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Cardinality versus Ordinality: A Suggested Compromise

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  • Michael Mandler

Abstract

By taking sets of utility functions as primitive, we define an ordering over assumptions on utility functions that gauges their measurement requirements. Cardinal and ordinal assumptions constitute two levels of measurability, but other assumptions lie between these extremes. We apply the ordering to explanations of why preferences should be convex. The assumption that utility is concave qualifies as a compromise between cardinality and ordinality, while the Arrow-Koopmans explanation, supposedly an ordinal theory, relies on utilities in the cardinal measurement class. In social choice theory, a concavity compromise between ordinality and cardinality is also possible and rationalizes the core utilitarian policies. (JEL D01)

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File URL: http://www.aeaweb.org/articles.php?doi=10.1257/aer.96.4.1114
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Bibliographic Info

Article provided by American Economic Association in its journal American Economic Review.

Volume (Year): 96 (2006)
Issue (Month): 4 (September)
Pages: 1114-1136

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Handle: RePEc:aea:aecrev:v:96:y:2006:i:4:p:1114-1136

Note: DOI: 10.1257/aer.96.4.1114
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Cited by:
  1. Pivato, Marcus, 2013. "Multiutility representations for incomplete difference preorders," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 196-220.
  2. Pivato, Marcus, 2010. "Approximate interpersonal comparisons of well-being," MPRA Paper 25224, University Library of Munich, Germany.
  3. Giarlotta, Alfio & Greco, Salvatore, 2013. "Necessary and possible preference structures," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 163-172.
  4. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
  5. Pivato, Marcus, 2010. "Aggregation of incomplete ordinal preferences with approximate interpersonal comparisons," MPRA Paper 25271, University Library of Munich, Germany.
  6. Pivato, Marcus, 2009. "Social choice with approximate interpersonal comparisons of well-being," MPRA Paper 17060, University Library of Munich, Germany.
  7. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.

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