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Decision theory and cognitive choice

  • Original Paper in Decision and Game Theory
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Abstract

The focus of this study is cognitive choice: the selection of one cognitive option (a hypothesis, a theory, or an axiom, for instance) rather than another. The study proposes that cognitive choice should be based on the plausibilities of states posited by rival cognitive options and the utilities of these options' information outcomes. The proposal introduces a form of decision theory that is novel because comparative; it permits many choices among cognitive options to be based on merely comparative plausibilities and utilities. This form of decision theory intersects with recommendations by advocates of decision theory for cognitive choice, on the one hand, and defenders of comparative evaluation of scientific hypotheses and theories, on the other. But it differs from prior decision-theoretic proposals because it requires no more than minimal precision in specifying plausibilities and utilities. And it differs from comparative proposals because none has shown how comparative evaluations can be carried out within a decision-theoretic framework.

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Notes

  1. The term ‘real agents’ includes software agents that may not be appropriately programmable with point-valued probabilities and utilities (Chu and Halpern 2008, 4–5, 25).

  2. Early work on interval probability functions includes Kyburg (1961), Good (1962), and Levi (1974, with further references on p. 407).

  3. There are also intriguing connections to a contrastive account of knowledge (Morton and Karjalainen 2003; Schaffer 2004).

  4. I have adapted Chu and Halpern’s set-theoretic statement to the propositional idiom.

  5. The example is adapted from Fishburn (1986, 339).

  6. This example is discussed in Levi (1986, 1–2).

  7. Paul Samuelson’s observation on Savage’s theory (along with Ramsey’s and de Finetti’s) is still worth noting: “it is important to realize that this is a purely ordinal theory and the same facts can be completely described without using privileged numerical indicators of utility or probability” (1952, 670 n1).

  8. ‘|’, which was defined in Section 2.2f) for incomparable plausibilities, utilities, and plausibilistic expectations, is used analogously here. A product such as uP can be thought of as the plausibilistic expectation of an act relative to a single state.

  9. Cf. “In nonquantitative cases the principle to maximize utility may not apply because options’ utilities may not exist. The absence of crucial probabilities and utilities may prevent computing them according to principles of expected utility analysis” (Weirich 2004, 59).

  10. Distinctions among cognitive, partly cognitive, and noncognitive decisions are introduced in Section 2.2c).

  11. I am grateful to an anonymous reviewer for European Journal for Philosophy of Science for raising this point.

  12. An analogous distinction can be drawn for probability. “Whether or not a given sentence is accepted depends not so much on its total probability taken in isolation, but on that probability as compared to the probabilities of the alternative hypotheses being considered” (Levi 1967, 98).

  13. Here I am indebted to an anonymous reviewer for European Journal for Philosophy of Science.

  14. Maher takes independence to be a requirement of rationality “when the preferences are relevant to a sufficiently important decision problem, and where there are no rewards attached to violating … independence” (1993, 12, 63–83).

  15. An alternative approach is explored by Ted Lockhart, who relies on ordinal probability rankings, second-order probabilities, integration to calculate average values, and the principle of indifference to address moral questions (2000, 62–66, 71–72).

  16. “Although an infinite number of options may arise under the idealization of unlimited cognitive power, in real cases the number of options is finite” (Weirich 2004, 142). Cf. Gärdenfors and Sahlin (1982, 366), Laudan (1984, 28), and Giere (1985, 87).

  17. Transitivity is discussed in greater depth in the writer’s “Real-Life Decisions and Decision Theory” (forthcoming).

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Acknowledgements

Prasanta Bandyopadhyay, James Franklin, Theo Kuipers, and Ana Portilla contributed insightful comments on an earlier version of this paper. Two anonymous referees and the editors of European Journal for Philosophy of Science offered highly constructive criticism of the present version. Audiences at the University of Groningen in the Netherlands, Complutense University and the University of Alcalá de Henares in Spain, and Visva Bharati University in India also provided valuable feedback. I am grateful to them all.

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  1. Department of Philosophy, Saint Louis University—Madrid Campus, 28003, Madrid, Spain

    John R. Welch

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Welch, J.R. Decision theory and cognitive choice. Euro Jnl Phil Sci 1, 147–172 (2011). https://doi.org/10.1007/s13194-010-0005-3

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