## Decision Theory

*04 Sep 2022 23:28*

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.

See also: Sequential Decision Making Under Stochastic Uncertainty

- Recommended, big picture:
- David Blackwell and M. A. Girshick, Theory of Games and Statistical Decisions
- Herbert Gintis, Game Theory Evolving
- Luce and Raiffa, Games and Decisions

- Recommended, close-ups:
- 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] - 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
- Identification for Prediction and Decision [Mini-review]
- "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

- To read:
- 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