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Roberts' theorem with neutrality: A Social welfare ordering approach

  • Debasis Mishra

    ()

    (Indian Statistical Institute, New Delhi)

  • Arunava Sen

    ()

    (Indian Statistical Institute, New Delhi)

We consider dominant strategy implementation in private values settings, when agents have multi-dimensional types, the set of alternatives is finite, monetary transfers are allowed, and agents have quasi-linear utilities. We show that any implementable and neutral social choice function must be a weighted welfare maximizer if the type space of every agent is an m-dimensional open interval, where m is the number of alternatives. When the type space of every agent is unrestricted, Roberts' theorem with neutrality (Roberts, 1979) becomes a corollary to our result. Our proof technique uses a social welfare ordering approach, commonly used in aggregation literature in social choice theory. We also prove the general (affine maximizer) version of Roberts' theorem for unrestricted type spaces of agents using this approach.

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File URL: http://www.isid.ac.in/~pu/dispapers/dp10-03.pdf
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Paper provided by Indian Statistical Institute, New Delhi, India in its series Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers with number 10-03.

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Length: 29 pages
Date of creation: Mar 2010
Date of revision:
Handle: RePEc:ind:isipdp:10-03
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  1. Gui Hongwei & Müller Rudolf & Vohra Rakesh, 2004. "Dominant Strategy Mechanisms with Multidimensional Types," Research Memorandum 047, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
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  9. Moldovanu, Benny & Meyer-ter-Vehn, Moritz, 2002. "Ex-post Implementation with Interdependent Valuations," Sonderforschungsbereich 504 Publications 02-08, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
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  11. Berger André & Müller Rudolf & Naeemi Seyed Hossein, 2010. "Path-Monotonicity and Incentive Compatibility," Research Memorandum 035, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  12. Philippe Jehiel & Moritz Meyer-ter-Vehn & Benny Moldovanu, 2008. "Ex-post implementation and preference aggregation via potentials," Economic Theory, Springer, vol. 37(3), pages 469-490, December.
  13. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
  14. Rochet, Jean-Charles, 1987. "A necessary and sufficient condition for rationalizability in a quasi-linear context," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 191-200, April.
  15. Ron Lavi & Ahuva Mu’alem & Noam Nisan, 2009. "Two simplified proofs for Roberts’ theorem," Social Choice and Welfare, Springer, vol. 32(3), pages 407-423, March.
  16. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-31, July.
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