Decision Theory

23 Oct 2024 10:37

Some years ago I was trying to decide whether or not to move to Harvard from Stanford. I had bored my friends silly with endless discussions. Finally, one of them said, "You're one of our leading decision theorists. Maybe you should make a list of costs and benefits and try to roughly calculate your expected utility." Without thinking, I blurted out, "Come on, Sandy, this is serious." --- Persi Diaconis, "The Problem of Thinking Too Much", pp. 36--37

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.

David Blackwell and M. A. Girshick, Theory of Games and Statistical Decisions
Herbert Gintis, Game Theory Evolving
Luce and Raiffa, Games and Decisions

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]
Truman F. Bewley, "Knightian decision theory. Part I", Decisions in Economics and Finance 25 (2002): 79--110 [PDF preprint. Thanks to Maxim Raginsky for the pointer. As a technical note, Bewley's "inertia" assumption rules out practical transitivity, and so some kind of money pumps. But the classical Dutch Book involves taking a combination of bets at once, not a preference cycle.]
Ken Binmore, "Rational Decisions in Large Worlds", Annales d'Économie et de Statistique 86 (2007): 25--41 ["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." Thanks to Nicolas Della Penna for the pointer]
Modibo K. Camara, "Computationally Tractable Choice" [PDF via Dr. Camara. My comments]
James Crotty, "Are Keynesian Uncertainty and Macrotheory Compatible? 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 [PDF preprint. Repeats Davidson's errors on ergodicity (see below), but has many suggestive remarks about the uses of conventions and institutions to reduce uncertainty.]
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 (practical) non-ergodicity, as all stationary processes are mixtures of ergodic ones (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. (Much, much more about this.) I find this sort of mistake extra annoying because has arguments could still work if he fixed this!]
Persi Diaconis, "The Problem of Thinking Too Much", Bulletin of the American Academy of Arts and Sciences 56 (2003): 26--38
Tilmann Gneiting, "Making and Evaluating Point Forecasts", Journal of the American Statistical Association 106 (2011): 746--762, arxiv:0912.0902
Daniel M. Hausman, "Mistakes about Preferences in the Social Sciences", Philosophy of the Social Sciences 41 (2011): 3--25
Joseph Y. Halpern, "Beyond Nash Equilibrium: Solution Concepts for the 21st Century", arxiv:0806.2139
Joseph Y. Halpern, Rafael Pass, "Iterated Regret Minimization: A More Realistic Solution Concept", arxiv:0810.3023
Andrew T. Little, "Directional Motives and Different Priors are Observationally Equivalent", OSF preprint, 2021 [This a very clearly written paper which is convincing as far as it goes. It considers semi-Bayesian agents who engage in "motivated reasoning", in the sense that their distribution of beliefs after conditioning on evidence minimizes the KL divergence from the correct Bayesian posterior, plus a sum of terms which reflect how strongly they want certain alternatives to be true. Little shows that this is always equivalent to doing correct Bayesian updating using a different prior, which puts more prior weight on the favored options. While, as I said, convincing as far as it goes, it strikes me as not a very good model of motivated reasoning. (Conversely, a Bayesian agent with a non-uniform prior is equivalent to someone who starts with a uniform prior and engages in motivated reasoning!) The formulation of motivated reasoning here strikes me as weird and unconvincing, though. Even if one wanted to do something along the lines of solving an information-theoretic optimization problem, Bayesian updating itself involves minimizing the divergence from the prior, plus a likelihood-based penalty, so why not just add the "directional" terms favoring particular conclusions to this problem? (I should probably just make this into a blog post, shouldn't I?)]
Charles Manski
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- "Actualist Rationality", Theory and Decision 71 (2011)
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.]
Amartya Sen, "Internal Consistency of Choice", Econometrica 61 (1993): 495--521 [JSTOR]
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.]
Edna Ullmann-Margalit, "Big Decisions: Opting, Converting, Drifting", Royal Institute of Philosophy Supplements 58 (2006): 157--172 [PDF reprint]
John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior

H. Spencer Banzhaf, "The Cold-War Origins of the Value of Statistical Life", Journal of Economic Perspectives 28 (2014): 213--226
Peter Bernstein, Against the Gods: The Remarkable Story of Risk
Ken Bimore, Rational Decisions
Lara Buchak, Risk and Rationality
N. N. Chentsov, Statistical Decision Rules and Optimal Inference
H. Chernoff and Moses, Elementary Decision Theory
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
Joseph Y. Halpern, Samantha Leung, "Minimizing regret in dynamic decision problems", Theory and Decision 81 (2016): 123--151
Jerry Hausman, "Contingent Valuation: From Dubious to Hopeless", Journal of Economic Perspectives 26 (2012): 43--56
Claire Hill, "The Rationality of Preference Construction (and the Irrationality of Rational Choice)", ssrn/1288652
Isaac Levi, "Money Pumps and Diachronic Books", Philosophy of Science 69 (2002): S235--S247
Jean-Pierre Ponssard, "On the Concept of the Value of Information in Competitive Situations", Management Science 22 (1976): 739--747 [JSTOR]
Joel Predd, Robert Seiringer, Elliott H. Lieb, Daniel Osherson, Vincent Poor, Sanjeev Kulkarni, "Probabilistic coherence and proper scoring rules", IEEE Transactions on Information Theory 55 (2009): 4786, arxiv:0710.3183
Tim Rakow, "Risk, uncertainty and prophet: The psychological insights of Frank H. Knight", Judgment and Decision Making 5 (2010): 458--466
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
Cass R. Sunstein, Worst-Case Scenarios
William Thomas, Rational Action: The Sciences of Policy in Britain and America, 1940--1960
Paul Weirich, Equilibrium and Rationality: Game Theory Revised by Decision Rules
Richard Wilson and Edmund A. C. Crouch, Risk/Benefit Analysis