IDEAS home Printed from https://ideas.repec.org/p/mtl/montde/2001-02.html
   My bibliography  Save this paper

Ranking Sets of Objects

Author

Listed:
  • BARBERA, Salvador
  • BOSSERT, Walter
  • PATTANAIK, Prasanta K.

Abstract

We provide a survey of the literature on ranking sets of objects. The interpretations of those set rankings include those employed in the theory of choice under complete uncertainty, rankings of opportunity sets, set rankings that appear in matching theory, and the structure of assembly preferences. The survey is prepared for the Handbook of Utility Theory, vol. 2, edited by Salvador Barberà, Peter Hammond, and Christian Seidl, to be published by Kluwer Academic Publishers. The chapter number is provisional.

Suggested Citation

  • BARBERA, Salvador & BOSSERT, Walter & PATTANAIK, Prasanta K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Universite de Montreal, Departement de sciences economiques.
  • Handle: RePEc:mtl:montde:2001-02
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/1866/343
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Lin Zhou & Stephen Ching, 2002. "Multi-valued strategy-proof social choice rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 569-580.
    2. Cohen, Michele & Jaffray, Jean-Yves, 1980. "Rational Behavior under Complete Ignorance," Econometrica, Econometric Society, vol. 48(5), pages 1281-1299, July.
    3. Barbera, S. & Barrett, C. R. & Pattanaik, Prasanta K., 1984. "On some axioms for ranking sets of alternatives," Journal of Economic Theory, Elsevier, vol. 33(2), pages 301-308, August.
    4. Fishburn, Peter C., 1984. "Comment on the Kannai-Peleg impossibility theorem for extending orders," Journal of Economic Theory, Elsevier, vol. 32(1), pages 176-179, February.
    5. Efe A. Ok & Laurence Kranich, 1998. "The measurement of opportunity inequality: a cardinality-based approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(2), pages 263-287.
    6. Pattanaik, Prasanta K. & Xu, Yongsheng, 2000. "On diversity and freedom of choice," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 123-130, September.
    7. Kelly, Jerry S, 1977. "Strategy-Proofness and Social Choice Functions without Singlevaluedness," Econometrica, Econometric Society, vol. 45(2), pages 439-446, March.
    8. Bandyopadhyay, Taradas, 1988. "Extension of an order on a set to the power set: some further observations," Mathematical Social Sciences, Elsevier, vol. 15(1), pages 81-85, February.
    9. Walter Bossert, 1996. "Opportunity sets and individual well-being," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(1), pages 97-112.
    10. Dekel, Eddie & Lipman, Barton L. & Rustichini, Aldo, 1998. "Recent developments in modeling unforeseen contingencies," European Economic Review, Elsevier, vol. 42(3-5), pages 523-542, May.
    11. Kranich, Laurence, 1996. "Equitable Opportunities: An Axiomatic Approach," Journal of Economic Theory, Elsevier, vol. 71(1), pages 131-147, October.
    12. Barbera, Salvador & Dutta, Bhaskar & Sen, Arunava, 2005. "Corrigendum to "Strategy-proof social choice correspondences" [J. Econ. Theory 101 (2001) 374-394]," Journal of Economic Theory, Elsevier, vol. 120(2), pages 275-275, February.
    13. Roemer, J.E., 1992. "A Pragmatic Theory of Responsibility for the Egalitarian Planner," Papers 391, California Davis - Institute of Governmental Affairs.
    14. Martin van Hees, 1998. "On the Analysis of Negative Freedom," Theory and Decision, Springer, vol. 45(2), pages 175-197, October.
    15. Herrero, Carmen, 1997. "Equitable opportunities: an extension," Economics Letters, Elsevier, vol. 55(1), pages 91-95, August.
    16. Nicolas Gravel, 1998. "Ranking opportunity sets on the basis of their freedom of choice and their ability to satisfy preferences: A difficulty," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(3), pages 371-382.
    17. Klaus Nehring & Clemens Puppe, 1999. "On the multi-preference approach to evaluating opportunities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(1), pages 41-63.
    18. Barbera, Salvador, 1977. "The Manipulation of Social Choice Mechanisms That Do Not Leave "Too Much" to Chance," Econometrica, Econometric Society, vol. 45(7), pages 1573-1588, October.
    19. Pattanaik, Prasanta K. & Xu, Yongsheng, 2000. "On Ranking Opportunity Sets in Economic Environments," Journal of Economic Theory, Elsevier, vol. 93(1), pages 48-71, July.
    20. Vitorocco Peragine, 1999. "The Distribution and Redistribution of Opportunity," Journal of Economic Surveys, Wiley Blackwell, vol. 13(1), pages 37-70, February.
    21. 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.
    22. Dirk Van de gaer & Marc Fleurbaey & Walter Bossert, 1999. "Responsibility, talent, and compensation: A second-best analysis," Review of Economic Design, Springer;Society for Economic Design, vol. 4(1), pages 35-55.
    23. N. Gravel & J.-F. Laslier & A. Trannoy, 1996. "Individual freedom of choice in a social setting," THEMA Working Papers 96-25, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    24. Goldman, Steven Marc, 1974. "Flexibility and the demand for money," Journal of Economic Theory, Elsevier, vol. 9(2), pages 203-222, October.
    25. Klaus Nehring, 1999. "Preference for Flexibility in a Savage Framework," Econometrica, Econometric Society, vol. 67(1), pages 101-120, January.
    26. Klaus NEHRING & Clemens PUPPE, 1995. "A Qualitative Theory of "Preference for Opportunities and Diversity"," Vienna Economics Papers vie9504, University of Vienna, Department of Economics.
    27. Partha Dasgupta & Douglas Gale & Oliver Hart & Eric Maskin (ed.), 1992. "Economic Analysis of Markets and Games: Essays in Honor of Frank Hahn," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262541599, December.
    28. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.
    29. Bossert, W., 1993. "Preference Extention Rules for Ranking Sets of Alternatives with a Fixed Cardinalty," Working Papers 9308, University of Waterloo, Department of Economics.
    30. Fishburn, Peter C., 1992. "Signed orders and power set extensions," Journal of Economic Theory, Elsevier, vol. 56(1), pages 1-19, February.
    31. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541, Elsevier.
    32. Gardenfors, Peter, 1976. "Manipulation of social choice functions," Journal of Economic Theory, Elsevier, vol. 13(2), pages 217-228, October.
    33. Robert Jones & Joseph Ostroy, 1976. "Liquidity as Flexibility," UCLA Economics Working Papers 073, UCLA Department of Economics.
    34. Dutta, Bhaskar & Masso, Jordi, 1997. "Stability of Matchings When Individuals Have Preferences over Colleagues," Journal of Economic Theory, Elsevier, vol. 75(2), pages 464-475, August.
    35. Herrero, Carmen & Iturbe-Ormaetxe, Inigo & Nieto, Jorge, 1998. "Ranking opportunity profiles on the basis of the common opportunities," Mathematical Social Sciences, Elsevier, vol. 35(3), pages 273-289, May.
    36. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    37. Dekel, Eddie & Lipman, Barton L & Rustichini, Aldo, 2001. "Representing Preferences with a Unique Subjective State Space," Econometrica, Econometric Society, vol. 69(4), pages 891-934, July.
    38. Pattanaik, Prasanta K., 1994. "Rights and freedom in welfare economics," European Economic Review, Elsevier, vol. 38(3-4), pages 731-738, April.
    39. Patrick Suppes, 1996. "The nature and measurement of freedom," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(2), pages 183-200, April.
    40. Tjalling C. Koopmans, 1962. "On Flexibility of Future Preference," Cowles Foundation Discussion Papers 150, Cowles Foundation for Research in Economics, Yale University.
    41. Bossert, Walter, 1989. "On the extension of preferences over a set to the power set: An axiomatic characterization of a quasi-ordering," Journal of Economic Theory, Elsevier, vol. 49(1), pages 84-92, October.
    42. Heiner, Ronald A. & Packard, Dennis J., 1984. "A uniqueness result for extending orders; with application to collective choice as inconsistency resolution," Journal of Economic Theory, Elsevier, vol. 32(1), pages 180-184, February.
    43. John Duggan & Thomas Schwartz, 2000. "Strategic manipulability without resoluteness or shared beliefs: Gibbard-Satterthwaite generalized," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(1), pages 85-93.
    44. Prasanta Pattanaik & Yongsheng Xu, 1998. "On Preference and Freedom," Theory and Decision, Springer, vol. 44(2), pages 173-198, April.
    45. Bossert, Walter, 2000. "Opportunity sets and uncertain consequences1," Journal of Mathematical Economics, Elsevier, vol. 33(4), pages 475-496, May.
    46. Jean-Pierre BenoÏt & Lewis A. Kornhauser, 1999. "On the separability of assembly preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(3), pages 429-439.
    47. Elisabeth Naeve-Steinweg & Jörg Naeve, 2002. "Lexicographic measurement of the information contained in opportunity sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(1), pages 155-173.
    48. Puppe, Clemens, 1996. "An Axiomatic Approach to "Preference for Freedom of Choice"," Journal of Economic Theory, Elsevier, vol. 68(1), pages 174-199, January.
    49. Goldman, Steven M., 1978. "Portfolio choice and flexibility : The precautionary motive," Journal of Monetary Economics, Elsevier, vol. 4(2), pages 263-279, April.
    50. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-577, May.
    51. Bossert Walter & Pattanaik Prasanta K. & Xu Yongsheng, 1994. "Ranking Opportunity Sets: An Axiomatic Approach," Journal of Economic Theory, Elsevier, vol. 63(2), pages 326-345, August.
    52. Prasanta K. Pattanaik & Yongsheng Xu & Walter Bossert, 2000. "Choice under complete uncertainty: axiomatic characterizations of some decision rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(2), pages 295-312.
    53. Nehring, Klaus & Puppe, Clemens, 1996. "Continuous Extensions of an Order on a Set to the Power Set," Journal of Economic Theory, Elsevier, vol. 68(2), pages 456-479, February.
    54. Peter C. Fishburn, 1967. "Methods of Estimating Additive Utilities," Management Science, INFORMS, vol. 13(7), pages 435-453, March.
    55. Fishburn, Peter C. & Roberts, Fred S., 1988. "Unique finite conjoint measurement," Mathematical Social Sciences, Elsevier, vol. 16(2), pages 107-143, October.
    56. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    57. Prasanta K. PATTANAIK & Yongsheng XU, 1990. "On Ranking Opportunity Sets in Terms of Freedom of Choice," Discussion Papers (REL - Recherches Economiques de Louvain) 1990036, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    58. Ok, Efe A., 1997. "On Opportunity Inequality Measurement," Journal of Economic Theory, Elsevier, vol. 77(2), pages 300-329, December.
    59. Bossert, Walter, 1997. "Uncertainty aversion in nonprobabilistic decision models," Mathematical Social Sciences, Elsevier, vol. 34(3), pages 191-203, October.
    60. Sen, Amartya, 1993. "Internal Consistency of Choice," Econometrica, Econometric Society, vol. 61(3), pages 495-521, May.
    61. Truman F. Bewley, 1986. "Knightian Decision Theory: Part 1," Cowles Foundation Discussion Papers 807, Cowles Foundation for Research in Economics, Yale University.
    62. Peragine, Vitorocco, 1999. "The Distribution and Redistribution of Opportunity," Journal of Economic Surveys, Wiley Blackwell, vol. 13(1), pages 37-69, February.
    63. Sen, Amartya K, 1977. "On Weights and Measures: Informational Constraints in Social Welfare Analysis," Econometrica, Econometric Society, vol. 45(7), pages 1539-1572, October.
    64. Dutta, Bhaskar & Sen, Arunava, 1996. "Ranking Opportunity Sets and Arrow Impossibility Theorems: Correspondence Results," Journal of Economic Theory, Elsevier, vol. 71(1), pages 90-101, October.
    65. Amartya SEN, 1990. "Welfare, Freedom and Social Choice: a Reply," Discussion Papers (REL - Recherches Economiques de Louvain) 1990040, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    66. Jones, Peter & Sugden, Robert, 1982. "Evaluating choice," International Review of Law and Economics, Elsevier, vol. 2(1), pages 47-65, June.
    67. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
    68. Barbera, Salvador & Pattanaik, Prasanta K., 1984. "Extending an order on a Set to the power set: Some remarks on Kannai and Peleg's approach," Journal of Economic Theory, Elsevier, vol. 32(1), pages 185-191, February.
    69. Sen, Amartya, 1988. "Freedom of choice : Concept and content," European Economic Review, Elsevier, vol. 32(2-3), pages 269-294, March.
    70. Nitzan, Shmuel I. & Pattanaik, Prasanta K., 1984. "Median-based extensions of an ordering over a set to the power set: An axiomatic characterization," Journal of Economic Theory, Elsevier, vol. 34(2), pages 252-261, December.
    71. Kannai, Yakar & Peleg, Bezalel, 1984. "A note on the extension of an order on a set to the power set," Journal of Economic Theory, Elsevier, vol. 32(1), pages 172-175, February.
    72. Bossert, W., 1995. "Choices, Consequences, and Rationality," Working Papers 9501, University of Waterloo, Department of Economics.
    73. Holzman, Ron, 1984. "An extension of Fishburn's theorem on extending orders," Journal of Economic Theory, Elsevier, vol. 32(1), pages 192-196, February.
    74. Sen, Amartya, 1991. "Welfare, preference and freedom," Journal of Econometrics, Elsevier, vol. 50(1-2), pages 15-29, October.
    75. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    76. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2000. "Single Agents and the Set of Many-to-One Stable Matchings," Journal of Economic Theory, Elsevier, vol. 91(1), pages 91-105, March.
    77. William Vickrey, 1960. "Utility, Strategy, and Social Decision Rules," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 74(4), pages 507-535.
    78. Laurence Kranich, 1996. "Equitable opportunities in economic environments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(1), pages 57-64.
    79. Basu, K. & Pattanaik, P. K. & Suzumura, K. (ed.), 1995. "Choice, Welfare, and Development: A Festschrift for Amartya K. Sen," OUP Catalogue, Oxford University Press, number 9780198287896.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Walter Bossert, 1998. "Opportunity Sets and the Measurement of Information," Discussion Papers 98/6, University of Nottingham, School of Economics.
    2. Bossert, Walter, 2000. "Opportunity sets and uncertain consequences1," Journal of Mathematical Economics, Elsevier, vol. 33(4), pages 475-496, May.
    3. Bossert, Walter, 1997. "Uncertainty aversion in nonprobabilistic decision models," Mathematical Social Sciences, Elsevier, vol. 34(3), pages 191-203, October.
    4. Ritxar Arlegi, 2001. "Rational Evaluation of Actions Under Complete Uncertainty," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 0114, Departamento de Economía - Universidad Pública de Navarra.
    5. Ricardo Arlegi, 2005. "Freedom Of Choice And Conflict Resolution," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 0502, Departamento de Economía - Universidad Pública de Navarra.
    6. Antoinette Baujard, 2006. "Conceptions of freedom and ranking opportunity sets. A typology," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 200611, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    7. Walter Bossert & Kotaro Suzumura, 2011. "Rationality, external norms, and the epistemic value of menus," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(4), pages 729-741, October.
    8. Arlegi, R. & Dimitrov, D.A., 2004. "On Procedural Freedom of Choice," Discussion Paper 2004-9, Tilburg University, Center for Economic Research.
    9. Vito Peragine & Ernesto Savaglio & Stefano Vannucci, 2008. "Poverty Rankings of Opportunity Profiles," Department of Economics University of Siena 548, Department of Economics, University of Siena.
    10. Gekker, Ruvin & van Hees, Martin, 2006. "Freedom, opportunity and uncertainty: A logical approach," Journal of Economic Theory, Elsevier, vol. 130(1), pages 246-263, September.
    11. James E. Foster, 2010. "Freedom, Opportunity and Wellbeing," Working Papers 2010-15, The George Washington University, Institute for International Economic Policy.
    12. BOSSERT, Walter & SLINKO, Arkadii, 2004. "Relative Uncertainty and Additively Representable Set Rankings," Cahiers de recherche 2004-13, Universite de Montreal, Departement de sciences economiques.
    13. Arlegi, Ritxar & Dimitrov, Dinko, 2016. "Power set extensions of dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 20-29.
    14. John Weymark, 2003. "Generalized Gini Indices of Equality of Opportunity," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(1), pages 5-24, April.
    15. Stefano Vannucci, 2013. "A characterization of height-based extensions of principal filtral opportunity rankings," Revista Cuadernos de Economia, Universidad Nacional de Colombia, FCE, CID, December.
    16. Sebastian Bervoets, 2007. "Freedom of choice in a social context: comparing game forms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(2), pages 295-315, September.
    17. Bervoets, Sebastian & Gravel, Nicolas, 2007. "Appraising diversity with an ordinal notion of similarity: An axiomatic approach," Mathematical Social Sciences, Elsevier, vol. 53(3), pages 259-273, May.
    18. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 21, pages 393-506, Elsevier.
    19. Bora Erdamar & M. Sanver, 2009. "Choosers as extension axioms," Theory and Decision, Springer, vol. 67(4), pages 375-384, October.
    20. Ballester, Miguel A. & de Miguel, Juan R. & Nieto, Jorge, 2004. "Set comparisons in a general domain: the Indirect Utility Criterion," Mathematical Social Sciences, Elsevier, vol. 48(2), pages 139-150, September.

    More about this item

    Keywords

    choice under comete uncertainty; oortunity sets; matching; assembly eferences;
    All these keywords.

    JEL classification:

    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mtl:montde:2001-02. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sharon BREWER (email available below). General contact details of provider: https://edirc.repec.org/data/demtlca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.