Bayes Without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice

In 1963, Anscombe and Aumann demonstrated that the introduction of an objective randomizing device into the Savage setting of subjective uncertainty considerably simplified the derivation of subjective probability from a decision maker's preferences over uncertain bets. The purpose of this paper is to present a more general derivation of classical subjective probability in such a framework, which neither assumes nor implies that the individual's risk preferences necessarily conform to the expected utility principle. We argue that the essence of "Bayesian rationality" is the assignment, correct manipulation, and proper updating of subjective event probablities when evaluating and comparing uncertain prospects, regardless of whether attitudes toward risk satisfy the expected utility property.

Duhemian Themes in Expected Utility Theory

This monographic chapter explains how expected utility (EU) theory arose in von Neumann and Morgenstern, how it was called into question by Allais and others, and how it gave way to non-EU theories, at least among the specialized quarters of decion theory. I organize the narrative around the idea that the successive theoretical moves amounted to resolving Duhem-Quine underdetermination problems, so they can be assessed in terms of the philosophical recommendations made to overcome these problems. I actually follow Duhem's recommendation, which was essentially to rely on the passing of time to make many experiments and arguments available, and evebntually strike a balance between competing theories on the basis of this improved knowledge. Although Duhem's solution seems disappointingly vague, relying as it does on "bon sens" to bring an end to the temporal process, I do not think there is any better one in the philosophical literature, and I apply it here for what it is worth. In this perspective, EU theorists were justified in resisting the first attempts at refuting their theory, including Allais's in the 50s, but they would have lacked "bon sens" in not acknowledging their defeat in the 80s, after the long process of pros and cons had sufficiently matured. This primary Duhemian theme is actually combined with a secondary theme - normativity. I suggest that EU theory was normative at its very beginning and has remained so all along, and I express dissatisfaction with the orthodox view that it could be treated as a straightforward descriptive theory for purposes of prediction and scientific test. This view is usually accompanied with a faulty historical reconstruction, according to which EU theorists initially formulated the VNM axioms descriptively and retreated to a normative construal once they fell threatened by empirical refutation. From my historical study, things did not evolve in this way, and the theory was both proposed and rebutted on the basis of normative arguments already in the 1950s. The ensuing, major problem was to make choice experiments compatible with this inherently normative feature of theory. Compability was obtained in some experiments, but implicitly and somewhat confusingly, for instance by excluding overtly incoherent subjects or by creating strong incentives for the subjects to reflect on the questions and provide answers they would be able to defend. I also claim that Allais had an intuition of how to combine testability and normativity, unlike most later experimenters, and that it would have been more fruitful to work from his intuition than to make choice experiments of the naively empirical style that flourished after him. In sum, it can be said that the underdetermination process accompanying EUT was resolved in a Duhemian way, but this was not without major inefficiencies. To embody explicit rationality considerations into experimental schemes right from the beginning would have limited the scope of empirical research, avoided wasting resources to get only minor findings, and speeded up the Duhemian process of groping towards a choice among competing theories

Properties of optimal forecasts under asymmetric loss and nonlinearity

Evaluation of forecast optimality in economics and Þnance has almost exclusively been conducted under the assumption of mean squared error loss. Under this loss function optimal forecasts should be unbiased and forecast errors serially uncorrelated at the single period horizon with increasing variance as the forecast horizon grows. Using analytical results we show in this paper that all the standard properties of optimal forecasts can be invalid under asymmetric loss and nonlinear data generating processes and thus may be very misleading as a benchmark for an optimal forecast. We establish instead that a suitable transformation of the forecast error- known as the generalized forecast error- possesses an equivalent set of properties

Can expected utility theory explain gambling?

We investigate the ability of expected utility theory to account for simultaneous gambling and insurance. Contrary to a previous claim that borrowing and lending in perfect capital markets removes the demand for gambles, we show expected utility theory with nonconcave utility functions can explain gambling. When the rates of interest and time preference are equal, agents seek to gamble unless income falls in a finite set of values. When they differ, there is a range of incomes where gambles are desired. Different borrowing and lending rates can account for persistent gambling provided the rates span the rate of time preference

Payoff Kinks in Preferences Over Lotteries

This paper identifies two distinct types of payoff kinks that can be exhibited by preference functions over monetary lotteries - "locally separable" vs. "locally nonseparable" - and illustrates their relationship to the payoff and probability derivatives of such functions. Expected utility and Fréchet differentiable preference functions are found to be incapable of exhibiting locally nonseparable payoff kinks; rank-dependent preference functions are incapable of avoiding them