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Individual versus group strategy-proofness: when do they coincide?

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  • Salvador Barberà

    ()

  • Dolors Berga

    ()

  • Bernardo Moreno

    ()

Abstract

A social choice function is group strategy-proof on a domain if no group of agents can manipulate its final outcome to their own benefit by declaring false preferences on that domain. Group strategy-proofness is a very attractive requirement of incentive compatibility. But in many cases it is hard or impossible to find nontrivial social choice functions satisfying even the weakest condition of individual strategy-proofness. However, there are a number of economically significant domains where interesting rules satisfying individual strategy-proofness can be defined, and for some of them, all these rules turn out to also satisfy the stronger requirement of group strategy-proofness. This is the case, for example, when preferences are single-peaked or single-dipped. In other cases, this equivalence does not hold. We provide sufficient conditions defining domains of preferences guaranteeing that individual and group strategy-proofness are equivalent for all rules defined on the

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Bibliographic Info

Paper provided by Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) in its series UFAE and IAE Working Papers with number 761.09.

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Length: 31
Date of creation: 04 Feb 2009
Date of revision:
Handle: RePEc:aub:autbar:761.09

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Keywords: Strategy-proofness; Group strategy-proofness; k-size strategy-proofness; Sequential inclusion; Single-peaked preferences; Single-dipped preferences; Separable preferences.;

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References

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  1. Alejandro Saporiti, 2007. "Strategy-Proofness and Single-Crossing," Wallis Working Papers WP48, University of Rochester - Wallis Institute of Political Economy.
  2. Bezalel Peleg & Peter Sudhölter, 1998. "Single-Peakedness and Coalition-Proofness," Working Papers 290, Bielefeld University, Center for Mathematical Economics.
  3. Klaus, Bettina, 2001. "Coalitional strategy-proofness in economies with single-dipped preferences and the assignment of an indivisible object," Open Access publications from Maastricht University urn:nbn:nl:ui:27-20043, Maastricht University.
  4. Barbera, Salvador & Jackson, Matthew O, 1995. "Strategy-Proof Exchange," Econometrica, Econometric Society, vol. 63(1), pages 51-87, January.
  5. Salvador Barbera & Hugo Sonnenschein & Lin Zhou, 1990. "Voting by Committees," Cowles Foundation Discussion Papers 941, Cowles Foundation for Research in Economics, Yale University.
  6. Sen, Amartya & Pattanaik, Prasanta K., 1969. "Necessary and sufficient conditions for rational choice under majority decision," Journal of Economic Theory, Elsevier, vol. 1(2), pages 178-202, August.
  7. Le Breton, Michel & Zaporozhets, Vera, 2006. "On the Equivalence of Coalitional and Individual Strategy-Proofness Properties," IDEI Working Papers 408, Institut d'Économie Industrielle (IDEI), Toulouse.
  8. Le Breton, M. & Weymark, J.A., 1993. "Strategy-Prrof Social Choice with Continuous Saparable Preferences," UBC Departmental Archives 93-29, UBC Department of Economics.
  9. Green, Jerry & Laffont, Jean-Jacques, 1979. "On Coalition Incentive Compatibility," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 243-54, April.
  10. Shigehiro Serizawa, 2006. "Pairwise Strategy-Proofness and Self-Enforcing Manipulation," Social Choice and Welfare, Springer, vol. 26(2), pages 305-331, April.
  11. Dasgupta, Partha S & Hammond, Peter J & Maskin, Eric S, 1979. "The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 185-216, April.
  12. Barbera, Salvador, 1979. "A Note on Group Strategy-Proof Decision Schemes," Econometrica, Econometric Society, vol. 47(3), pages 637-40, May.
  13. Kim, Ki Hang & Roush, Fred W., 1980. "Special domains and nonmanipulability," Mathematical Social Sciences, Elsevier, vol. 1(1), pages 85-92, September.
  14. Schummer, James & Vohra, Rakesh V., 2002. "Strategy-proof Location on a Network," Journal of Economic Theory, Elsevier, vol. 104(2), pages 405-428, June.
  15. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
  16. Peleg, Bezalel, 1998. "Almost all equilibria in dominant strategies are coalition - proof," Economics Letters, Elsevier, vol. 60(2), pages 157-162, August.
  17. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  18. 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.
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Citations

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Cited by:
  1. 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).
  2. John Weymark, 2011. "A unified approach to strategy-proofness for single-peaked preferences," SERIEs, Spanish Economic Association, vol. 2(4), pages 529-550, December.
  3. Hans Peters & Souvik Roy & Ton Storcken, 2011. "Strategy-proof voting rules on a multidimensional policy space for a continuum of voters with elliptic preferences," SERIEs, Spanish Economic Association, vol. 2(4), pages 485-496, December.
  4. EHLERS, Lars & WESTKAMP, Alexander, 2011. "Strategy-Proof Tie-Breaking," Cahiers de recherche 09-2011, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. Salvador Barberà & Dolors Berga & and Bernardo Moreno, 2009. "Single-dipped preferences," Working Papers 418, Barcelona Graduate School of Economics.
  6. Jamal Nazrul Islam & Haradhan Kumar Mohajan & Pahlaj Moolio, 2009. "Political Economy and Social Welfare with Voting Procedure," KASBIT Journal of Management & Social Science (fmkaspk), Khadim Ali Shah Bukhari Institute of Technology (KASBIT), vol. 2(1), pages 42-66, December.
  7. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2011. "Two Necessary Conditions for Strategy-Proofness: on What Domains are they also Sufficient?," UFAE and IAE Working Papers 892.11, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  8. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2012. "Group strategy-proof social choice functions with binary ranges and arbitrary domains: characterization results," International Journal of Game Theory, Springer, vol. 41(4), pages 791-808, November.
  9. Le Breton, Michel & Zaporozhets, Vera, 2006. "On the Equivalence of Coalitional and Individual Strategy-Proofness Properties," IDEI Working Papers 408, Institut d'Économie Industrielle (IDEI), Toulouse.
  10. Jordi Massé & Inés Moreno de Barreda, 2010. "On Strategy-proofness and Symmetric Single-Peakedness," Working Papers 421, Barcelona Graduate School of Economics.
  11. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2012. "Assigning agents to a line," Discussion Papers of Business and Economics 11/2012, Department of Business and Economics, University of Southern Denmark.
  12. Ernesto Savaglio & Stefano Vannucci, 2012. "Strategy-proofness and unimodality in bounded distributive lattices," Department of Economics University of Siena 642, Department of Economics, University of Siena.
  13. Salvador Barberà, 2010. "Strategy-proof social choice," Working Papers 420, Barcelona Graduate School of Economics.
  14. MAULEON, Ana & MOLIS, Elena & VANNETELBOSCH, Vincent & VERGOTE, Wouter, 2011. "Absolutely stable roommate problems," CORE Discussion Papers 2011029, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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