Mitigating Ambiguity Aversion via Counterfactual Priors: A Resolution of Ellsberg's Paradox

Koundouri, Phoebe and Pittis, Nikitas and Samartzis, Panagiotis (2022): Mitigating Ambiguity Aversion via Counterfactual Priors: A Resolution of Ellsberg's Paradox. Published in:

Abstract

Ellsberg-type preferences violate one of the principles for Bayesian rationality, namely Savageís Sure Thing Principle, and are among the main empirical results against Subjective Expected Utility theory. In this paper, we propose a novel strategy for dealing with ambiguity aversion and the resulting Ellsberg-type choices. First, we identify the presence of "asymmetric information" as the main cause of ambiguity aversion. Second, we develop a solution for Ellsberg's paradox which emerges as a direct application of counterfactual thinking, implemented to the specific choice problem described by Ellsberg. Third we analyze the psychological, methodological and logical merits of the developed counterfactual strategy, and show that its application solves the problems of "error correction" and "unconceived alternatives", two of the main complaints about Bayesian Confirmation Theory.

• Item Type: MPRA Paper
• Language: English
• Keywords: counterfactual priors, ambiguity, ellsberg paradox. JEL ClassiÖcation: C44, D81, D83, D89
• Subjects: C - Mathematical and Quantitative Methods > C0 - General; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods

References

Adams, E. (1965). The logic of conditionals. Inquiry, 8, 166-197.

Adams, E. (1975). The logic of conditionals. Dordrecht: Reidel.

Adams, E. (1990). Review of Conditionals, by Frank Jackson. Philosophical Review, 99(3), 433-435.

Arlo-Costa, H. (1999). Belief revision conditionals: basic iterated systems. Annals of Pure and Applied Logic, 96(1-3), 3-28.

Bacchus, F., Kyburg, H. E., Thalos, M. (1990). Against conditionalization. Synthese, 475-506.

Carnap, R. (1962). Logical Foundations of Probability. 2nd ed. University of Chicago Press.

Carnap, R. (1971). Inductive logic and rational decision. Studies in Inductive Logic and Probability, 1, 5-31.

Curley, S.P., Yates, J.F. and Abrams, R.A. (1986). Psychological sources of ambiguity avoidance. Organizational behavior and human decision processes, 38(2), 230-256.

Duhem, P. (1954). The Aim and Structure of Physical Theory, translated from 2nd ed. by P. W. Wiener; originally published in 1914 as La Theorie Physique: Son Objet et sa Structure (Paris: Marcel Riviera & Cie.), Princeton, NJ: Princeton University Press.

Edgington, D. (1986). Do conditionals have truth conditions?. Critica: Revista Hispanoamericana de Filosofia, 3-39.

Ellsberg, D. (1961). Risk, ambiguity, and the Savage axioms. Quarterly Journal of Economics, 75, 643ñ669.

Elster, J. (1979). Ulysses and the Sirens: Studies in Rationality and Irrationality. Cambridge University Press.

Evans, J. S. B., Handley, S. J., Neilens, H., and Over, D. E. (2007). Thinking about conditionals: A study of individual di§erences. Memory & cognition, 35(7), 1772-1784.

Fox, C. R. and Tversky, A. (1995). Ambiguity aversion and comparative ignorance. The Quarterly Journal of Economics, 110(3), 585-603.

Gardner, M. R. (1982). Predicting novel facts. The British Journal for the Philosophy of Science, 33(1), 1-15.

Gilboa, I. and Schmeidler, D. (1989). Maxmin expected utility with a nonunique prior. Journal of Mathematical Economics, 18, 141-153.

Glymour, C. (1980). Theory and Evidence. Princeton: Princeton University Press.

Gul, F. and Pesendorfer, W. (2001). Temptation and self-control. Econometrica, 69(6), 1403-1435.

Hajek, A. (2011). Conditional probability. In P. Bandyopadhyay & M. Forster (Eds.), Handbook for philosophy of statistics, Amsterdam: Elsevier

Heath, C. and Tversky, A. (1991). Preference and belief: Ambiguity and competence in choice under uncertainty. Journal of Risk and Uncertainty, 4(1), 5-28.

Howson, C. (1984). Bayesianism and Support by Novel Facts. The British Journal for the Philosophy of Science, 35, 245-251.

Howson, C. (1991). The 'Old Evidence Problem', The British Journal for the Philosophy of Science, 42(4), 547-55.

Humphreys, M. S. and Revelle, W. (1984). Personality, motivation, and per- formance: a theory of the relationship between individual differences and information processing. Psychological review, 91(2), 153-184.

Jackson, F. (1980). Conditionals and possibilia. Proceedings of the Aristotelian Society, 81, 125-137.

Jaynes, E. (1968). Prior probabilities. IEEE Transactions On Systems Science and Cybernetics, 4(3), 227-241. 391-418.

Leon, M. R. and Revelle, W. (1985). E§ects of anxiety on analogical reasoning: a test of three theoretical models. Journal of Personality and Social Psychology, 49(5), 1302-1315.

Levi, I. (1980), The Enterprise of Knowledge. Cambridge: The MIT Press.

Levi, I. (1985). Imprecision and indeterminacy in probability judgment. Philosophy of Science, 52, 390-409.

Lewis, D. (1976). Probabilities of conditionals and conditional probabilities. Philosophical Review, 85, 297-315.

Lewis, D. (1994). Humean Supervenience Debugged. Mind, 103(412), 473-490.

Lewis, D. (1980). A Subjectivist's Guide to Objective Chance, in Richard C. Jeffrey (ed.) Studies in Inductive Logic and Probability, Vol II., 263-294.

MacCrimmon, K. R. and Larson, S. (1979). Utility theory: axioms versus paradoxes. Expected Utility Hypotheses and the Allais Paradox (ed. Allais, M. and Hagen, O.), 333-410.

Meacham, C. J. (2008). Sleeping Beauty and the Dynamics of De Se Beliefs. Philosophical Studies, 138, 245-70.

Meacham, C. J. (2016). Ur-priors, conditionalization, and ur-prior conditionalization. Ergo: An Open Access Journal of Philosophy, 3.

Raidl, E. (2019). Completeness for counter-doxa conditionalsñusing ranking semantics. The Review of Symbolic Logic, 12(4), 861-891.

Raiffa, H. (1961). Risk, Ambiguity, and the Savage Axioms: Comment. The Quarterly Journal of Economics, 75(4), 690-694.

Rowbottom, D.P. (2019). Extending the argument from unconceived alternatives: observations, models, predictions, explanations, methods, instruments, experiments, and values. Synthese, 196, 3947-3959.

Ramsey, F. P. (1929). General Propositions and Causality. Philosophical Papers, edited by D. H. Mellor, 1990, 145-63.

Savage, L. (1954). The foundations of statistics. New-York, John Wiley.

Schmeidler, D. (1989). Subjective probability and expected utility without additivity. Econometrica, 57(3), 571-587.

Skyrms, B. (1983). Zenoís paradox of measure. Physics, Philosophy and Psychoanalysis, 223-254.

Slovic, P. and Tversky, A. (1974). Who accepts Savageís axiom?. Behavioral science, 19(6), 368-373.

Stanford, P. K. (2006). Exceeding Our Grasp: Science, History, and the Problem of Unconceived Alternatives, New York: Oxford University Press.

Titelbaum, M. G. (2013). Quitting certainties: A Bayesian framework modeling degrees of belief. Oxford University Press.