two simplified proofs for Roberts' theorem

Ron Lavi^*, Ahuva Mu'Alem, Noam Nisan

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

Roberts (Aggregation and Revelation of Preferences. Papers presented at the 1st European Summer Workshop of the Econometric Society, pp. 321-349. North-Holland, 1979) showed that every social choice function that is ex-post implementable in private value settings must be weighted VCG, i.e. it maximizes the weighted social welfare. This paper provides two simplified proofs for this. The first proof uses the same underlying key-point, but significantly simplifies the technical construction around it, thus helps to shed light on it. The second proof builds on monotonicity conditions identified by Rochet (J Math Econ 16:191-200, 1987) and Bikhchandani et al. (Econometrica 74(4):1109-1132, 2006). This proof is for a weaker statement that assumes an additional condition of "player decisiveness".

Original language	English
Pages (from-to)	407-423
Number of pages	17
Journal	Social Choice and Welfare
Volume	32
Issue number	3
DOIs	https://doi.org/10.1007/s00355-008-0331-y
State	Published - Mar 2009

Bibliographical note

Funding Information:
Supported by grants from the Israeli Ministry of Science and the Israeli Academy of Sciences.

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Two simplified proofs for Roberts' theorem

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