Theory and Decision

, Volume 68, Issue 4, pp 463–487

What are the minimal requirements of rational choice? Arguments from the sequential-decision setting

Article

Abstract

There are at least two plausible generalisations of subjective expected utility (SEU) theory: cumulative prospect theory (which relaxes the independence axiom) and Levi’s decision theory (which relaxes at least ordering). These theories call for a re-assessment of the minimal requirements of rational choice. Here, I consider how an analysis of sequential decision making contributes to this assessment. I criticise Hammond’s (Economica 44(176):337–350, 1977; Econ Philos 4:292–297, 1988a; Risk, decision and rationality, 1988b; Theory Decis 25:25–78, 1988c) ‘consequentialist’ argument for the SEU preference axioms, but go on to formulate a related diachronic-Dutch-book-style’ argument that better achieves Hammond’s aims. Some deny the importance of Dutch-book sure losses, however, in which case, Seidenfeld’s (Econ Philos 4:267–290, 1988a) argument that distinguishes between theories that relax independence and those that relax ordering is relevant. I unravel Seidenfeld’s argument in light of the various criticisms of it and show that the crux of the argument is somewhat different and much more persuasive than what others have taken it to be; the critical issue is the modelling of future choices between ‘indifferent’ decision-tree branches in the sequential setting. Finally, I consider how Seidenfeld’s conclusions might nonetheless be resisted.

Keywords

Sequential choice Dynamic decision making Independence axiom Ordering axiom Diachronic Dutch book argument Expected utility theory 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anscombe F.J., Aumann R.J. (1963) A definition of subjective probability. Annals of Mathematical Statistics 34: 199–205CrossRefGoogle Scholar
  2. Hájek A. (2003) Conditional probability is the very guide of life. In: Kyburg H.E. Jr., Thalos M. (eds) Probability is the very guide of life: The philosophical uses of chance. Open Court, ChicagoGoogle Scholar
  3. Hammond P.J. (1976) Changing tastes and coherent dynamic choice. The Review of Economic Studies 43(1): 159–173CrossRefGoogle Scholar
  4. Hammond P.J. (1977) Dynamic restrictions on metastatic choice. Economica 44(176): 337–350CrossRefGoogle Scholar
  5. Hammond P.J. (1988a) Orderly decision theory: A comment on professor seidenfeld. Economics and Philosophy 4: 292–297CrossRefGoogle Scholar
  6. Hammond P.J. (1988b) Consequentialism and the independence axiom. In: Munier B.R. (eds) Risk, decision and rationality. D. Reidel, DordrechtGoogle Scholar
  7. Hammond P.J. (1988c) Consequentialist foundations for expected utility theory. Theory and Decision 25: 25–78CrossRefGoogle Scholar
  8. Joyce J.M. (1999) The foundations of causal decision theory. Cambridge University Press, Cambridge, NYCrossRefGoogle Scholar
  9. Kreps D.M. (1988) Notes on the theory of choice. Westview Press, Boulder, COGoogle Scholar
  10. Levi I. (1974) On indeterminate probabilities. Journal of Philosophy 71(13): 391–418CrossRefGoogle Scholar
  11. Levi I. (1985) Imprecision and indeterminacy in probability judgment. Philosophy of Science 52(3): 390–409CrossRefGoogle Scholar
  12. Levi I. (1986) Hard choices: Decision making under unresolved conflict. Cambridge University Press, Cambridge, NYGoogle Scholar
  13. Levi I. (1991) Consequentialism and sequential choice. In: Bacharach M., Hurley S. (eds) Foundations of decision theory. Oxford, Basil BlackwellGoogle Scholar
  14. Machina M.J. (1989) Dynamic consistency and non-expected utility models of choice under uncertainty. Journal of Economic Literature 27: 1622–1668Google Scholar
  15. Maher P. (1992) Diachronic rationality. Philosophy of Science 59(1): 120–141CrossRefGoogle Scholar
  16. McClennen E.F. (1988) Ordering and independence: A comment on Professor Seidenfeld. Economics and Philosophy 4: 298–308CrossRefGoogle Scholar
  17. McClennen E.F. (1990) Rationality and dynamic choice: foundational explorations. Cambridge University Press, CambridgeGoogle Scholar
  18. Rabinowicz W. (1995) To have one’s cake and eat it too: Sequential choice and expected-utility violations. Journal of Philosophy 92(11): 586–620CrossRefGoogle Scholar
  19. Rabinowicz W. (2000) Preference stability and substitution of indifferents: A rejoinder to Seidenfeld. Theory and Decision 48: 311–318CrossRefGoogle Scholar
  20. Resnik M.D. (1987) Choices: An introduction to decision theory. University of Minnesota Press, MinneapolisGoogle Scholar
  21. Savage L.J. (1972) The foundations of statistics (2nd ed). Dover, New YorkGoogle Scholar
  22. Seidenfeld T. (1988a) Decision theory without “independence” or without “ordering”. Economics and Philosophy 4: 267–290CrossRefGoogle Scholar
  23. Seidenfeld T. (1988b) Rejoinder [to Hammond and McClennen]. Economics and Philosophy 4: 309–315CrossRefGoogle Scholar
  24. Seidenfeld T. (1994) When normal and extensive form decisions differ. Logic, Methodology and Philosophy of Science IX: 451–463Google Scholar
  25. Seidenfeld T. (2000a) Substitution of indifferent options at choice nodes and admissibility: A reply to Rabinowicz. Theory and Decision 48: 305–310CrossRefGoogle Scholar
  26. Seidenfeld T. (2000b) The independence postulate, hypothetical and called-off acts: A further reply to Rabinowicz. Theory and Decision 48: 319–322CrossRefGoogle Scholar
  27. Sen A.K. (1970) Collective choice and social welfare. Holden-Day, San FranciscoGoogle Scholar
  28. Skyrms B. (1993) A mistake in dynamic coherence arguments?. Philosophy of Science 60(2): 320–328CrossRefGoogle Scholar
  29. Steele K.S. (2007) Distinguishing indeterminate belief from ‘risk-averse’ preferences. Synthese 158(2): 189–205CrossRefGoogle Scholar
  30. Tversky A., Kahneman D. (1992) Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty 5: 297–323CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  1. 1.Department of Philosophy, Logic and Scientific MethodLondon School of Economics and Political Sciences (LSE)LondonUK

Personalised recommendations