Appraising diversity with an ordinal notion of similarity: An axiomatic approach
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.
(This abstract was borrowed from another version of this item.)
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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
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.:
- Pattanaik, Prasanta K. & Xu, Yongsheng, 2000.
"On diversity and freedom of choice,"
Mathematical Social Sciences,
Elsevier, vol. 40(2), pages 123-130, September.
- Prasanta K. Pattanaik & Yongsheng Xu,, "undated". "On Diversity and Freedom of Choice," Discussion Papers 97/18, University of Nottingham, School of Economics.
- Sugden, Robert, 1985. "Liberty, Preference, and Choice," Economics and Philosophy, Cambridge University Press, vol. 1(02), pages 213-229, October.
- 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.
- Bossert, W., 1994. "Opportunity Sets and Individual Well-Being," Working Papers 9414, University of Waterloo, Department of Economics.
- Klaus Nehring & Clemens Puppe, 2002. "A Theory of Diversity," Econometrica, Econometric Society, vol. 70(3), pages 1155-1198, May.
- Nehring,K. und C.Puppe, 1999. "A Theory of Diversity," Discussion Paper Serie A 605, University of Bonn, Germany.
- Martin L. Weitzman, 1998. "The Noah's Ark Problem," Econometrica, Econometric Society, vol. 66(6), pages 1279-1298, November.
- Martin L. Weitzman, 1992. "On Diversity," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 363-405.
- Weitzman, M.L., 1991. "On Diversity," Harvard Institute of Economic Research Working Papers 1553, Harvard - Institute of Economic Research.
- 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.
- 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..
- 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.
- Romero-Medina, Antonio, 1998. "More on preference and freedom," UC3M Working papers. Economics 4140, Universidad Carlos III de Madrid. Departamento de Economía.
- 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.
- Martin L. Weitzman, 1993. "What to Preserve? An Application of Diversity Theory to Crane Conservation," The Quarterly Journal of Economics, Oxford University Press, vol. 108(1), pages 157-183.
- 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.
- Sebastian Bervoets & Nicolas Gravel, 2003. "Appraising diversity with an ordinal notion of similarity: an Axiomatic approach," IDEP Working Papers 0308, Institut d'economie publique (IDEP), Marseille, France.
- Nicolas Gravel & Sebastian Bervoets, 2004. "Appraising Diversity with an Ordinal Notion of Similarity: An Axiomatic Approach," Working Papers 2004.45, Fondazione Eni Enrico Mattei.
- Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-577, May.
- 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.
- BARBERA, Salvador & BOSSERT, Walter & PATTANAIK, Prasanta K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Universite de Montreal, Departement de sciences economiques.
- Nehring, Klaus & Puppe, Clemens, 2003. "Diversity and dissimilarity in lines and hierarchies," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 167-183, April.
- 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.
- Jones, Peter & Sugden, Robert, 1982. "Evaluating choice," International Review of Law and Economics, Elsevier, vol. 2(1), pages 47-65, June.
- Sen, Amartya, 1988. "Freedom of choice : Concept and content," European Economic Review, Elsevier, vol. 32(2-3), pages 269-294, March.
- Weitzman, M.L., 1992. "Diversity Functions," Harvard Institute of Economic Research Working Papers 1610, Harvard - Institute of Economic Research. Full references (including those not matched with items on IDEAS)