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Strategy-proof rules on partially single-peaked domains

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  • Gopakumar Achuthankutty

    (Indira Gandhi Institute of Development Research)

  • Souvik Roy

    (Economic Research Unit, Indian Statistical Institute, Kolkata)

Abstract

We consider domains that exhibit single-peakedness only over a subset of linearly ordered set of alternatives. We call such domains partially single-peaked and provide a characterization of the unanimous and strategy-proof social choice functions on these domains. We obtain the following interesting auxiliary results: (i) we characterize all unanimous and strategyproof social choice functions on generalized top-connected domains, which are an important sub-class of the maximal single-peaked domain, (ii) we show that strategy-proofness and group strategy-proofness are equivalent on partially single-peaked domains, and (iii) lastly, we identify and characterize the unanimous and strategy-proof SCFs on partially single-peaked domains that are close to being anonymous. As an application of this result, we obtain a characterization of the unanimous and strategy-proof social choice functions on multi-peaked domains (Stiglitz (1974), Epple and Romano (1996a)), multiple single-peaked domains (Reffgen (2015)) and single-peaked domains on graphs (Demange (1982)), Schummer and Vohra (2002)).

Suggested Citation

  • Gopakumar Achuthankutty & Souvik Roy, 2020. "Strategy-proof rules on partially single-peaked domains," Indira Gandhi Institute of Development Research, Mumbai Working Papers 2020-020, Indira Gandhi Institute of Development Research, Mumbai, India.
  • Handle: RePEc:ind:igiwpp:2020-020
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    1. John Weymark, 2011. "A unified approach to strategy-proofness for single-peaked preferences," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 529-550, December.
    2. Feld, Scott L. & Grofman, Bernard, 1988. "Ideological Consistency as a Collective Phenomenon," American Political Science Review, Cambridge University Press, vol. 82(3), pages 773-788, September.
    3. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2010. "Individual versus group strategy-proofness: When do they coincide?," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1648-1674, September.
    4. Stiglitz, J. E., 1974. "The demand for education in public and private school systems," Journal of Public Economics, Elsevier, vol. 3(4), pages 349-385, November.
    5. Anderberg, Dan, 1999. "Determining the mix of public and private provision of insurance by majority rule," European Journal of Political Economy, Elsevier, vol. 15(3), pages 417-440, September.
    6. Anup Pramanik, 2015. "Further results on dictatorial domains," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 379-398, September.
    7. 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.
    8. Reffgen, Alexander, 2015. "Strategy-proof social choice on multiple and multi-dimensional single-peaked domains," Journal of Economic Theory, Elsevier, vol. 157(C), pages 349-383.
    9. Arribillaga, R. Pablo & Massó, Jordi, 2016. "Comparing generalized median voter schemes according to their manipulability," Theoretical Economics, Econometric Society, vol. 11(2), May.
    10. Shurojit Catterji & Jordi Massó, 2015. "On Strategy-proofness and the Salience of Single-peakedness," Working Papers 828, Barcelona School of Economics.
    11. Pappi, Franz Urban & Eckstein, Gabriele, 1998. "Voters' Party Preferences in Multiparty Systems and Their Coalitional and Spatial Implications: Germany after Unification," Public Choice, Springer, vol. 97(3), pages 229-255, December.
    12. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 389-396, December.
    13. Gopakumar Achuthankutty & Souvik Roy, 2018. "On single-peaked domains and min–max rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 753-772, December.
    14. Ireland, Norman J., 1990. "The mix of social and private provision of goods and services," Journal of Public Economics, Elsevier, vol. 43(2), pages 201-219, November.
    15. Shurojit Chatterji & Huaxia Zeng, 2015. "On Random Social Choice Functions with the Tops-only Property," Working Papers 11-2015, Singapore Management University, School of Economics.
    16. Chatterji, Shurojit & Sanver, Remzi & Sen, Arunava, 2013. "On domains that admit well-behaved strategy-proof social choice functions," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1050-1073.
    17. Shin Sato, 2010. "Circular domains," Review of Economic Design, Springer;Society for Economic Design, vol. 14(3), pages 331-342, September.
    18. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    19. Barzel, Yoram, 1973. "Private Schools and Public School Finance," Journal of Political Economy, University of Chicago Press, vol. 81(1), pages 174-186, Jan.-Feb..
    20. Hinich, Melvin J & Munger, Michael C, 1998. "Empirical Studies in Comparative Politics," Public Choice, Springer, vol. 97(3), pages 219-227, December.
    21. Niemi, Richard G., 1969. "Majority Decision-Making with Partial Unidimensionality," American Political Science Review, Cambridge University Press, vol. 63(2), pages 488-497, June.
    22. Barbera Salvador & Gul Faruk & Stacchetti Ennio, 1993. "Generalized Median Voter Schemes and Committees," Journal of Economic Theory, Elsevier, vol. 61(2), pages 262-289, December.
    23. Schummer, James & Vohra, Rakesh V., 2002. "Strategy-proof Location on a Network," Journal of Economic Theory, Elsevier, vol. 104(2), pages 405-428, June.
    24. Thomas Romer & Howard Rosenthal, 1979. "Bureaucrats Versus Voters: On the Political Economy of Resource Allocation by Direct Democracy," The Quarterly Journal of Economics, Oxford University Press, vol. 93(4), pages 563-587.
    25. Davis, Otto A. & Hinich, Melvin J. & Ordeshook, Peter C., 1970. "An Expository Development of a Mathematical Model of the Electoral Process," American Political Science Review, Cambridge University Press, vol. 64(2), pages 426-448, June.
    26. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    27. Raquel Fernandez & Richard Rogerson, 1995. "On the Political Economy of Education Subsidies," Review of Economic Studies, Oxford University Press, vol. 62(2), pages 249-262.
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    Cited by:

    1. Shurojit Chatterji & Huaxia Zeng, 2022. "A Taxonomy of Non-dictatorial Unidimensional Domains," Papers 2201.00496, arXiv.org, revised Oct 2022.
    2. Chatterji, Shurojit & Roy, Souvik & Sadhukhan, Soumyarup & Sen, Arunava & Zeng, Huaxia, 2022. "Probabilistic fixed ballot rules and hybrid domains," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    3. Shurojit Chatterji & Souvik Roy & Soumyarup Sadhukhan & Arunava Sen & Huaxia Zeng, 2021. "Probabilistic Fixed Ballot Rules and Hybrid Domains," Papers 2105.10677, arXiv.org, revised Jan 2022.
    4. Karmokar, Madhuparna & Roy, Souvik & Storcken, Ton, 2019. "A characterization of possibility domains under Pareto optimality and group strategy-proofness," Economics Letters, Elsevier, vol. 183(C), pages 1-1.

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    More about this item

    Keywords

    Partially single-peaked domain; strategy-proofness; group strategy-proofness; partly dictatorial min-max rules;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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