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.
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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
de Finetti B. (1937) La prévision: ses lois logiques, ses sources subjectives. Annals de L’Institut Henri Poincaré 7: 1–68
Ellsberg D. (1961) Risk, ambiguity, and the Savage axioms. The Quarterly Journal of Economics 75: 643–669
Ellsberg D. (2001) Risk, ambiguity and decision. Garland Publishing, New York
Fishburn P. (2001) The theory of social choice. Princeton University Press, Princeton, NJ
Gardenfors P., Sahlin N. E. (1982) Unreliable probabilities, risk taking, and decision making. Synthese 53: 361–386
Gigerenzer G., Selten R. (2001) Bounded rationality: The adaptive toolbox. MIT Press, Cambridge, MA
Gilboa I., Schmeidler D. (1989) Maximin expected utility with non-unique prior. Journal of Mathematical Economics 18: 141–153
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
Kadane J., Schervish M., Seidenfeld T. (1999) Rethinking the foundations of statistics. Cambridge University, New York
Kahneman D., Tversky A. (1979) Prospect theory: An analysis of decision under risk. Econometrica 47(2): 263–291
Kahneman D., Tversky A. (2000) Choices, values, and frames. Cambridge University, New York
Keeney R., Raiffa H. (1993) Decisions with multiple objectives: Preferences and value tradeoffs. Cambridge University, New York
Keynes J. M. (1921) A treatise on probability. MacMillan, London
Knight F. H. (1921) Risk, uncertainty and profit. Houghton-Mifflin, New York
Kreps D. (1988) Notes on the theory of choice. Westview Press, Boulder, CO
Kyburg H. E. (1968) Bets and beliefs. American Philosophical Quarterly 5: 63–78
Lehmann D. (2001) Nonmonotonic logics and semantics. Journal of Logic and Computation 11(2): 229–256
Levi I. (1974) On indeterminate probabilities. Journal of Philosophy 71: 391–418
Levi, I. (1980) The enterprise of knowledge. MIT Press.
Levi I. (1986) Hard choices: Decision making under unresolved conflict. Cambridge University, Cambridge
Levi I. (1990) Compromising Bayesianism: A plea for indeterminacy. Journal of Statistical Planning and Inference 25: 347–362
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
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
Rott H. (1993) Belief contraction in the context of the general theory of rational choice. Journal of Symbolic Logic 58: 1426–1450
Rubinstein A. (2006) Lecture notes in microeconomic theory. Princeton University, Princeton, NJ
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
Seidenfeld T. (2004) A contrast between two decision rules for use with (convex) sets of probabilities. Synthese 140: 69–88
Seidenfeld T., Schervish M., Kadane J. (1989) On the shared preferences of two Bayesian decision makers. The Journal of Philosophy 86(5): 225–244
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
Sen A. (1977) Social choice theory: A re-examination. Econometrica 45(1): 53–88
Sen A. (1997) Maximization and the act of choice. Econometrica 65(4): 745–779
Sen A. (2002) Rationality and freedom. Harvard University, Cambridge, MA
Suppes P. (2002) Representation and invariance of scientific structures. CSLI, Stanford, CA
Szpilrajn E. (1930) Sur l’extension de l’ordre partiel. Fundamenta Matematicae 16: 386–389
Troffaes M. (2007) Decision making under uncertainty using imprecise probabilities. International Journal of Approximate Reasoning 45: 17–29
Tversky A., Kahneman D. (1974) Judgment under uncertainty: Heuristics and biases. Science 185: 1124–1131
van Fraassen B. (2008) Scientific representation. Oxford University Press, New York
von Neumann J., Morgenstern O. (1944) Theory of games and economic behavior. Princeton University Press, Princeton, NJ
Walley P. (1990) Statistical reasoning with imprecise probabilities. Chapman and Hall, London
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Helzner, J. Rationalizing two-tiered choice functions through conditional choice. Synthese 190, 929–951 (2013). https://doi.org/10.1007/s11229-011-0056-9
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DOI: https://doi.org/10.1007/s11229-011-0056-9