A critique of benchmark theory

Philosophical Review, 2010

It is a platitude among decision theorists that agents should choose their actions so as to maximize expected value. But exactly how to define expected value is contentious. Evidential decision theory (henceforth EDT), causal decision theory (henceforth CDT), and a theory proposed by Ralph Wedgwood that I will call benchmark theory (BT) all advise agents to maximize different types of expected value. Consequently, their verdicts sometimes conflict. In certain famous cases of conflict-medical Newcomb problems-CDT and BT seem to get things right, while EDT seems to get things wrong. In other cases of conflict, including some recent examples suggested by Egan 2007, EDT and BT seem to get things right, while CDT seems to get things wrong. In still other cases, EDT and CDT seem to get things right, while BT gets things wrong.

2004

The theory of rational choice can be interpreted in several ways. One can regard the theory as a representing the choices of agents. The theory is interpreted as an empirical hypothesis for further research. Alternatively, one can regard the theory as an axiomatic modeling assumption for social theory. However, in this essay I will not discuss these descriptive and predictive interpretations of the theory. I will be concerned with the normative interpretation of the theory. On this interpretation the theory of rational choice is a systematic account of how agents ought to choose so as to realize their goals or preferences. The theory is, therefore, instrumentalist. The theory is neutral with regards to the goals or preferences of the agent. It takes these as a given input for its recommendations.

The Nash equilibrium paradigm, and Rational Choice Theory in general , rely on agents acting independently from each other. This note shows how this assumption is crucial in the definition of Rational Choice Theory. It explains how a consistent Alternate Rational Choice Theory, as suggested by Jean-Pierre Dupuy, can be built on the exact opposite assumption, and how it provides a viable account for alternate, actually observed behavior of rational agents that is based on correlations between their decisions. The end goal of this note is threefold: (i) to motivate that the Perfect Prediction Equilibrium, implementing Dupuy's notion of projected time and previously called " projected equilibrium " , is a reasonable approach in certain real situations and a meaningful complement to the Nash paradigm, (ii) to summarize common misconceptions about this equilibrium, and (iii) to give a concise motivation for future research on non-Nashian game theory.

Behavioral and Brain Sciences, 2003

Psychological game theory encompasses formal theories designed to remedy game-theoretic indeterminacy and to predict strategic interaction more accurately. Its theoretical plurality entails second-order indeterminacy, but this seems unavoidable. Orthodox game theory cannot solve payoff-dominance problems, and remedies based on interval-valued beliefs or payoff transformations are inadequate. Evolutionary game theory applies only to repeated interactions, and behavioral ecology is powerless to explain cooperation between genetically unrelated strangers in isolated interactions. Punishment of defectors elucidates cooperation in social dilemmas but leaves punishing behavior unexplained. Team reasoning solves problems of coordination and cooperation, but aggregation of individual preferences is problematic. I am grateful to commentators for their thoughtful and often challenging contributions to this debate. The commentaries come from eight different countries and an unusually wide range of disciplines, including psychology, economics, philosophy, biology, psychiatry, anthropology, and mathematics. The interdisciplinary character of game theory and experimental games is illustrated in Lazarus's tabulation of more than a dozen disciplines studying cooperation. The richness and fertility of game theory and experimental games owe much to the diversity of disciplines that have contributed to their development from their earliest days. The primary goal of the target article is to argue that the standard interpretation of instrumental rationality as expected utility maximization generates problems and anomalies when applied to interactive decisions and fails to explain certain empirical evidence. A secondary goal is to outline some examples of psychological game theory, designed to solve these problems. Camerer suggests that psychological and behavioral game theory are virtually synonymous, and I agree that there is no pressing need to distinguish them. The examples of psychological game theory discussed in the target article use formal methods to model reasoning processes in order to explain powerful intuitions and empirical observations that orthodox theory fails to explain. The general aim is to broaden the scope and increase the explanatory power of game theory, retaining its rigor without being bound by its specific assumptions and constraints. Rationality demands different standards in different domains. For example, criteria for evaluating formal arguments and empirical evidence are different from standards of rational decision making (Manktelow & Over 1993; Nozick 1993). For rational decision making, expected utility maximization is an appealing principle but, even when it is combined with consistency requirements, it does not appear to provide complete and intuitively convincing prescriptions for rational conduct in all situations of strategic interdependence. This means that we must either accept that rationality is radically and permanently limited and riddled with holes, or try to plug the holes by discovering and testing novel principles. In everyday life, and in experimental laboratories, when orthodox game theory offers no prescriptions for choice, people do not become transfixed like Buridan's ass. There are even circumstances in which people reliably solve problems of coordination and cooperation that are insoluble with the tools of orthodox game theory. From this we may infer that strategic interaction is governed by psychological game-theoretic principles that we can, in principle, discover and understand. These principles need to be made explicit and shown to meet minimal standards of coherence, both internally and in relation to other plausible standards of rational behavior. Wherever possible, we should test them experimentally. In the paragraphs that follow, I focus chiefly on the most challenging and critical issues raised by commentators. I scrutinize the logic behind several attempts to show that the problems discussed in the target article are spurious or that they can be solved within the orthodox theoretical framework, and I accept criticisms that appear to be valid. The commentaries also contain many supportive and elaborative observations that speak for themselves and indicate broad agreement with many of the ideas expressed in the target article. I am grateful to Hausman for introducing the important issue of rational beliefs into the debate. He argues that games can be satisfactorily understood without any new interpretation of rationality, and that the anomalies and problems that arise in interactive decisions can be eliminated by requiring players not only to choose rational strategies but also to hold rational beliefs. The only requirement is that subjective probabilities "must conform to the calculus of probabilities." Rational beliefs play an important role in Bayesian decision theory. Kreps and Wilson (1982b) incorporated them into a refinement of Nash equilibrium that they called perfect Bayesian equilibrium, defining game-theoretic equilibrium for the first time in terms of strategies and beliefs. In perfect Bayesian equilibrium, strategies are best replies to one another, as in standard Nash equilibrium, and beliefs are sequentially rational in the sense of specifying actions that are optimal for the players, given those beliefs. Kreps and Wilson defined these notions precisely using the conceptual apparatus of Bayesian decision theory, including belief updating according to Bayes' rule. These ideas prepared the ground for theories of rationalizability (Bernheim 1984; Pearce 1984), discussed briefly in section 6.5 of the target article, and the psychological games of Geanakoplos et al. (1989), to which I shall return in section R7 below. Hausman invokes rational beliefs in a plausible -though I believe ultimately unsuccessful -attempt to solve the payoff-dominance problem illustrated in the Hi-Lo Matching game (Fig. in the target article). He acknowledges that a player cannot justify choosing H by assigning particular probabilities to the co-player's actions, because this leads to a contradiction (as explained in section 5.6 of the target article). 1 He therefore offers the following suggestion: "If one does not require that the players have point priors, then Player I can believe that the probability that Player II will play H is not less than one-half, and also believe that Player II believes the same of Player I. Player I can then reason that Player II will definitely play H, update his or her subjective probability accordingly, and play H." This involves the use of interval-valued (or set-valued) probabilities, tending to undermine Hausman's claim that it "does not need a new theory of rationality." Intervalvalued probabilities have been axiomatized and studied ), but they are problematic, partly because stochastic independence, on which the whole edifice of probability theory is built, cannot be satisfactorily defined for them, and partly because technical problems arise when Bayesian updating is applied to interval-valued priors. Leaving these problems aside, the proposed solution cleverly eliminates the contradiction that arises when a player starts by specifying a point probability,

arXiv: General Economics, 2020

This paper presents a novel approach to analyze human decision-making that involves comparing the behavior of professional chess players relative to a computational benchmark of cognitively bounded rationality. This benchmark is constructed using algorithms of modern chess engines and allows investigating behavior at the level of individual move-by-move observations, thus representing a natural benchmark for computationally bounded optimization. The analysis delivers novel insights by isolating deviations from this benchmark of bounded rationality as well as their causes and consequences for performance. The findings document the existence of several distinct dimensions of behavioral deviations, which are related to asymmetric positional evaluation in terms of losses and gains, time pressure, fatigue, and complexity. The results also document that deviations from the benchmark do not necessarily entail worse performance. Faster decisions are associated with more frequent deviations ...

Analyse & Kritik

The increasingly wide spread use of RCM, rational choice modeling, and RCT, rational choice theory, in disciplines like economics, law, ethics, psychology, sociology, political science, management facilitates interdisciplinary exchange. This is a great achievement. Yet it nurtures the hope that a unified account of rational (inter-)active choice making might arise from ‘reason’ in (a priori) terms of intuitively appealing axioms. Such ‘rationalist’ characterizations of rational choice neglect real human practices and empirical accounts of those practices. This is theoretically misleading and practically dangerous. Searching for a wide reflective equilibrium, WRE, on RCT in evidence-oriented ways can explicate ‘rational’ without rationalism.

Dao, 2003

Synthese, 2012

Games, 2010

Game and decision theory start from rather strong premises. Preferences, represented by utilities, beliefs represented by probabilities, common knowledge and symmetric rationality as background assumptions are treated as "given." A richer language enabling us to capture the process leading to what is "given" seems superior to the stenography of decision making in terms of utility cum probability. However, similar to traditional rational choice modeling, boundedly rational choice modeling, as outlined here, is far from being a "global" theory with empirical content; rather it serves as a tool to formulate "local" theories with empirical content.

The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk (like Pascal's Mugging), and intolerably paradoxical in cases like the St. Petersburg and Pasadena games. In this paper I show that, under certain conditions, stochastic dominance reasoning can capture most of the plausible implications of expectational reasoning while avoiding most of its pitfalls. Specifically, given sufficient background uncertainty about the choiceworthiness of one's options, many expectation-maximizing gambles that do not stochastically dominate their alternatives "in a vacuum" become stochastically dominant in virtue of that background uncertainty. But, even under these conditions, stochastic dominance will generally not require agents to accept extreme gambles like Pascal's Mugging or the St. Petersburg game. The sort of background uncertainty on which these results depend looks unavoidable for any agent who measures the choiceworthiness of her options in part by the total amount of value in the resulting world. At least for such agents, then, stochastic dominance offers a plausible general principle of choice under uncertainty that can explain more of the apparent rational constraints on such choices than has previously been recognized.