Compromises Between Cardinality and Ordinality in Preference Theory and Social Choice
AbstractBy taking sets of utility functions as a primitive description of agents, we define an ordering over assumptions on utility functions that gauges their implicit measurement requirements. Cardinal and ordinal assumptions constitute two types of measurement requirements, but several standard assumptions in economics lie between these extremes. We first apply the ordering to different theories for why consumer preferences should be convex and show that diminishing marginal utility, which for complete preferences implies convexity, is an example of a compromise between cardinality and ordinality. In contrast, the Arrow-Koopmans theory of convexity, although proposed as an ordinal theory, relies on utility functions that lie in the cardinal measurement class. In a second application, we show that diminishing marginal utility, rather than the standard stronger assumption of cardinality, also justifies utilitarian recommendations on redistribution and axiomatizes the Pigou-Dalton principle. We also show that transitivity and order-density (but not completeness) characterize the ordinal preferences that can be induced from sets of utility functions, present a general cardinality theorem for additively separable preferences, and provide sufficient conditions for orderings of assumptions on utility functions to be acyclic and transitive.
Download InfoIf 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.
Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1322.
Length: 39 pages
Date of creation: Aug 2001
Date of revision:
Contact details of provider:
Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
More information through EDIRC
Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
Find related papers by JEL classification:
- D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
- D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
This paper has been announced in the following NEP Reports:
- NEP-ALL-2001-11-27 (All new papers)
- NEP-ENT-2001-11-27 (Entrepreneurship)
- NEP-NET-2001-11-27 (Network Economics)
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.:
- Juan Dubra & Fabio Maccheroni & Efe Oki, 2001.
"Expected utility theory without the completeness axiom,"
ICER Working Papers - Applied Mathematics Series
11-2001, ICER - International Centre for Economic Research.
- Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
- Juan Dubra & Fabio Maacheroni & Efe A. Ok, 2001. "Expected Utility Theory without the Completeness Axiom," Cowles Foundation Discussion Papers 1294, Cowles Foundation for Research in Economics, Yale University.
- Hammond, Peter J, 1976. "Equity, Arrow's Conditions, and Rawls' Difference Principle," Econometrica, Econometric Society, vol. 44(4), pages 793-804, July.
- Roberts, Kevin W S, 1980. "Possibility Theorems with Interpersonally Comparable Welfare Levels," Review of Economic Studies, Wiley Blackwell, vol. 47(2), pages 409-20, January.
- Sen, Amartya, 1970. "Interpersonal Aggregation and Partial Comparability," Econometrica, Econometric Society, vol. 38(3), pages 393-409, May.
- Roberts, Kevin W S, 1980. "Interpersonal Comparability and Social Choice Theory," Review of Economic Studies, Wiley Blackwell, vol. 47(2), pages 421-39, January.
- Basu, Kaushik, 1982. "Determinateness of the Utility Function: Revisiting a Controversy of the Thirties," Review of Economic Studies, Wiley Blackwell, vol. 49(2), pages 307-11, April.
- Hanoch, G & Levy, Haim, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Wiley Blackwell, vol. 36(107), pages 335-46, July.
- Debreu, Gerard, 1976. "Least concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 121-129, July.
- Moulin,Hervi, 1991. "Axioms of Cooperative Decision Making," Cambridge Books, Cambridge University Press, number 9780521424585, December.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Glena Ames).
If references are entirely missing, you can add them using this form.