Advanced Search
MyIDEAS: Login

Appraising Diversity with an Ordinal Notion of Similarity: An Axiomatic Approach

Contents:

Author Info

  • Nicolas Gravel

    (IDEP-GREQAM and Université de la Méditerranée)

  • Sebastian Bervoets

    (IDEP-GREQAM and Université de la Méditerranée)

Abstract

This paper provides an axiomatic characterization of two rules for comparing alternative sets of objects on the basis of the diversity that they offer. The framework considered assumes a finite universe of objects and an a priori given ordinal quadernary relation that compares alternative pairs of objects on the basis of their ordinal dissimilarity. Very few properties of this quadernary relation are assumed (beside completeness, transitivity and a very natural form of symmetry). The two rules that we characterize are the maxi-max criterion and the lexi-max criterion. The maxi-max criterion considers that a set is more diverse than another if and only if the two objects that are the most dissimilar in the former are weakly as dissimilar as the two most dissimilar objects in the later. The lexi-max criterion is defined as usual as the lexicographic extension of the maxi-max criterion. Some connections with the broader issue of measuring freedom of choice are also provided.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.feem.it/userfiles/attach/Publication/NDL2004/NDL2004-045.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2004.45.

as in new window
Length:
Date of creation: Mar 2004
Date of revision:
Handle: RePEc:fem:femwpa:2004.45

Contact details of provider:
Postal: Corso Magenta, 63 - 20123 Milan
Phone: 0039-2-52036934
Fax: 0039-2-52036946
Email:
Web page: http://www.feem.it/
More information through EDIRC

Related research

Keywords: Diversity; Measurement; Axioms; Freedom of choice;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Gravel, N. & Laslier, J.F. & Trannoy, A., 1996. "Individual Freedom of Choice in a Social Setting," Papers 9625, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  2. Weitzman, Martin L, 1992. "On Diversity," The Quarterly Journal of Economics, MIT Press, vol. 107(2), pages 363-405, May.
  3. Sugden, Robert, 1985. "Liberty, Preference, and Choice," Economics and Philosophy, Cambridge University Press, vol. 1(02), pages 213-229, October.
  4. Pattanaik, Prasanta K. & Xu, Yongsheng, 2000. "On diversity and freedom of choice," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 123-130, September.
  5. Jones, Peter & Sugden, Robert, 1982. "Evaluating choice," International Review of Law and Economics, Elsevier, vol. 2(1), pages 47-65, June.
  6. BARBERA, Salvador & BOSSERT, Walter & PATTANAIK, Prasanta K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Universite de Montreal, Departement de sciences economiques.
  7. Weitzman, Martin L, 1993. "What to Preserve? An Application of Diversity Theory to Crane Conservation?," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 157-83, February.
  8. Nicolas Gravel & Sebastian Bervoets, 2004. "Appraising Diversity with an Ordinal Notion of Similarity: An Axiomatic Approach," Working Papers 2004.45, Fondazione Eni Enrico Mattei.
  9. Nehring,K. und C.Puppe, 1999. "A Theory of Diversity," Discussion Paper Serie A 605, University of Bonn, Germany.
  10. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-77, May.
  11. Walter Bossert, 1996. "Opportunity sets and individual well-being," Social Choice and Welfare, Springer, vol. 14(1), pages 97-112.
  12. Weitzman, M.L., 1992. "Diversity Functions," Harvard Institute of Economic Research Working Papers 1610, Harvard - Institute of Economic Research.
  13. Nehring, Klaus & Puppe, Clemens, 2003. "Diversity and dissimilarity in lines and hierarchies," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 167-183, April.
  14. 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.
  15. Martin L. Weitzman, 1998. "The Noah's Ark Problem," Econometrica, Econometric Society, vol. 66(6), pages 1279-1298, November.
  16. Antonio Romero-Medina, 2001. "More on preference and freedom," Social Choice and Welfare, Springer, vol. 18(1), pages 179-191.
  17. Sen, Amartya, 1988. "Freedom of choice : Concept and content," European Economic Review, Elsevier, vol. 32(2-3), pages 269-294, March.
  18. Patrick Suppes, 1996. "The nature and measurement of freedom," Social Choice and Welfare, Springer, vol. 13(2), pages 183-200, April.
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 in new window

Cited by:
  1. Sebastian Bervoets, 2010. "An axiomatic approach to predictability of outcomes in an interactive setting," Theory and Decision, Springer, vol. 68(3), pages 311-323, March.
  2. 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.
  3. Gaetano Gaballo & Ernesto Savaglio, 2012. "On revealed diversity," Working Papers 254, ECINEQ, Society for the Study of Economic Inequality.
  4. Nicolas Gravel & Sebastian Bervoets, 2004. "Appraising Diversity with an Ordinal Notion of Similarity: An Axiomatic Approach," Working Papers 2004.45, Fondazione Eni Enrico Mattei.
  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. Marcello Basili & Stefano Vannucci, 2013. "Diversity as width," Social Choice and Welfare, Springer, vol. 40(3), pages 913-936, March.
  7. Johan Gustafsson, 2010. "Freedom of choice and expected compromise," Social Choice and Welfare, Springer, vol. 35(1), pages 65-79, June.
  8. Martin Hees, 2010. "The specific value of freedom," Social Choice and Welfare, Springer, vol. 35(4), pages 687-703, October.
  9. Clemens Puppe & Yongsheng Xu, 2010. "Essential alternatives and freedom rankings," Social Choice and Welfare, Springer, vol. 35(4), pages 669-685, October.
  10. S. Aulong & K. Erdlenbruch & C. Figuières, 2005. "Un tour d'horizon des critères d'évaluation de la diversité biologique," Post-Print hal-00452144, HAL.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:fem:femwpa:2004.45. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (barbara racah).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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