Compromises Between Cardinality and Ordinality in Preference Theory and Social Choice
By 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.
|Date of creation:||Aug 2001|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
More information through EDIRC
|Order Information:|| Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA|
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.:
- 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.
- 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.
- Debreu, Gerard, 1976. "Least concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 121-129, July.
- 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.
- 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 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.
- Sen, Amartya, 1970. "Interpersonal Aggregation and Partial Comparability," Econometrica, Econometric Society, vol. 38(3), pages 393-409, May.
- 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. "Interpersonal Comparability and Social Choice Theory," Review of Economic Studies, Wiley Blackwell, vol. 47(2), pages 421-39, January.
- 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.
- repec:cup:cbooks:9780521424585 is not listed on IDEAS
When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:1322. 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: (Glena Ames)
If references are entirely missing, you can add them using this form.