Standard Decision Theory Corrected: Assessing Options When Probability is Infinitely and Uniformly Spread
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Synthese 122 (3):261-290 (2000)
Where there are infinitely many possible [equiprobable] basic states of the world, a standard probability function must assign zero probability to each state—since any finite probability would sum to over one. This generates problems for any decision theory that appeals to expected utility or related notions. For it leads to the view that a situation in which one wins a million dollars if any of a thousand of the equally probable states is realized has an expected value of zero (since each such state has probability zero). But such a situation dominates the situation in which one wins nothing no matter what (which also has an expected value of zero), and so surely is more desirable. I formulate and defend some principles for evaluating options where standard probability functions cannot strictly represent probability—and in particular for where there is an infinitely spread, uniform distribution of probability. The principles appeal to standard probability functions, but overcome at least some of their limitations in such cases.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Peter Vallentyne (2000). Standard Decision Theory Corrected. Synthese 122 (3):261-290.
Teddy Seidenfeld, Mark J. Schervish & Joseph B. Kadane (2010). Coherent Choice Functions Under Uncertainty. Synthese 172 (1):157 - 176.
Vieri Benci, Leon Horsten & Sylvia Wenmackers (2013). Non-Archimedean Probability. Milan Journal of Mathematics 81 (1):121-151.
Peter J. Lewis (2010). Probability in Everettian Quantum Mechanics. Manuscrito 33:285--306.
Reed Richter (1984). Rationality Revisited. Australasian Journal of Philosophy 62 (4):392 – 403.
Charles G. Morgan (1999). Conditionals, Comparative Probability, and Triviality: The Conditional of Conditional Probability Cannot Be Represented in the Object Language. Topoi 18 (2):97-116.
Stephen Spielman (1976). Bayesian Inference with Indeterminate Probabilities. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1976:185 - 196.
Alan Hájek (2001). Probability, Logic, and Probability Logic. In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Blackwell Publishers. 362--384.
Patrick Maher (2010). Bayesian Probability. Synthese 172 (1):119 - 127.
Roman Frič & Martin Papčo (2010). A Categorical Approach to Probability Theory. Studia Logica 94 (2):215 - 230.
E. G. Beltrametti & S. Bugajski (2002). Quantum Mechanics and Operational Probability Theory. Foundations of Science 7 (1-2):197-212.
Ellery Eells (1983). Objective Probability Theory Theory. Synthese 57 (3):387 - 442.
Peter C. Fishburn (1974). Convex Stochastic Dominance with Finite Consequence Sets. Theory and Decision 5 (2):119-137.
Added to index2010-12-22
Total downloads7 ( #173,266 of 1,096,270 )
Recent downloads (6 months)3 ( #84,313 of 1,096,270 )
How can I increase my downloads?