Abstract
Behaviour norms are considered for decision trees which allow both objective probabilities and uncertain states of the world with unknown probabilities. Terminal nodes have consequences in a given domain. Behaviour is required to be consistent in subtrees. Consequentialist behaviour, by definition, reveals a consequence choice function independent of the structure of the decision tree. It implies that behaviour reveals a revealed preference ordering satisfying both the independence axiom and a novel form of sure-thing principle. Continuous consequentialist behaviour must be expected utility maximizing. Other plausible assumptions then imply additive utilities, subjective probabilities, and Bayes' rule.
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References
Allais, M.: 1953, ‘Le comportement de l'homme rationnel devant le risque: critique des postulats et des axiomes de l'école américaine’, Econometrica 21, 503–546.
Allais, M.: 1979, ‘The foundations of a positive theory of choice involving risk and a criticism of the postulates and axioms of the American school’, in The Expected Utility Hypothesis and the Allais Paradox, M. Allais and O. Hagen (eds.), 27–145. Dordrecht: D. Reidel.
Anscombe, F. J. and R. J. Aumann: 1963, ‘A definition of subjective probability’, Annals of Mathematical Statistics 34, 199–205.
Anscombe, G. E. M.: 1958, ‘Modern moral philosophy’, Philosophy 33, 1–19.
Blume, L. E.: 1986, ‘Lexicographic refinements of Nash equilibrium’, Economics Discussion Paper, University of Michigan.
Brandenburger, A. and E. Dekel: 1986, ‘On an axiomatic approach to refinements of Nash equilibrium’, Economic Theory Discussion Paper No. 104, University of Cambridge.
Broome, J.: 1986, ‘Should a rational person conform to the sure-thing principle?’, presented at the 3rd International Conference on the Foundations and Applications of Utility, Risk and Decision Theories, Aix-en-Provence.
Brown, P. M.: 1976, ‘Conditionalization and expected utility’, Philosophy of Science 43, 415–419.
Chipman, J. S.: 1960, ‘The foundations of utility’, Econometrica 28, 193–224.
Dehez, P. and J. H. Drèze: 1982, ‘State-dependent utility, the demand for insurance and the value of safety’, in The Value of Life and Safety: Proceedings of a Conference Held by the ‘Geneva Association’, M. W. Jones-Lee (ed.), 41–65. Amsterdam: North-Holland.
Diaconis, P.: 1978, Review of Shafer (1976), Journal of American Statistical Association 73, 677–678.
Drèze, J. H.: 1958, ‘On the Identifiability of Subjective Probabilities and Cardinal Utilities’ (abstract), Econometrica 26, 319–320.
Drèze, J. H.: 1961, ‘Les fondements logiques de l'utilité cardinale et de la probabilité subjective’, in La décision, Colloques Internationaux du CNRS (Paris), pp. 73–87.
Drèze, J. H.: 1962, ‘L'utilité sociale d'une vie humaine’, Revue française de recherche opérationnelle 6, 93–118.
Drèze, J. H.: 1986, ‘Moral expectation with moral hazard’, in Contributions to Mathematical Economics in Honor of Gerard Debreu, W. Hildebrand and A. Mas-Colell (eds.), ch. 11, 187–204. Amsterdam: North-Holland.
Drèze, J. H.: 1987, Essays on Economic Decisions under Uncertainty. Cambridge: Cambridge University Press.
Ellsberg, D.: 1961, ‘Risk, ambiguity, and the Savage axioms’, Quarterly Journal of Economics 75, 643–669.
Fishburn, P. C.: 1982, The Foundations of Expected Utility. Dordrecht: D. Reidel.
Gärdenfors, P. and N.-E. Sahlin: 1982, ‘Unreliable probabilities, risk taking, and decision making’, Synthese 53, 361–386.
Hacking, I.: 1967, ‘Slightly more realistic probability’, Philosophy of Science 34, 311–325.
Hammond, P. J.: 1976, ‘Changing tastes and coherent dynamic choice’, Review of Economic Studies 43, 159–173.
Hammond, P. J.: 1977, ‘Dynamic restrictions on metastatic choice’, Economica 44, 337–350.
Hammond, P. J.: 1983, ‘Ex-post optimality as a dynamically consistent objective for collective choice under uncertainty’, in Social Choice and Welfare, P. K. Pattanaik and M. Salles (eds.), ch. 10, 175–205. Amsterdam: North-Holland.
Hammond, P. J.: 1986, ‘Consequentialist social norms for public decisions’, in Social Choice and Public Decision Making: Essays in Honor of Kenneth J. Arrow, Vol. I, W. P. Heller, R. M. Starr and D. A. Starrett (eds.), ch. 1, 3–27. Cambridge: Cambridge University Press.
Hammond, P. J.: 1987a, ‘On reconciling Arrow's theory of social choice with Harsanyi's fundamental utilitarianism’, in Arrow and the Foundations of the Theory of Economic Policy, G. R. Feiwel (ed.), ch. 4, 179–222. London: Macmillan.
Hammond, P. J.: 1987b, ‘Consequentialism and the independence axiom’, to appear in Munier (1987).
Harsanyi, J. C.: 1978, ‘Bayesian decision theory and utilitarian ethics’, American Economic Review, Papers and Proceedings 68, 223–228.
Hausner, M.: 1954, ‘Multidimensional utilities’, in R. M. Thrall, C. H. Coombs and R. L. Davis (eds.), Decision Processes, ch. 12, 167–180. New York: John Wiley.
Herstein, I. N. and J. Milnor: 1953, ‘An axiomatic approach to measurable utility’, Econometrica 21, 291–297.
Johnsen, T. H. and J. B. Donaldson: 1985, ‘The structure of intertemporal preferences under uncertainty and time consistent plans’, Econometrica 53, 1451–1458.
Karni, E. and Z. Safra: 1986, ‘Dynamic consistency in English auctions and expected utility theory’, mimeo.
Karni, E., Schmeidler, D. and K. Vind: 1983, ‘On state dependent preferences and subjec- tive probabilities’, Econometrica 51, 1021–1031.
McClennen, E. F.: 1986, ‘Dynamic choice and rationality’, to appear in Munier (1987).
McClennen, E. F.: 1987, Rationality and Dynamic Choice: Foundational Explorations.
Morrison, D. G.: 1967, ‘On the consistency of preference in Allais' paradox’, Behavioral Science 12, 373–383.
Munier, B.(ed.): 1987, Risk, Decision and Rationality: Proceedings of the 3rd International Conference on the Foundations and Applications of Utility, Risk and Decision Theories. Dordrecht: D. Reidel, forthcoming.
Myerson, R. B.: 1979, ‘An axiomatic derivation of subjective probability, utility and evaluation functions’, Theory and Decision 11, 339–352.
Raiffa, H.: 1961, ‘Risk, ambiguity, and the Savage axioms’, Quarterly Journal of Econom- ics 75, 690–694.
Raiffa, H.: 1968, Decision Analysis: Introductory Lectures on Choices under Uncertainty. Reading, Mass.: Addison-Wesley.
Samuelson, P. A.: 1952, ‘Probability, utility, and the independence axiom’, Econometrica 20, 670–678.
Savage, L. J.: 1954, The Foundations of Statistics. New York: John Wiley.
Sen, A. K. and B. Williams (eds.): 1982, Utilitarianism and Beyond. Cambridge: Cambridge University Press.
Shafer, G.: 1976, A Mathematical Theory of Evidence. Princeton: Princeton University Press.
Skala, H. J.: 1975, Non-Archimedean Utility Theory. Dordrecht: D. Reidel.
Teller, P.: 1973, ‘Conditionalization and observation’, Synthese 26, 218–258.
von Neumann, J. and O. Morgenstern: 1944, Theory of Games and Economic Behavior. Princeton: P.rinceton University Press.
Weller, P. A.: 1978, ‘Consistent intertemporal decision making under uncertainty’, Review of Economic Studies 45, 263–266.
Williams, B. A. O.: 1973, ‘A critique of utilitarianism’, in Utilitarianism for and against, J. J. C. Smart and B. A. O. Williams (eds.). Cambridge: Cambridge University Press.
Williams, B.: 1985, Ethics and the Limits of Philosophy. London: Fontana Press/Collins.
Wilson, R. B.: 1968, ‘The theory of syndicates’, Econometrica 36, 119–132.
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Hammond, P.J. Consequentialist foundations for expected utility. Theor Decis 25, 25–78 (1988). https://doi.org/10.1007/BF00129168
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DOI: https://doi.org/10.1007/BF00129168