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.
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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
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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)
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- 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.
- 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.
- 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.
- 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.
- Moulin,Hervi, 1991. "Axioms of Cooperative Decision Making," Cambridge Books, Cambridge University Press, number 9780521424585, October.
- Debreu, Gerard, 1976. "Least concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 121-129, July.
- Hammond, Peter J, 1976. "Equity, Arrow's Conditions, and Rawls' Difference Principle," Econometrica, Econometric Society, vol. 44(4), pages 793-804, July.
- 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.
- Roberts, Kevin W S, 1980. "Interpersonal Comparability and Social Choice Theory," Review of Economic Studies, Wiley Blackwell, vol. 47(2), pages 421-39, January.
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