Abstract
The classical account of decision-making derives from seminal work done by Frank P. Ramsey (Truth and probability. In: Braithwaite R (ed) The foundation of mathematics and other logical essays (1931). Routledge and Kegan, London, 1926a; Math Ga 13:185–194, 1926b) and later on by Von Neumann and Morgenstern (Theory of games and economic behavior (2nd edn). Princeton University Press, Princeton, 1947). This work culminates later on with the influential account of Leonard Savage (The foundations of statistics. Wiley, New York (2nd ed. in 1972, Dover), 1954), Ascombe and Aumann (Ann Math Stat 34:199–205, 1963) and de Finetti (Annales de l’Institut Henri Poincare 7:1–68, 1974). We can recapitulate here in a compact form the classical presentation by Von Neumann and Morgenstern. Define a lottery as follows: If A1, … , Am is a partition of the possible outcomes of an experiment with αj = Pr(Aj) for each j, then the lottery (α1, … , αm) awards prize zj if Aj occur. We can assume that the choice of the partition events does not affect the lottery. We can then introduce some central axioms for preferences among lotteries.
Horacio Arló-Costa was deceased at the time of publication.
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Suggested Further Reading
A classical and still rather useful book presenting the received view in decision theory is Savage’s influential and seminal book: The Foundations of Statistics, Dover Publications; 2 Revised edition (June 1, 1972). A slightly more accessible but pretty thorough textbook presentation of Savage’s account and beyond is the monograph by David Kreps: Notes on the Theory of Choice, Westview Press (May 12, 1988).
The classical essay by Daniel Ellsberg introducing his now famous paradox continues to be a very important source in this area: “Risk, Ambiguity and the Savage Axioms,” Quarterly Journal of Economics, 75: 643-669, 1961. Isaac Levi presented a unified normative view of both Allais and Ellsberg in: “The Paradoxes of Allais and Ellsberg,” Economics and Philosophy, 2: 23-53, 1986. This solution abandons ordering rather than independence unlike the solution proposed by Ellsberg himself. Solutions abandoning independence have been in general more popular. Some of the classical papers in this tradition appear in the bibliography of the paper by Gilboa and Marinacci reprinted here. Many of the responses to Allais have been descriptive rather than normative. Prospect theory is a classical type of response along these lines. We reprint here an article that intends to present a unified descriptive response to both Allais and Ellsberg. The reader can find an excellent, thorough and mathematically mature presentation of the contemporary state of the art in Prospect theory in a recent book published by Peter Wakker: Prospect Theory for Risk and Ambiguity, Cambridge University Press, Cambridge, 2011.
The debate about the foundations of causal decision theory is in a way still open. An excellent presentation of causal decision theory can be found in an important book by Jim Joyce: The Foundations of Causal Decision Theory, Cambridge Studies in Probability, Induction and Decision Theory, Cambridge, 2008. Joyce has also written an interesting piece answering challenges to causal decision theory: “Regret and Instability in Causal Decision Theory,” forthcoming in the second volume of a special issue of Synthese devoted to the foundations of the decision sciences (eds.) Horacio Arlo-Costa and Jeffrey Helzner. This special issue contains as well an essay by Wolfgang Spohn that intends to articulate the main ideas of causal decision theory by appealing to techniques used in Bayesian networks: “Reversing 30 Years of Discussion: Why Causal Decision Theorists should be One-Box.” This is a promising line of investigation that has also been considered preliminary in an insightful article by Christopher Meek and Clark Glymour: “Conditioning and Intervening”, British Journal for the Philosophy of Science 45, 1001-1021, 1994. With regard to issues related to actual causation a useful collection is the book: Causation and Counterfactuals, edited by J. Collins, N. Hall and L.A. Paul, MIT Press, 2004.
Finally a paper by Joseph Halpern and Judea Pearl offers a definition of actual causes using structural equations to model counterfactuals, Halpern, J. Y. and Pearl, J. (2005) “Causes and explanations: a structural-model approach. Part I: Causes”, British Journal for Philosophy of Science 56:4, 843-887. This paper articulates ideas about causation based on recent work on Bayesian networks and related formalisms. Current work in this area seems to point to an unification of causal decision theory and an account of causation based on Bayesian networks.
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Arló-Costa, H., Hendricks, V.F., van Benthem, J. (2016). Introduction. In: Arló-Costa, H., Hendricks, V., van Benthem, J. (eds) Readings in Formal Epistemology. Springer Graduate Texts in Philosophy, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-20451-2_18
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