decisions, uncertainty and the brain

TL;DR: The rational actor model is a basic organizing principle in economic theory as mentioned in this paper, and it has been used in many areas of psychology, including behavioral game theory, animal behavior, gene-culture coevolution, and neuroeconomics.

TL;DR: This work suggests that the human mind has been structured by natural selection to use a mental calculus for reckoning uncertainty and making decisions in the face of risk that can be substantially different from probability theory, propositional calculus, or economic rationality.

Abstract: The subjective expected utility (SEU) model rests on very strong assumptions about the consistency of decision-making across a wide range of situations. The descriptive validity of these assumptions has been extensively challenged by behavioral psychologists during the last few decades, and the normative validity of the assumptions has also been reappraised by many statisticians, philosophers, and economists, motivating the development of more general utility theories and decision models. These generalized models are characterized by features such as imprecise probabilities, nonlinearly weighted probabilities, source-dependent risk attitudes, and state-dependent utilities, permitting the pattern of the decision maker’s behavior to change with the decision context and to perhaps satisfy the usual SEU assumptions only locally. Recent research in the emerging field of neuroeconomics sheds light on the physiological basis of decision making, the nature of preferences and beliefs, and interpersonal differences in decision competence. These findings do not necessarily invalidate the use of SEU-based decision analysis tools, but they suggest that care needs to be taken to structure preferences and to assess beliefs and risk attitudes in a manner that is appropriate for the decision and also for the decision maker. Advances: Extensions of SEU Page 2 of 43 Ch 14 060226 V05 CONTENTS The SEU Model and Its Assumptions Incomplete Preferences, Imprecise Probabilities and Robust Decision Analysis Allais’ Paradox, Transformed Probabilities, and Rank-Dependent Utility Ellsberg’s Paradox, Knightian Decision Theory, Maxmin Expected Utility, and SecondOrder Utility State-Preference Theory, State-Dependent Utility, and Decision Analysis with RiskNeutral Probabilities Neuroeconomics: The Next (and Final?) Frontier The SEU Model and its Assumptions The subjective expected utility (SEU) model provides the conceptual and computational framework that is most often used to analyze decisions under uncertainty. In the SEU model, uncertainty about the future is represented by a set of states of the world, which are mutually exclusive and exhaustive events. Possible outcomes for the decision maker are represented by a set of consequences, which could be amounts of money in the bank or more general “states of the person” such as health, happiness, pleasant or unpleasant experiences, and so on. A decision alternative, known as an act, is defined by an assignment of consequences to states of the world. In the case where the set of states is a finite set (E1, ..., En), an act can be written as a vector x = (x1, ..., xn) where xi is the consequence that is received or experienced in state Ei. The decision maker’s beliefs concerning states of the world are represented by a subjective probability distribution p = (p1, ..., pn), where pi is the probability of Ei, and her values for consequences are Advances: Extensions of SEU Page 3 of 43 Ch 14 060226 V05 represented by a utility function v(x), in terms of which the value she assigns to an act x for decision-making purposes is its subjective expected utility: SEU(x) = Ep[v(x)] = 1 n i= ∑ pi v(xi). (1) This recipe for rational decision making has ancient roots: it was first proposed by Daniel Bernoulli (1738) to explain aversion to risk in problems of gambling and insurance as well as to solve the famous St. Petersburg Paradox. Bernoulli recognized that different individuals might display different risk attitudes, especially if they differ in wealth, and he recommended using the logarithmic utility function v(x) = log(x) because it implies that “the utility resulting from any small increase in wealth will be inversely proportionate to the quantity of goods previously possessed.” The idea of seeking to maximize the expected value of a utility function— particularly a logarithmic one—was discarded and even ridiculed by later generations of economists, who doubted that utility could ever be measured on a cardinal numerical scale. (See Stigler 1950 for an excellent historical review.) However, it was revived and rehabilitated in dramatic fashion by von Neumann and Morgenstern (1944/1947) and Savage (1954), who showed that the expected-utility model could be derived from simple and seemingly reasonable axioms of consistent preferences under risk and uncertainty, in which a pivotal role is played by an independence condition known as the “sure-thing principle” (Fishburn and Wakker 1995). Von Neumann and Morgenstern considered the special case in which states of the world have objectively known probabilities (as in games of chance), and Savage extended the model to include situations where probabilities are subjectively determined by the decision maker. The key axioms of Savage are as follows. (P1) Preferences among acts are weakly ordered, i.e., complete and transitive. (P2) Preferences satisfy the independence condition (sure-thing principle) which requires that if two acts “agree” (i.e., yield the same consequence) in some Advances: Extensions of SEU Page 4 of 43 Ch 14 060226 V05 state, it doesn’t matter how they agree there. This permits a natural definition of conditional preferences, namely that x is preferred to y conditional on event E if x is preferred to y and they agree in the event not-E. (P3) Preferences among consequences are state-independent in the sense that conditional preferences between “constant” acts (those which yield the same consequence in all states) do not depend on the conditioning event. (P4) Events can be unambiguously ordered by probability in the following way: if x and y are any two consequences such that x is preferred to y (as a constant act), and if the act that yields x if E and y if not-E is preferred to the act that yields x if F and y if not-F, then E is revealed to be at least as probable as F. These four substantive behavioral postulates, together with a few purely technical assumptions, imply the SEU formula. (Other systems of axioms also lead to SEU, e.g., Anscombe and Aumann 1963, Wakker 1989.) The SEU model had a revolutionary impact on statistical decision theory and social science in the 1950’s and 1960’s, providing the mathematical foundation for a broad range of social and economic theories under the general heading of “rational choice,” including the development of Bayesian methods of statistical inference, the emergence of decision analysis as an applied science taught in engineering and business schools, the establishment of game theory as a foundation for microeconomics, and the development of expected-utility-based models of portfolio optimization and competitive equilibria in asset markets by finance theorists. The logarithmic utility function originally proposed by Bernoulli even came to be hailed as the “premier” utility model for investors in financial markets (Rubinstein 1976). The SEU model also had its early detractors, most notably Allais (1953) and Ellsberg (1961) who constructed famous paradoxes consisting of thought-experiments in which most individuals willingly violate the independence axiom (Savage’s P2), but nevertheless for several Advances: Extensions of SEU Page 5 of 43 Ch 14 060226 V05 decades it was widely accepted as both an appropriate normative standard and a useful descriptive model, as if it were self-evident that a thinking person should be an expected-utility maximizer. That consensus began to break down in the late 1970’s, however, as an emerging body of behavioral decision research showed that subjects in laboratory experiments display an array of predictable “heuristics and biases” that are inconsistent with SEU theory, even beyond the paradoxical behavior identified by Allais and Ellsberg. The normative status of the SEU model was also questioned, insofar as violations of completeness or independence do not necessarily expose a decision maker to exploitation as long as she respects more fundamental principles such as dominance and transitivity. In response to these developments, decision theorists and economists proceeded to extend the SEU model by weakening various of its axioms, giving rise to a host of theories of “non-expected utility” (e.g., Kahneman and Tversky 1979, Machina 1982, Fishburn 1982, Quiggin 1982, Loomes and Sugden 1982, Bell 1982, 1985, Chew 1983, Luce and Narens 1985, Yaari 1987, Becker and Sarin 1987, Schmeidler 1989, Gilboa and Schmeidler 1989, Tversky and Kahneman 1992, Wakker and Tversky 1993). This chapter provides a non-technical summary of some extensions of the SEU model which appear most relevant to decision analysis and which can be defended normatively as well as descriptively. For more breadth and technical depth, the recent surveys by Starmer (2000), Sugden (2004) and Ulrich (2004) are highly recommended; a vast on-line bibliography has been compiled by Wakker (2005). Incomplete Preferences, Imprecise Probabilities and Robust Decision Analysis Arguably the strongest and most unrealistic assumption of the SEU model is that the decision maker’s preferences are complete, meaning that between any two alternatives that might be Advances: Extensions of SEU Page 6 of 43 Ch 14 060226 V05 proposed, no matter how complicated or hypothetical or even counterfactual, the decision maker is always able to say either that she strictly prefers one to the other or else she is exactly indifferent between them: she is never “undecided.” This assumption is somewhat antithetical to the spirit of decision analysis, which provides tools for constructing preferences where they may not already exist. The completeness assumption also amplifies the effects of all the other axioms, making it relatively easy to generate examples in which they are violated. Incompleteness of preferences is implicitly acknowledged whenever ad hoc methods of sensitivity analysis are applied to subjectively-assessed probabilities and utilities, which are often among the most controversial and hard-to-measure parameters in a decision model

TL;DR: In this paper, Camerer and Loewenstein argue that behavioral economics complements standard theory rather than promising to supplant it, and they generally join the more florid critics in supposing that microeconomics is bound to improve its empirical relevance to the extent that it substitutes the study of people for that of abstract economic agents.