Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T13:53:40.041Z Has data issue: false hasContentIssue false
Series:   Elements in Decision Theory and Philosophy

Rational Choice Using Imprecise Probabilities and Utilities

Published online by Cambridge University Press:  02 February 2021

Paul Weirich
Paul Weirich
Affiliation:
University of Missouri, Columbia

Summary

An agent often does not have precise probabilities or utilities to guide resolution of a decision problem. I advance a principle of rationality for making decisions in such cases. To begin, I represent the doxastic and conative state of an agent with a set of pairs of a probability assignment and a utility assignment. Then I support a decision principle that allows any act that maximizes expected utility according to some pair of assignments in the set. Assuming that computation of an option's expected utility uses comprehensive possible outcomes that include the option's risk, no consideration supports a stricter requirement.
Get access

Keywords

decision theorygame theoryimprecise probabilitiessequences of choicesimprecise utilities
Type
Element
Information
Series: Elements in Decision Theory and Philosophy
Online ISBN: 9781108582209
Publisher: Cambridge University Press
Print publication: 25 February 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allais, M. 1953. “Le comportement de l’homme rationnel devant le risque: Critique des postulats et axioms de l’école Américaine.” Econometrica 21: 503–546.Google Scholar
Al-Najjar, N. and Weinstein, J.. 2009. “The Ambiguity Aversion Literature: A Critical Assessment.” Economics and Philosophy 25: 249–284.Google Scholar
Armendt, B. 1992. “Dutch Strategies for Diachronic Rules: When Believers See the Sure Loss Coming.” In Hull, D., Forbes, M., and Okruhlik, K., eds., PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1, pp. 217–229. Chicago: University of Chicago Press.Google Scholar
Augustin, T., Coolen, F., de Cooman, G., and Troffaes, M.. 2014. Introduction to Imprecise Probabilities. Hoboken, NJ: Wiley.CrossRefGoogle Scholar
Baccelli, J. and Mongin, P.. 2020. “Can Redescriptions of Outcomes Salvage the Axioms of Decision Theory.” Manuscript available at SSRN: ssrn.com/abstract=3610869ordx.doi.org/10.2139/ssrn.610869CrossRefGoogle Scholar
Bales, A., Cohen, D., and Handfield, T.. 2014. “Decision Theory for Agents with Incomplete Preferences.” Australasian Journal of Philosophy 92: 453–470.Google Scholar
Bradley, S. 2015. “How to Choose among Choice Functions.” Paper presented at the 9th International Symposium on Imprecise Probability: Theories and Applications, Pescara, Italy, July 20–24.Google Scholar
Bradley, S. 2019. “Imprecise Probabilities.” In E. Zalta, ed., Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/archives/fall2018/entries/fundamentality/Google Scholar
Bradley, S. and Steele, K.. 2016. “Can Free Evidence Be Bad? Value of Information for the Imprecise Probabilist.” Philosophy of Science 83: 1–28.Google Scholar
Buchak, L. 2013. Risk and Rationality. Oxford: Oxford University Press.Google Scholar
Carnap, R. 1962. Logical Foundations of Probability. 2nd ed. Chicago: University of Chicago Press.Google Scholar
Castro, C. and Hart, C.. 2019. “The Imprecise Impermissivist’s Dilemma.” Synthese 196: 1623–1640.Google Scholar
Chang, R., ed. 1997. Incommensurability, Incomparability, and Practical Reason. Cambridge, MA: Harvard University Press.Google Scholar
Christensen, D. 2004. Putting Logic in Its Place. Oxford: Oxford University Press.CrossRefGoogle Scholar
de Finetti, B. [1937] 1964. “Foresight: Its Logical Laws, Its Subjective Sources.” In Kyburg, H. and Smokler, H., eds., Studies in Subjective Probability, pp. 93–158. New York: Wiley.Google Scholar
Easwaran, K. and Fitelson, B.. 2012. “An ‘Evidentialist’ Worry about Joyce’s Argument for Probabilism.” Dialectica 66: 425–433.Google Scholar
Elga, A. 2010. “Subjective Probabilities Should Be Sharp.” Philosophers’ Imprint 10(5): 1–11. www.philosophersimprint.org/010005/Google Scholar
Ellsberg, D. 1961. “Risk, Ambiguity, and the Savage Axioms.” Quarterly Journal of Economics 75: 643–669.Google Scholar
Evans, G. 1979. “Reference and Contingency.” The Monist 62: 161–189.Google Scholar
Gaifman, H. 1983. “Paradoxes of Infinity and Self-Applications, I.” Erkenntnis 20: 131–155.Google Scholar
Gärdenfors, P. and Sahlin, N.-E.. 1982. “Unreliable Probabilities, Risk Taking, and Decision Making.” Synthese 53: 361–386.CrossRefGoogle Scholar
Good, I. J. 1952. “Rational Decisions.” Journal of the Royal Statistical Society, Series B, 14: 107–114.Google Scholar
Greco, D. and Hedden, B.. 2016. “Uniqueness and Metaepistemology.” Journal of Philosophy 113: 365–395.CrossRefGoogle Scholar
Hammond, P. 1988. “Orderly Decision Theory: A Comment on Professor Seidenfeld.” Economics and Philosophy 4: 292–297.Google Scholar
Hart, C. and Titelbaum, M.. 2015. “Intuitive Dilation.” Thought 4: 252–262. doi.org/10.1002/tht3.185CrossRefGoogle Scholar
Hedden, B. 2015. “Time-Slice Rationality.” Mind 124: 449–491.Google Scholar
Howson, C. and Urbach, P.. 2006. Scientific Reasoning: The Bayesian Approach. 3rd ed. Chicago: Open Court.Google Scholar
Jackson, E. and Turnbull, M.. Forthcoming. “Permissivism, Underdetermination, and Evidence.” In Lasonen-Aarnio, M. and Littlejohn, C., eds., Routledge Handbook for the Philosophy of Evidence. Abingdon: Routledge.Google Scholar
Jeffrey, R. [1965] 1990. The Logic of Decision. 2nd ed., paperback. Chicago: University of Chicago Press.Google Scholar
Joyce, J. 1998. “A Nonpragmatic Vindication of Probabilism.” Philosophy of Science 65: 575–603.Google Scholar
Joyce, J. 2010. “A Defense of Imprecise Credences in Inference and Decision Making.” Philosophical Perspectives, 24: 281–323.Google Scholar
Konek, J. and Levinstein, B.. 2019. “The Foundations of Epistemic Decision Theory.” Mind 128: 69–107.Google Scholar
Krantz, D., Luce, R. D., Suppes, P., and Tversky, A.. 1971. Foundations of Measurement, Vol. 1: Additive and Polynomial Representations. New York: Academic Press.Google Scholar
Lassiter, D. 2020. “Representing Credal Imprecision: From Sets of Measures to Hierarchical Bayesian Models.” Philosophical Studies 177: 1463–1485.Google Scholar
Levi, I. 1974. “On Indeterminate Probabilities.” Journal of Philosophy 71: 391–418.Google Scholar
Levi, I. 1980. The Enterprise of Knowledge: An Essay on Knowledge, Credal Probability, and Chance.Cambridge, MA: MIT Press.Google Scholar
Mahtani, A. 2019. “Imprecise Probabilities.” In Pettigrew, R. and Weisberg, J., eds., Open Handbook of Formal Epistemology, pp. 107–130. PhilPapers Foundation. https://philpapers.org/archive/PETTOH-2.pdfGoogle Scholar
Meacham, C. and Weisberg, J.. 2011. “Representation Theorems and the Foundations of Decision Theory.” Australasian Journal of Philosophy 89: 641–663.Google Scholar
Paul, L. A. 2014. Transformative Experience. Oxford: Oxford University Press.Google Scholar
Pedersen, A. P. and Wheeler, G.. 2014. “Demystifying Dilation.” Erkenntnis 79: 1305–1342.Google Scholar
Perea, A. 2012. Epistemic Game Theory. Cambridge: Cambridge University Press.Google Scholar
Ramsey, F. P. 1931. “Truth and Probability.” In Braithwaite, R. B., ed., The Foundations of Mathematics and other Logic Essays, pp. 156–198. New York: Harcourt, Brace and Company.Google Scholar
Samuelson, P. 1963. “Risk and Uncertainty: A Fallacy of Large Numbers.” Scientia 98: 108–113.Google Scholar
Savage, L. J. [1954] 1972. The Foundations of Statistics. 2nd ed.New York: Dover.Google Scholar
Schoenfield, M. 2014. “Decision Making in the Face of Parity.” Philosophical Perspectives 28: 263–277.Google Scholar
Schoenfield, M. 2017. “The Accuracy and Rationality of Imprecise Credences.” Noûs 51: 667–685.Google Scholar
Seidenfeld, T., Schervish, M., and Kadane, J.. 2010. “Coherent Choice Functions under Uncertainty.” Synthese 172: 157–176.Google Scholar
Seidenfeld, T., Schervish, M., and Kadane, J.. 2012. “Forecasting with Imprecise Probabilities.” International Journal of Approximate Reasoning 53: 1248–1261.CrossRefGoogle Scholar
Shafer, G. 1976. A Mathematical Theory of Evidence. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Siniscalchi, M. 2009. “Two out of Three Ain’t Bad: A Comment on ‘The Ambiguity Aversion Literature: A Critical Assessment’.” Economics and Philosophy 25: 335–356.Google Scholar
Skyrms, B. 1987. “Coherence.” In Rescher, N., ed., Scientific Inquiry in Philosophical Perspective, pp. 225–42. Pittsburgh: University of Pittsburgh Press.Google Scholar
Titelbaum, M. Forthcoming. Fundamentals of Bayesian Epistemology. New York: Oxford University Press.Google Scholar
Troffaes, M. and de Cooman, G.. 2014. Lower Previsions. Hoboken, NJ: Wiley.Google Scholar
Walley, P. 1991. Statistical Reasoning with Imprecise Probabilities. London: Chapman and Hall.Google Scholar
Weirich, P. 1998. Equilibrium and Rationality: Game Theory Revised by Decision Rules. Cambridge: Cambridge University Press.Google Scholar
Weirich, P. 2001. Decision Space: Multidimensional Utility Analysis. Cambridge: Cambridge University Press.Google Scholar
Weirich, P. 2004. Realistic Decision Theory: Rules for Nonideal Agents in Nonideal Circumstances. New York: Oxford University Press.Google Scholar
Weirich, P. 2012. “Calibration.” In de Regt, H., Hartmann, S., and Okasha, S., eds., EPSA Philosophy of Science: Amsterdam 2009, pp. 415–425. Dordrecht: Springer. doi.org/10.1007/978-94-007-2404-4_34/Google Scholar
Weirich, P. 2015a. Models of Decision-Making: Simplifying Choices. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Weirich, P. 2015b. “Decisions without Sharp Probabilities.” Philosophia Scientiae 19: 213–225.Google Scholar
Weirich, P. 2018. “Rational Plans.” In Bermudez, J. L., ed., Self-Control, Decision Theory, and Rationality, pp. 72–95. Cambridge: Cambridge University Press.Google Scholar
Weirich, P. 2020. Rational Responses to Risks. New York: Oxford University Press.Google Scholar
Weisberg, J. 2009. “Commutativity or Holism? A Dilemma for Conditionalizers.” British Journal for the Philosophy of Science 60: 793–812.CrossRefGoogle Scholar
White, R. 2010. “Evidential Symmetry and Mushy Credence.” In Szabo Gendler, T and Hawthorne, J., eds., Oxford Studies in Epistemology, Vol. 3, pp. 161–186. Oxford: Oxford University Press.Google Scholar
Zaffalon, M. and Miranda, E.. 2018. “Desirability Foundations of Robust Rational Decision Making.” Synthese: 1–42. https://doi.org/10.1007/s11229-018-02010-xGoogle Scholar
Zynda, L. 2000. “Representation Theorems and Realism About Degrees of Belief.” Philosophy of Science 67: 45–69.Google Scholar

Save element to Kindle

To save this element to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Rational Choice Using Imprecise Probabilities and Utilities
  • Paul Weirich, University of Missouri, Columbia
  • Online ISBN: 9781108582209
Available formats
×

Save element to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Rational Choice Using Imprecise Probabilities and Utilities
  • Paul Weirich, University of Missouri, Columbia
  • Online ISBN: 9781108582209
Available formats
×

Save element to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Rational Choice Using Imprecise Probabilities and Utilities
  • Paul Weirich, University of Missouri, Columbia
  • Online ISBN: 9781108582209
Available formats
×