Decision Theory

15 Dec 2009 09:35

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By which I mean the various mathematical theories of optimal decison-making; a division of both statistics and economics. This is a fairly distinct topic from actual human decision-making, since people do not seem to conform very well to any of the theoretical ideals. This sometimes leads to much wailing and gnashing of teeth over our irrationality; if anything, however, it leads me to doubt that these theories are good formalizations of rationality. Nonetheless, they're mathematically interesting, and they do have certain very nice properties in the situations where you can actually get them to work.

See also: Sequential Decision Making Under Stochastic Uncertainty

Recommended:
• F. Bacchus, H. E. Kyburg and M. Thalos, "Against Conditionalization," Synthese 85 (1990): 475--506 [Why "Dutch book" arguments do not, in fact, mean that rational agents must be Bayesian reasoners. PDF preprint]
• Ken Binmore, Making Decisions in Large Worlds ["This paper argues that we need to look beyond Bayesian decision theory for an answer to the general problem of making rational decisions under uncertainty." PDF manuscript; thanks to Nicolas Della Penna for the pointer]
• David Blackwell and M. A. Girshick, Theory of Games and Statistical Decisions
• Paul Davidson, "Is Probability Theory Relevant for Uncertainty? A Post Keynesian Perspective", The Journal of Economic Perspectives 5 (1991): 129--143 [JSTOR. An extremely interesting discussion of the distinctions between "objective probability", i.e. an actual stochastic process, "subjective probability" (in a degrees-of-belief sense), and genuine uncertainty, when one doesn't have a clue, and the implications of the latter for economics, especially macroeconomics. However, he does make some annoying mistakes about ergodic theory (especially on and around p. 132, especially fn. 3, which asserts "Nonstationarity is a sufficient, but not a necessary condition, for nonergodicity."). In particular: (i) non-stationary processes can certainly be ergodic, e.g., asymptotically mean stationary ones are (see ch. 23 on the almost-sure ergodic theorem in Almost None of the Theory of Stochastic Processes); (ii) non-stationarity is a necessary condition for non-ergodicity, as all stationary processes are ergodic (ibid.); (iii) non-stationary, non-ergodic processes can perfectly well be extrapolated statistically if the form of the non-stationarity is known, as in the case (to give a trivial example) of a random walk. I find this sort of mistake extra annoying because has arguments could still work if he fixed this!]
• Charles Manski
  • Identification for Prediction and Decision [Mini-review]
  • "Actualist Rationality" [PDF preprint]
• Mark E. J. Newman, Michelle Girvan, and J. Doyne Farmer, "Optimal design, robustness, and risk aversion," cond-mat/0202330
• Spyros Skouras, "Decisionmetrics: Towards a Decision-Based Approach to Econometrics," SFI Working Paper 2001-11-064 [Applies far outside econometrics. If what you really want to do is to minimize a known loss function, optimizing a conventional accuracy measure, e.g. least squares, can be highly counterproductive.]
• John Sutton, "Flexibility, Profitability and Survival in an (Objective) Model of Knightian Uncertainty" [PDF preprint. Decision-making when the crucial variable is the indicator function of an unmeasurable set, i.e., one which doesn't actually have a probability.]

To read:
• Peter Bernstein, Against the Gods: The Remarkable Story of Risk
• Ken Bimore, Rational Decisions [Blurb]
• N. N. Chentsov, Statistical Decision Rules and Optimal Inference
• H. Chernoff and Moses, Elementary Decision Theory
• James Crotty, "Are Keynesian Uncertainty and Macrotheory Incompatible? Conventional Decision Making, Instititional Structures and Conditional Stability in Keyneian Macromodels", pp. 105--142 in G. Dymski and R. Pollin (eds.), New Perspectives in Monetary Macroeconomics: Explorations in the Tradition of Hyman Minsky [Supposedly includes modeling of decision-making under actual uncertainty]
• Peter D. Grunwald and A. Philip Dawid, "Game theory, maximum entropy, minimum discrepancy and robust Bayesian decision theory", Annals of Statistics 32 (2004): 1367--1433 = math.ST/0410076
• Isaac Levi, "Money Pumps and Diachronic Books", Philosophy of Science 69 (2002): S235--S247
• Luce and Raiffa, Games and Decisions
• Rustem and Howe, Algorithms for Worst-Case Design and Applications to Risk Management
• Kristin S. Shrader-Frechette, Risk and Rationality: Philosophical Foundations for Populist Reforms [On the philosophy of risk assessment; blurb; full text]
• Cass R. Sunstein, Worst-Case Scenarios [Blurb]
• Paul Weirich, Equilibrium and Rationality: Game Theory Revised by Decision Rules [blurb]
• Richard Wilson and Edmund A. C. Crouch, Risk/Benefit Analysis [Blurb]