Cardinalism pp 209-221 | Cite as

The Short Step from Ordinal to Cardinal Utility

Part of the Theory and Decision Library book series (TDLA, volume 19)


Let us start with the unrealistic but simple case of a consumer in a two-goods world or, if you prefer, a person whose freedom of choice is limited to allocating a budget between buying two goods. We choose an arbitrary starting point with quantities of the two goods, and by trial and error we find other combinations that the consumer deems equivalent. We can thus construct an approximation of one indifference curve. The process is repeated a number of times with new starting points. We attach numbers to the curves in inverse order of preference. We now have an incomplete ordinal preference function. It does not sound too complicated, but try to actually do it!


Marginal Utility Preference Function Utility Theory Indifference Curve Cardinal Utility 
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  1. Allais, Maurice (1952) ‘Fondements d’une theorie positive des choix comportrant un risque et critique des postulats et axiomes de l’Ecole Americaine’, Colloques Internationaux du Centre National de la Recherche, Vol. XL, Paris 1953.Google Scholar
  2. Allais, Maurice (1979a) ‘Foundations of a positive theory of choices involving risk and a criticism of the postulates and axioms of the American School’, see Allais, and Hagen (1979).Google Scholar
  3. Allais, Maurice (1979b) ‘The so-called Allais paradox and rational decisions under uncertainty’, see Allais and Hagen (eds.) (1979).Google Scholar
  4. Allais, Maurice (1983) ‘The foundations of the theory of utility and risk’, see Hagen and Wenstoep (eds.) (1984).Google Scholar
  5. Allais, Maurice (1985a) ‘Three theorems on the theory of cardinal utility and random choice’, Eberlein and Berghel (eds.), Reidel, 1987.Google Scholar
  6. Allais, Maurice (1986) ‘The general theory of random choices in relation to the invariant cardinal utility function and the specific probability function. The (U, 0) model’, in Munier (ed.), Risk, Decision and Rationality. Reidel, 1987.Google Scholar
  7. Allais, Maurice (1988) Scientific Papers on Risk and Utility Theory — Theory, Experience, and Applications. Forthcoming, Reidel. Ch. XVIII, Cardinal Utility — History, Empirical Findings, and Applications.Google Scholar
  8. Allais, Maurice and Hagen, Ole (eds.) (1979) Expected Utility Hypotheses and the Allais Paradox — Contemporary discussions of rational decisions under risk with Allais’ rejoinder, Reidel, Dordrecht.Google Scholar
  9. Bell, D. (1982) ‘Regret in decision making under uncertainty’, Operations Research 33, 1–27.CrossRefGoogle Scholar
  10. Broome, J. (1985) ‘A mistaken argument against the expected utility theory of rationality’, Theory and Decision 18, 313–318.CrossRefGoogle Scholar
  11. Camacho, A. (1979) ‘Maximizing expected utility and the rule of long run success’. See Allais and Hagen (1979).Google Scholar
  12. Chew, S. and MacCrimmon, K. (1979) ‘Alpha-nu choice theory: a generalization of expected utility theory’, Working Paper 669, University of British Columbia.Google Scholar
  13. Daboni et al. (eds.), Recent Developments in the Foundations of Utility and Risk Theory, Reidel, Dordrecht.Google Scholar
  14. Elster, J. (1983) Sour Grapes, Cambridge University Press.Google Scholar
  15. Fishburn, Peter C. (1987) ‘Reconsiderations in the foundations of decision uncertainty’, The Economic Journal 8(97), 825–841.CrossRefGoogle Scholar
  16. Hagen, Ole (1979) ‘Towards a positive theory of decisions under risk’, see Allais and Hagen (1979).Google Scholar
  17. Hagen, Ole (1984) ‘Relativity in decision theory’, see Hagen and Wenstoep (1984), pp. 237-249.Google Scholar
  18. Hagen, Ole (1985) ‘Rules of behavior and expected utility theory. Compatibility versus dependence’, Theory and Decision 18(1), January, 31–46.CrossRefGoogle Scholar
  19. Hagen, Ole and Wenstoep, Fred (eds.) (1984) Progress in Utility and Risk Theory, Reidel, Dordrecht.Google Scholar
  20. Hey, John D. and Lambert, Peter J. (eds.) (1987) Surveys in the Economics of Uncertainty, Basil Blackwell, Oxford.Google Scholar
  21. Loomes, G. and Sugden, R. (1985) ‘Regret theory: an alternative theory of rational choice under uncertainty’, Economic Journal 92, 805–824.CrossRefGoogle Scholar
  22. Loomes, G. and Sugden, R.,’ some implications of a more general form of regret theory’, available from authors.Google Scholar
  23. MacCrimmon, K.R. and Larsson, S. (1979) ‘Utility theory: axioms versus “paradoxes’”, see Allais and Hagen (1979).Google Scholar
  24. Machina, Mark J. (1983) ‘Generalized expected utility analysis and the nature of observed violations of the independence axiom’, see Stigum and Wenstoep (eds.) (1983).Google Scholar
  25. Schoemaker, P. (1982) ‘The expected utility model: its variants, purposes, evidence and limitations’, Journal of Economic Literature 20, 529–563.Google Scholar
  26. Sugden, Robert (1985) ‘Regret, recrimination and rationality’, Theory and Decision 19(1), July, 77–100.CrossRefGoogle Scholar
  27. Sugden, Robert, ‘New developments in the theory of choice under uncertainty’, see Hey and Lambert (1987).Google Scholar
  28. Stigum, B.P. and Wenstoep, F. (eds.) (1983) Foundations of Utility and Risk Theory with Applications, Reidel, Dordrecht.Google Scholar
  29. Ståhl, I. (1980) ‘Review of Allais and Hagen (eds.) q. v.’, Scandinavian Journal of Economics, pp. 413-417.Google Scholar
  30. Thore, S. (1983) ‘Hotelling utility functions’, in Stigum and Wenstoep (1983).Google Scholar

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© Springer Science+Business Media Dordrecht 1994

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