Skip to main content
SpringerLink
Log in

Rationalizing two-tiered choice functions through conditional choice

  • Published:
Synthese Aims and scope Submit manuscript

Abstract

Set-valued choice functions provide a framework that is general enough to encompass a wide variety of theories that are significant to the study of rationality but, at the same time, offer enough structure to articulate consistency conditions that can be used to characterize some of the theories within this encompassed variety. Nonetheless, two-tiered choice functions, such as those advocated by Isaac Levi, are not easily characterized within the framework of set-valued choice functions. The present work proposes conditional choice functions as the proper carriers of synchronic rationality. The resulting framework generalizes the familiar one mentioned above without emptying it and, moreover, provides a natural setting for two-tiered choice rules.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aizerman M. A., Malishevski A. V. (1981) General theory of best variants of choice: Some aspects. IEEE Transactions on Automatic Control 26: 1030–1040

    Article  Google Scholar 

  • de Finetti B. (1937) La prévision: ses lois logiques, ses sources subjectives. Annals de L’Institut Henri Poincaré 7: 1–68

    Google Scholar 

  • Ellsberg D. (1961) Risk, ambiguity, and the Savage axioms. The Quarterly Journal of Economics 75: 643–669

    Article  Google Scholar 

  • Ellsberg D. (2001) Risk, ambiguity and decision. Garland Publishing, New York

    Google Scholar 

  • Fishburn P. (2001) The theory of social choice. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Gardenfors P., Sahlin N. E. (1982) Unreliable probabilities, risk taking, and decision making. Synthese 53: 361–386

    Article  Google Scholar 

  • Gigerenzer G., Selten R. (2001) Bounded rationality: The adaptive toolbox. MIT Press, Cambridge, MA

    Google Scholar 

  • Gilboa I., Schmeidler D. (1989) Maximin expected utility with non-unique prior. Journal of Mathematical Economics 18: 141–153

    Article  Google Scholar 

  • Helzner, J. (2009a). Indeterminacy and choice. In B. Löwe, E. Pacuit, & J. Romeijn (Eds.), Foundations of the formal sciences VI: Reasoning about probabilities and probabilistic reasoning. Studies in logic (Vol. 16, pp. 31–48). London: College Publications.

  • Helzner J. (2009b) On the application of multiattribute utility theory to models of choice. Theory and Decision 66(4): 301–315

    Article  Google Scholar 

  • Kadane J., Schervish M., Seidenfeld T. (1999) Rethinking the foundations of statistics. Cambridge University, New York

    Book  Google Scholar 

  • Kahneman D., Tversky A. (1979) Prospect theory: An analysis of decision under risk. Econometrica 47(2): 263–291

    Article  Google Scholar 

  • Kahneman D., Tversky A. (2000) Choices, values, and frames. Cambridge University, New York

    Google Scholar 

  • Keeney R., Raiffa H. (1993) Decisions with multiple objectives: Preferences and value tradeoffs. Cambridge University, New York

    Google Scholar 

  • Keynes J. M. (1921) A treatise on probability. MacMillan, London

    Google Scholar 

  • Knight F. H. (1921) Risk, uncertainty and profit. Houghton-Mifflin, New York

    Google Scholar 

  • Kreps D. (1988) Notes on the theory of choice. Westview Press, Boulder, CO

    Google Scholar 

  • Kyburg H. E. (1968) Bets and beliefs. American Philosophical Quarterly 5: 63–78

    Google Scholar 

  • Lehmann D. (2001) Nonmonotonic logics and semantics. Journal of Logic and Computation 11(2): 229–256

    Article  Google Scholar 

  • Levi I. (1974) On indeterminate probabilities. Journal of Philosophy 71: 391–418

    Article  Google Scholar 

  • Levi, I. (1980) The enterprise of knowledge. MIT Press.

  • Levi I. (1986) Hard choices: Decision making under unresolved conflict. Cambridge University, Cambridge

    Book  Google Scholar 

  • Levi I. (1990) Compromising Bayesianism: A plea for indeterminacy. Journal of Statistical Planning and Inference 25: 347–362

    Article  Google Scholar 

  • Luce, R. D., & Raiffa, H. (1989). Games and decisions: Introduction and critical survey. New York: Dover (republication of the 1957 work).

  • Moulin H. (1985) Choice functions over a finite set: A summary. Social Choice and Welfare 2: 147–160

    Article  Google Scholar 

  • Pedersen, A. (2009). Rational choice and belief change: An essay in formal epistemology. Master’s thesis, Carnegie Mellon University.

  • Poproski, R. (2009). The rationalizability of two-step choices. In The sixth annual formal epistemology workshop.

  • Ramsey F. P. (1931) Truth and probability. In: Braithwaite R. B. (eds) The foundations of mathematics and other logical essays. Routledge and Kegan Paul, London, pp 156–198

    Google Scholar 

  • Rott H. (1993) Belief contraction in the context of the general theory of rational choice. Journal of Symbolic Logic 58: 1426–1450

    Article  Google Scholar 

  • Rubinstein A. (2006) Lecture notes in microeconomic theory. Princeton University, Princeton, NJ

    Google Scholar 

  • Savage, L. J. (1972). The foundations of statistics. New York: Dover (republication of the 1954 work).

  • Schervish, M., Seidenfeld, T., Kadane, J., & Levi, I. (2003). Extensions of expected utility theory and some limitations of pairwise comparisons. In Proceedings of the third international symposium on imprecise probability: Theories and applications.

  • Seidenfeld T. (1988) Decision theory without ‘independence’ or without ‘ordering’: What is the difference?. Economics and Philosophy 4: 267–290

    Article  Google Scholar 

  • Seidenfeld T. (2004) A contrast between two decision rules for use with (convex) sets of probabilities. Synthese 140: 69–88

    Article  Google Scholar 

  • Seidenfeld T., Schervish M., Kadane J. (1989) On the shared preferences of two Bayesian decision makers. The Journal of Philosophy 86(5): 225–244

    Article  Google Scholar 

  • Seidenfeld, T., Schervish, M., & Kadane, J. (2007). Coherent choice functions under uncertainty. In Proceedings of the fifth international symposium on imprecise probability: Theories and applications.

  • Sen A. (1971) Choice functions and revealed preference. Review of Economic Studies 38(3): 307–317

    Article  Google Scholar 

  • Sen A. (1977) Social choice theory: A re-examination. Econometrica 45(1): 53–88

    Article  Google Scholar 

  • Sen A. (1997) Maximization and the act of choice. Econometrica 65(4): 745–779

    Article  Google Scholar 

  • Sen A. (2002) Rationality and freedom. Harvard University, Cambridge, MA

    Google Scholar 

  • Suppes P. (2002) Representation and invariance of scientific structures. CSLI, Stanford, CA

    Google Scholar 

  • Szpilrajn E. (1930) Sur l’extension de l’ordre partiel. Fundamenta Matematicae 16: 386–389

    Google Scholar 

  • Troffaes M. (2007) Decision making under uncertainty using imprecise probabilities. International Journal of Approximate Reasoning 45: 17–29

    Article  Google Scholar 

  • Tversky A., Kahneman D. (1974) Judgment under uncertainty: Heuristics and biases. Science 185: 1124–1131

    Article  Google Scholar 

  • van Fraassen B. (2008) Scientific representation. Oxford University Press, New York

    Book  Google Scholar 

  • von Neumann J., Morgenstern O. (1944) Theory of games and economic behavior. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Walley P. (1990) Statistical reasoning with imprecise probabilities. Chapman and Hall, London

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Columbia University, New York, NY, USA

    Jeffrey Helzner

Authors
  1. Jeffrey Helzner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jeffrey Helzner.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Helzner, J. Rationalizing two-tiered choice functions through conditional choice. Synthese 190, 929–951 (2013). https://doi.org/10.1007/s11229-011-0056-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11229-011-0056-9

Keywords

Search

Navigation