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Arrow on domain conditions: a fruitful road to travel

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  • Salvador Barberà
  • Dolors Berga
  • Bernardo Moreno

Abstract

We stress the importance that Arrow attached to studying the role of domain conditions in determining the validity of his impossibility theorem, a subject to which he devoted two chapters of Social Choice and Individual Values. Then we partially survey recent results about the role of domain conditions on the possibility to design satisfactory aggregation rules and social choice functions, as a proof of the continued vitality of this subject, that he pioneered, as he did with so many others.

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  • Salvador Barberà & Dolors Berga & Bernardo Moreno, 2019. "Arrow on domain conditions: a fruitful road to travel," Working Papers 1095, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:1095
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    1. Massó, Jordi & Moreno de Barreda, Inés, 2011. "On strategy-proofness and symmetric single-peakedness," Games and Economic Behavior, Elsevier, vol. 72(2), pages 467-484, June.
    2. Wulf Gaertner, 2005. "De jure naturae et gentium: Samuel von Pufendorf's contribution to social choice theory and economics," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 231-241, December.
    3. Alvin E. Roth, 2009. "What Have We Learned from Market Design?," Innovation Policy and the Economy, University of Chicago Press, vol. 9(1), pages 79-112.
    4. Austen-Smith, David & Banks, Jeffrey S., 1996. "Information Aggregation, Rationality, and the Condorcet Jury Theorem," American Political Science Review, Cambridge University Press, vol. 90(1), pages 34-45, March.
    5. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 389-396, December.
    6. Gans, Joshua S. & Smart, Michael, 1996. "Majority voting with single-crossing preferences," Journal of Public Economics, Elsevier, vol. 59(2), pages 219-237, February.
    7. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2012. "Two necessary conditions for strategy-proofness: On what domains are they also sufficient?," Games and Economic Behavior, Elsevier, vol. 75(2), pages 490-509.
    8. Barbera, S. & Masso, J. & Serizawa, S., 1998. "Strategy-Proof Voting on Compact Ranges," Games and Economic Behavior, Elsevier, vol. 25(2), pages 272-291, November.
    9. Alejandro Saporiti & Fernando Tohmé, 2006. "Single-Crossing, Strategic Voting and the Median Choice Rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 363-383, April.
    10. Barberà, Salvador & Moreno, Bernardo, 2011. "Top monotonicity: A common root for single peakedness, single crossing and the median voter result," Games and Economic Behavior, Elsevier, vol. 73(2), pages 345-359.
    11. Graciela Chichilnisky, 1982. "Social Aggregation Rules and Continuity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 97(2), pages 337-352.
    12. 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.
    13. Michel Breton & Vera Zaporozhets, 2009. "On the equivalence of coalitional and individual strategy-proofness properties," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 287-309, August.
    14. 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.
    15. Peter C. Fishburn, 2002. "Acyclic sets of linear orders: A progress report," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(2), pages 431-447.
    16. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
    17. Nehring, Klaus & Puppe, Clemens, 2007. "The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces," Journal of Economic Theory, Elsevier, vol. 135(1), pages 269-305, July.
    18. Bordes, Georges & Campbell, Donald E & Le Breton, Michel, 1995. "Arrow's Theorem for Economic Domains and Edgeworth Hyperboxes," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 36(2), pages 441-454, May.
    19. 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.
    20. David Austen-Smith & Timothy Feddersen, 2005. "Deliberation and Voting Rules," Studies in Choice and Welfare, in: David Austen-Smith & John Duggan (ed.), Social Choice and Strategic Decisions, pages 269-316, Springer.
    21. Norman Schofield, 1978. "Instability of Simple Dynamic Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 45(3), pages 575-594.
    22. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2016. "Group Strategy-Proofness in Private Good Economies," American Economic Review, American Economic Association, vol. 106(4), pages 1073-1099, April.
    23. Gaertner,Wulf, 2006. "Domain Conditions in Social Choice Theory," Cambridge Books, Cambridge University Press, number 9780521028745, October.
    24. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2022. "Restricted environments and incentive compatibility in interdependent values models," Games and Economic Behavior, Elsevier, vol. 131(C), pages 1-28.
    25. Schmitz, Norbert, 1977. "A further note on arrow's impossibility theorem," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 189-196, August.
    26. Bordes, Georges & Breton, Michel Le, 1989. "Arrovian theorems with private alternatives domains and selfish individuals," Journal of Economic Theory, Elsevier, vol. 47(2), pages 257-281, April.
    27. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
    28. Chichilnisky, Graciela & Heal, Geoffrey, 1983. "Necessary and sufficient conditions for a resolution of the social choice paradox," Journal of Economic Theory, Elsevier, vol. 31(1), pages 68-87, October.
    29. Myerson, Roger B, 1979. "Incentive Compatibility and the Bargaining Problem," Econometrica, Econometric Society, vol. 47(1), pages 61-73, January.
    30. Redekop, James, 1991. "Social welfare functions on restricted economic domains," Journal of Economic Theory, Elsevier, vol. 53(2), pages 396-427, April.
    31. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    32. Partha Dasgupta & Peter Hammond & Eric Maskin, 1979. "The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(2), pages 185-216.
    33. Chichilnisky, Graciela, 1980. "Social choice and the topology of spaces of preferences," MPRA Paper 8006, University Library of Munich, Germany.
    34. Shurojit Chatterji & Jordi Massó, 2018. "On Strategy†Proofness And The Salience Of Single†Peakedness," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(1), pages 163-189, February.
    35. Border, Kim C., 1983. "Social welfare functions for economic environments with and without the pareto principle," Journal of Economic Theory, Elsevier, vol. 29(2), pages 205-216, April.
    36. 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.
    37. John List & Matti Liski, 2005. "Introduction," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 31(2), pages 121-121, June.
    38. 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.
    39. Ehlers, Lars & Storcken, Ton, 2008. "Arrow's Possibility Theorem for one-dimensional single-peaked preferences," Games and Economic Behavior, Elsevier, vol. 64(2), pages 533-547, November.
    40. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2002. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 1, number 1.
    41. Berga, Dolors, 1998. "Strategy-proofness and single-plateaued preferences," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 105-120, March.
    42. Austen-Smith, David & Feddersen, Timothy J., 2006. "Deliberation, Preference Uncertainty, and Voting Rules," American Political Science Review, Cambridge University Press, vol. 100(2), pages 209-217, May.
    43. Ehud Kalai & Eitan Muller & Mark Satterthwaite, 1979. "Social welfare functions when preferences are convex, strictly monotonic, and continuous," Public Choice, Springer, vol. 34(1), pages 87-97, March.
    44. Harris Milton & Townsend, Robert M, 1981. "Resource Allocation under Asymmetric Information," Econometrica, Econometric Society, vol. 49(1), pages 33-64, January.
    45. McKelvey, Richard D., 1976. "Intransitivities in multidimensional voting models and some implications for agenda control," Journal of Economic Theory, Elsevier, vol. 12(3), pages 472-482, June.
    46. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    47. Davis, Otto A & DeGroot, Morris H & Hinich, Melvin J, 1972. "Social Preference Orderings and Majority Rule," Econometrica, Econometric Society, vol. 40(1), pages 147-157, January.
    48. Herrade Igersheim, 2019. "The death of welfare economics : history of a controversy," Post-Print hal-03095907, HAL.
    49. Muller, Eitan, 1982. "Graphs and Anonymous Social Welfare Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(3), pages 609-622, October.
    50. Elizabeth Maggie Penn & John W. Patty & Sean Gailmard, 2011. "Manipulation and Single‐Peakedness: A General Result," American Journal of Political Science, John Wiley & Sons, vol. 55(2), pages 436-449, April.
    51. Miguel Ballester & Guillaume Haeringer, 2011. "A characterization of the single-peaked domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(2), pages 305-322, February.
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    3. Rajsbaum, Sergio & Raventós-Pujol, Armajac, 2022. "A Combinatorial Topology Approach to Arrow's Impossibility Theorem," MPRA Paper 112004, University Library of Munich, Germany.

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