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Maximal domain for strategy-proof probabilistic rules in economies with one public good

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  • Shuhei Morimoto

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    Abstract

    We consider the problem of choosing a level of a public good on an interval of the real line among a group of agents. A probabilistic rule chooses a probability distribution over the interval for each preference profile. We investigate strategy-proof probabilistic rules in the case where distributions are compared based on stochastic dominance relations. First, on a “minimally rich domain”, we characterize the so-called probabilistic generalized median rules (Ehlers et al., J Econ Theory 105:408–434, 2002 ) by means of stochastic-dominance (sd) strategy-proofness and ontoness. Next, we study how much we can enlarge a domain to allow for the existence of sd-strategy-proof probabilistic rules that satisfy ontoness and the no-vetoer condition. We establish that the domain of “convex” preferences is the unique maximal domain including a minimally rich domain for these properties. Copyright Springer-Verlag Berlin Heidelberg 2013

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    File URL: http://hdl.handle.net/10.1007/s00355-012-0700-4
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    Bibliographic Info

    Article provided by Springer in its journal Social Choice and Welfare.

    Volume (Year): 41 (2013)
    Issue (Month): 3 (September)
    Pages: 637-669

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    Handle: RePEc:spr:sochwe:v:41:y:2013:i:3:p:637-669

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    1. Serizawa Shigehiro, 1995. "Power of Voters and Domain of Preferences Where Voting by Committees Is Strategy-Proof," Journal of Economic Theory, Elsevier, vol. 67(2), pages 599-608, December.
    2. Kentaro Hatsumi & Dolors Berga & Shigehiro Serizawa, 2011. "A maximal domain for strategy-proof and no-vetoer rules in the multi-object choice model," ISER Discussion Paper 0809, Institute of Social and Economic Research, Osaka University, revised Feb 2013.
    3. Jordi Massó & Inés Moreno de Barreda, 2010. "On Strategy-proofness and Symmetric Single-peakedness," UFAE and IAE Working Papers 809.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    4. Ehlers, Lars & Peters, Hans & Storcken, Ton, 2002. "Strategy-Proof Probabilistic Decision Schemes for One-Dimensional Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 105(2), pages 408-434, August.
    5. Hideyuki Mizobuchi & Shigehiro Serizawa, 2005. "Maximal Domain for Strategy-Proof Rules in Allotment Economies," ISER Discussion Paper 0628, Institute of Social and Economic Research, Osaka University.
    6. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    7. Barbera, Salvador, 1979. "A Note on Group Strategy-Proof Decision Schemes," Econometrica, Econometric Society, vol. 47(3), pages 637-40, May.
    8. Dolors Berga, 2002. "Single-peakedness and strategy-proofness of generalized median voter schemes," Social Choice and Welfare, Springer, vol. 19(1), pages 175-192.
    9. Alejandro Neme & Jordi MassÔ & Salvador BarberÁ, 1999. "Maximal domains of preferences preserving strategy-proofness for generalized median voter schemes," Social Choice and Welfare, Springer, vol. 16(2), pages 321-336.
    10. Barbera, Salvador, 1979. "Majority and Positional Voting in a Probabilistic Framework," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 379-89, April.
    11. Berga, D & Serizawa, S, 1996. "Maximal Domain for Strategy-Proof Rules with one Public Good," UFAE and IAE Working Papers 353.96, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    12. Border, Kim C & Jordan, J S, 1983. "Straightforward Elections, Unanimity and Phantom Voters," Review of Economic Studies, Wiley Blackwell, vol. 50(1), pages 153-70, January.
    13. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    14. Ehlers, Lars & Klaus, Bettina, 2001. " Solidarity and Probabilistic Target Rules," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 3(2), pages 167-84.
    15. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-81, April.
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