Eclectic Decision Theory

Itzhak Gilboa, Questions in Decision Theory (August 2009).

Itzhak Gilboa is a prominent economist who has made large contributions to decision theory, including the theory of decisionmaking under uncertainty (as opposed to risk) and the use of case-based or analogical strategies of reasoning, both of which are important topics for legal theory.  In this unpublished paper, Gilboa offers a relatively informal and accessible overview of conceptual and empirical problems in and with decision theory.  Gilboa writes as a sympathetic and informed critic from within, rather than a hostile critic from without, which gives his analysis all the more weight.

Gilboa provides an introduction to five theoretical questions currently troubling the field: the status and nature of the rationality assumption, the meaning of “probability” and the limits of the Bayesian approach to probability, the meaning of “utility” and the relationship(s) between utility and notions such as well-being and happiness, the choice between rules and analogies as strategies of reasoning, and the problem of group decisionmaking, including the key question whether and when groups make better or worse decisions than the individuals who constitute them (“the wisdom of crowds” versus “the madness of crowds”).  All five sections are highly illuminating, but I will discuss only one, which is Gilboa’s treatment of probability and uncertainty.  The issues are central for legal and political decisionmaking, in which information costs are high and experiments – natural or otherwise – are usually unthinkable, so that certainty is rare.

Gilboa starts with the question “will the U.S. President six years from now be a Democrat?” (p. 8).  Who knows?  This seems a good case in which to admit that there is such a thing as genuine uncertainty, as opposed to quantifiable probabilities (risk).  If you are exceptionally self-confident and have a clear probability estimate for this example, you might try Jon Elster’s famous question whether “Norway in the year 3000 will be a democracy or a dictatorship.”  Uncertainty is real but, as Gilboa notes (p. 8), the Bayesian approach to probability that reigns in economics prohibits agents from simply confessing ignorance.  Rather the agents are constrained to provide a subjective probability for the event in question, even if only an implicit subjective probability elicited by an experimenter who offers the subject a series of bets over alternatives.

Insofar as normative decision theory is concerned – thus putting aside the massive body of positive work, in psychology and behavioral economics, on whether agents do in fact behave in a Bayesian fashion — there are at least three related problems with the Bayesian approach.  (1) In Gilboa’s words, “for many events of interest we simply do not have enough data to generate probabilities” (p. 11).  (2) Subjective probabilities, even if generated, may lack any epistemic standing or warrant.  As Cass Sunstein has been known to say, his dog Perry seems to attach subjective probabilities to various events, probabilities that are wildly off the mark.  (3) Pragmatically, even if an agent could be induced to vomit forth a subjective probability estimate about the nature of the Norwegian political regime in the year 3000, “would anyone even contemplate acting on the basis of this numerical magnitude?” (Jon Elster, Explaining Technical Change (1983), p. 199).

In light of these problems, why are so many economists (and the rationalist political scientists who adopt their methods, with a lag) wedded to the Bayesian approach?  Its basic appeal, according to Gilboa, is that it is mathematically tractable and elegant, even if it is often not true (p. 9-10).  I would merely add that the Bayesian approach makes it easier to standardize graduate training in economics and rationalist political science and easier for the average graduate of such programs to produce “results.”  In reality, however, many of these results are spurious.  The Bayesian approach makes perfect sense for some decision problems, such as searching for consumer goods in a static market, but is a misfit for other problems, such as choosing climate change policies or counterterrorism policies.

Gilboa calls the Bayesian approach an “ideological and almost religious belief” (p. 9), observes that “the popularity of the Bayesian approach in economics is an interesting sociological phenomenon” (p. 8), and says “I do not think that there exists any other field in which Bayesianism is so overwhelmingly dominant, or in which it is practiced with such generality, as in economic theory” (p. 8).  My own impression, which is worth almost nothing compared to Gilboa’s, is that the best economists have become more hospitable to genuine uncertainty in recent years, perhaps in part as a result of the implausibility or conspicuous failures of risk-based modeling in the Long-Term Capital Management debacle and in the economic collapse of 2008.  Doubtless, however, it will take a generation or so for the new open-mindedness of the best economists to spread widely within the discipline and beyond.

Gilboa’s master impulse, which pervades the paper, is to urge an eclectic approach to controversies in and about decision theory.  The eclectic theorist chooses tools and assumptions to fit the nature of the problem at hand.  This can seem opportunistic, but it is superior to the ideological cast of a great deal of work in the rationalist vein, in which the problems are stretched or trimmed so that they can be worked upon with a given tool, to which the analyst is passionately attached.  The eclectic analyst is promiscuous, even cold-hearted; she does not fall in love with any of her instruments but exploits them all indifferently, as occasion requires.  Or so I interpret Gilboa’s admirable view that “[d]ecision theory should therefore retain a degree of open-mindedness, allowing for the possibility that different models and even different basic concepts be used in different problems” (p. 28).

 
 
Discussion

2 comments
  1. 1

    Gilboa has a very odd definition of subjective rationality which entail that recalcitrant individuals are more rational than thoughtful individuals.

     
  2. 2

    Two brief bibliographic comments:

    — This paper was prepared for the Annual Reviews in Economics;
    — David Schmeidler, who was my advisor, was the first to suggest a general-purpose, axiomatically-based decision theory that generalized the classical one (expected utility with subjective probabilities).

    On rationality: the (admittedly odd) notion of subjective rationality is designed to facilitate discourse in decision theory, and it may be of no use in the legal domain. Surely the law is interested in subjective terms much less than decision theory is. (This parallels the distinction between classical and Bayesian statistics.) But perhaps subjective rationality may have some counterparts in questions of sanity and moral responsibility?