IDEAS home Printed from https://ideas.repec.org/p/nav/ecupna/0610.html
   My bibliography  Save this paper

Ranking Sets Additively in Decisional Contexts: An Axiomatic Characterization

Author

Listed:

Abstract

Ranking finite subsets of a given set X of elements is the formal object of analysis in this paper. This problem has found a wide range of economic interpretations in the literature. The focus of the paper is on the family of rankings that are additively representable. Existing characterizations are too complex and hard to grasp in decisional contexts. Furthermore, Fishburn [13] showed that the number of sufficient and necessary conditions that are needed to characterize such a family has no upper bound as the cardinality of X increases. In turn, this paper proposes a way to overcome these difficulties and allows for the characterization of a meaningful (sub)family of additively representable rankings of sets by means of a few simple axioms. Pattanaik and Xu's [21] characterization of the cardinalitybased rule will be derived from our main result, and other new rules that stem from our general proposal are discussed and characterized in even simpler terms. In particular, we analyze restricted-cardinality based rules, where the set of "focal" elements is not given ex-ante; but brought out by the axioms.

Suggested Citation

  • Ritxar Arlegi & José C. R. Alcantud, 2006. "Ranking Sets Additively in Decisional Contexts: An Axiomatic Characterization," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 0610, Departamento de Economía - Universidad Pública de Navarra.
    • Handle: RePEc:nav:ecupna:0610
    as

    Download full text from publisher

    File URL: http://www2.unavarra.es/gesadj/depEconomia/repec/DocumentosTrab/DT0610.PDF
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    3. Chateauneuf, Alain, 1985. "On the existence of a probability measure compatible with a total preorder on a Boolean algebra," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 43-52, February.
    4. Walter Bossert & Arkadii Slinko, 2006. "Relative uncertainty aversion and additively representable set rankings," International Journal of Economic Theory, The International Society for Economic Theory, vol. 2(2), pages 105-122, June.
    5. Antonio Romero-Medina, 2001. "More on preference and freedom," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 179-191.
    6. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    7. Ritxar Arlegi, 2003. "A note on Bossert, Pattanaik and Xu's “Choice under complete uncertainty: axiomatic characterization of some decision rules”," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(1), pages 219-225, August.
    8. Herbert A. Simon, 1955. "A Behavioral Model of Rational Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 69(1), pages 99-118.
    9. Prasanta Pattanaik & Yongsheng Xu, 1998. "On Preference and Freedom," Theory and Decision, Springer, vol. 44(2), pages 173-198, April.
    10. Puppe, Clemens, 1996. "An Axiomatic Approach to "Preference for Freedom of Choice"," Journal of Economic Theory, Elsevier, vol. 68(1), pages 174-199, January.
    11. Arlegi, Ricardo, 2007. "Sequentially consistent rules of choice under complete uncertainty," Journal of Economic Theory, Elsevier, vol. 135(1), pages 131-143, July.
    12. 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.
    13. 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.
    14. 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).
    15. Patrick Suppes, 1987. "Maximizing Freedom of Decision: an Axiomatic Analysis," Palgrave Macmillan Books, in: George R. Feiwel (ed.), Arrow and the Foundations of the Theory of Economic Policy, chapter 6, pages 243-254, Palgrave Macmillan.
    16. Jones, Peter & Sugden, Robert, 1982. "Evaluating choice," International Review of Law and Economics, Elsevier, vol. 2(1), pages 47-65, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Andreas Darmann & Christian Klamler, 2019. "Using the Borda rule for ranking sets of objects," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(3), pages 399-414, October.

    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. Barbera, S. & Bossert, W. & Pattanaik, P.K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. José Alcantud & Ritxar Arlegi, 2012. "An axiomatic analysis of ranking sets under simple categorization," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 227-245, March.
    3. Vito Peragine & Antonio Romero-Medina, 2006. "On Preference, Freedom and Diversity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(1), pages 29-40, August.
    4. Arlegi, Ritxar & Dimitrov, Dinko, 2016. "Power set extensions of dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 20-29.
    5. Arlegi, R. & Dimitrov, D.A., 2004. "On Procedural Freedom of Choice," Discussion Paper 2004-9, Tilburg University, Center for Economic Research.
    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. Ernesto Screpanti, 2006. "Taxation, Social Goods And The Distribution Of Freedom," Metroeconomica, Wiley Blackwell, vol. 57(1), pages 1-12, February.
    8. 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.
    9. Arlegi, Ritxar & Dimitrov, Dinko, 2011. "On freedom, lack of information and the preference for easy choices," Center for Mathematical Economics Working Papers 364, Center for Mathematical Economics, Bielefeld University.
    10. Prasanta Pattanaik & Yongsheng Xu, 1998. "On Preference and Freedom," Theory and Decision, Springer, vol. 44(2), pages 173-198, April.
    11. Ricardo Arlegi & Dinko Dimitrov, 2006. "On Freedom of Choice, Ambiguity, and the Preference for Easy Choices," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 0607, Departamento de Economía - Universidad Pública de Navarra.
    12. Gekker, Ruvin, 2001. "On the axiomatic approach to freedom as opportunity: a general characterization result," Mathematical Social Sciences, Elsevier, vol. 42(2), pages 169-177, September.
    13. Baharad, Eyal & Nitzan, Shmuel, 2003. "Essential alternatives and set-dependent preferences--an axiomatic approach," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 121-129, April.
    14. Martin Hees, 2010. "The specific value of freedom," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 687-703, October.
    15. Ballester, Miguel A. & De Miguel, Juan R., 2006. "On freedom of choice and infinite sets: The Suprafinite Rule," Journal of Mathematical Economics, Elsevier, vol. 42(3), pages 291-300, June.
    16. Sebastiano Bavetta & Marco Del Seta, 2001. "Constraints and the Measurement of Freedom of Choice," Theory and Decision, Springer, vol. 50(3), pages 213-238, May.
    17. Gaetano Gaballo & Ernesto Savaglio, 2012. "On revealed diversity," Working Papers 254, ECINEQ, Society for the Study of Economic Inequality.
    18. Xu, Yongsheng, 2003. "On ranking compact and comprehensive opportunity sets," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 109-119, April.
    19. 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.
    20. Walter Bossert, 1998. "Opportunity Sets and the Measurement of Information," Discussion Papers 98/6, University of Nottingham, School of Economics.

    More about this item

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • 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:nav:ecupna:0610. 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: Javier Puértolas (email available below). General contact details of provider: https://www.unavarra.es/departamento-economia .

    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.