Humans and animals make inferences about the world under limited time and knowledge. In contrast, many models of rational inference treat the mind as a Laplacean Demon, equipped with unlimited time, knowledge, and computational might. Following H. Simon’s notion of satisficing, the authors have proposed a family of algorithms based on a simple psychological mechanism: one reason decision making. These fast and frugal algorithms violate fundamental tenets of classical rationality: They neither look up nor integrate all information. By computer simulation, the authors held a competition between the satisficing “Take The Best ” algorithm and various “rational ” inference procedures (e.g., multiple regression). The Take The Best algorithm matched or outperformed all competitors in inferential speed and accuracy. This result is an existence proof that cognitive mechanisms capable of successful performance in the real world do not need to satisfy the classical norms of rational inference. Organisms make inductive inferences. Darwin (1872/1965) observed that people use facial cues, such as eyes that waver and lids that hang low, to infer a person’s guilt. Male toads, roaming through swamps at night, use the pitch of a rival’s croak to infer its size when deciding whether to fight (Krebs & Davies, 1987). Stock brokers must make fast decisions about which of several stocks to trade or invest when only limited information is available. The list goes on. Inductive

This study tests between two modern theories of decision making. Rank- and sign-dependent utility (RSDU) models, including cumulative prospect theory (CPT), imply stochastic dominance and two cumulative independence conditions. Configural weight models, with parameters estimated in previous research, predict systematic violations of these properties for certain choices. Experimental data systematically violate all three properties, contrary to RSDU but consistent with configural weight models. This study also tests whether violations of stochastic dominance can be explained by violations of transitivity. Violations of transitivity may be evidence of a dominance detecting mechanism. Although some transitivity violations were observed, most choice triads violated stochastic dominance without violating transitivity. Judged differences between gambles were not consistent with the CPT model. Data were not consistent with the editing principles of cancellation and combination. The main findings are interpreted in terms of coalescing, the principle that equal outcomes can be combined in a gamble by adding their probabilities. RSDU Address correspondence and reprint requests to Michael H. Birnbaum, Department of Psychology,

Subjects judged the values of lotteries from 3 points of view: the highest price that a buyer should pay, the lowest price that a seller should accept, and the "fair " price. The rank order of judgments changed as a function of point of view. Data also showed violations of branch independence and monotonicity (dominance). These findings pose difficulties for nonconfigural theories of decision making, such as subjective expected utility theory, but can be described by configural-weight theory. Configural weighting is similar to rank-dependent utility theory, except that the weight of the lowest outcome in a gamble depends on the viewpoint, and 0-valued outcomes receive differential weighting. Configural-weight theory predicted the effect of viewpoint, the violations of branch independence, and the violations of monotonicity, using a single scale of utility that is independent of the lottery and the point of view. In order to study how people evaluate and choose among alternatives, experimental psychologists have investigated judgments of lotteries. With lotteries, one can manipulate what appear to be crucial ingredients in judgment and decision making: the alternatives, the outcomes, and probabilities of the outcomes. Gambles therefore seem to provide a fruitful paradigm for the investigation of decisions (Edwards, 1954;

ited only to students. Perhaps students do not understand probability or misunderstand the task for some other reason. I wanted to test people holding doctorate degrees who had read at least one book or scientific article on decision making. 1 California State University, Fullerton and Decision Research Center, Fullerton, USA. E--mail: mbirnbaum@fullerton.edu URL: http://psych.fullerton.edu/mbirnbaum/home.htm This research was supported by National Science Foundation Grants, SBR-9410572 and SES 99-86436. I thank Jonathan Baron, David Budescu, and an anonymous reviewer for helpful comments on the manuscript. 24 Michael H. Birnbaum From my previous experience with studies of experts (Birnbaum & Hynan, 1986; Birnbaum & Stegner, 1981), I was aware of the difficulties and costs of recruiting and testing by postal mail. In such a survey, one must pay expenses of printing materials, addressing the envelopes, and postage for mailing the packets eac

SUNY at Stony Brook

Quality-adjusted life years (QALY) utility models are multiattribute utility models of survival duration and health quality. This paper formulates six classes of QALY utility models and axiomatizes these models under expected utility (EU) and rank-dependent utility (RDU) assumptions. The QALY models investigated in this paper include the standard linear QALY model, the power and exponential multiplicative models, and the general multiplicative model. Emphasis is placed on a preference assumption, the zero condition, that greatly simplifies the axiomatizations under EU and RDU assumptions. The RDU axiomatizations of QALY models are generally similar to their EU counterparts, but in some cases, they require modification because linearity in probability is no longer assumed, and rank dependence introduces asymmetries between the domains of better-than-death health states and worsethan-death health states. 1999 Academic Press This paper concerns the foundations of quality-adjusted life years (QALY) utility models. QALY utility models are widely used in the expected utility analysis of health decisions because they provide an outcome measure that integrates the duration and quality of survival. Before discussing the specifics of these models, it will be helpful to motivate the discussion by describing the role played by QALY utility models in health decision analysis (Weinstein et al., 1980; Sox, Blatt,

In order to investigate derived scales for the utility, or subjective value of money, subjects were instructed to perform four tasks: in two tasks, they judged “ratios” and “differences” of strengths of preference for monetary amounts; in two other tasks, they judged the values of gambles from buyer’s or seller’s points of view. The two arrays of data for “ratios” and “differences” were consistent with the hypothesis that most subjects used only one operation to compare monetary amounts, although a few subjects appeared to use two operations. The buyer’s and seller’s prices would lead to two different utility functions for money under expected utility theory, subjective expected utility theory, or any theory that is additive across outcomes. However, configural-weight utility theory can predict these changes in rank order with an invariant utility function, by postulating that the configural weight of the smaller amount depends on point of view. The data also reveal systematic violations of dominance (monotonicity) that can be described by assuming that the configural weight of zero, when it is the lower value, has smaller weight at low probabilities than nonzero outcomes. Disregarding the minority of subjects who appeared to utilize two operations for judging “ratios ” and “differences” in utility, the majority of the data can be well-approximated using a single scale of utility, the subtractive model for “ratio” and “difference” comparisons, and the configurai weight, rank-dependent model for buyer’s and seller’s prices.

During the last 25 years, prospect theory and its successor, cumulative prospect theory, replaced expected utility as the dominant descriptive theories of risky decision making. Although these models account for the original Allais paradoxes, 11 new paradoxes show where prospect theories lead to self-contradiction or systematic false predictions. The new findings are consistent with and, in several cases, were predicted in advance by simple “configural weight ” models in which probability-consequence branches are weighted by a function that depends on branch probability and ranks of consequences on discrete branches. Although they have some similarities to later models called “rank-dependent utility, ” configural weight models do not satisfy coalescing, the assumption that branches leading to the same consequence can be combined by adding their probabilities. Nor do they satisfy cancellation, the “independence ” assumption that branches common to both alternatives can be removed. The transfer of attention exchange model, with parameters estimated from previous data, correctly predicts results with all 11 new paradoxes. Apparently, people do not frame choices as prospects but, instead, as trees with branches.

The author outlines a radically dfferent decision-making model form the one widely used in Economics and in Psychology. Accordingly, most choices are made on the basis of emotional involvements and value commitments. Information processing is often excluded. In other areas of choices, emotions and values allow for some subsets of options to be rationally considered but ‘color ’ them and/or short cut the deliberations. In a still other subset emotion/values require rational decision-malung. Emotions and values are not necessarily disruptive; they have positive functions. Cognitivists ’ objections to the concept of emotions are responded to. Problems of operationalization are raised. The question, if the concepts of emotions and values can be incorporated into the neoclassical paradigm, is explored. 1. Normative-affective persons Intellectual circles in Europe were preoccupied for more than a century shadow boxing with the ghost of Karl Marx, trying again and again to show that history is not dominated by economic or materialistic factors, that ideas matter. Similarly, social scientists and attending intellectuals, on both sides of the Atlantic Ocean, have been preoccupied- and still are- with extolling, questioning, and attempting to shore up the notion of Rational Man (or homoeconomicus). Indeed, even those who challenge this notion, often define their position in * For a more extensive treatment of this subject, see Etzioni (1988).

This paper characterizes the conditions for risk aversion in cumulative prospect theory where risk aversion is defined in the strong sense of Rothschild and Stiglitz (1970). Under weaker assumptions than differentiability we show that risk aversion implies convex weighting functions for gains and for losses but not necessarily a concave utility function. Also, we investigate the exact relationship between loss aversion and risk aversion. We illustrate the analysis by considering two special cases of cumulative prospect theory and show that risk aversion and convex utility may coexist.