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This paper is an update of a paper that five of us published in 1992. The areas of multiple criteria decision making (MCDM) and multiattribute utility theory (MAUT) continue to be active areas of management science research and application. This paper extends the history of these areas and discusses topics we believe to be important for the future of these fields.

In this paper we study resource allocation problems that involve multiple self-interested parties or players and a central decision maker. We introduce and study the price of fairness, which is the relative system efficiency loss under a \"fair\" allocation assuming that a fully efficient allocation is one that maximizes the sum of player utilities. We focus on two well-accepted, axiomatically justified notions of fairness, viz., proportional fairness and max-min fairness. For these notions we provide a tight characterization of the price of fairness for a broad family of problems.

Our society is increasingly relying on the digitized, aggregated opinions of others to make decisions. We therefore designed and analyzed a large-scale randomized experiment on a social news aggregation Web site to investigate whether knowledge of such aggregates distorts decision-making. Prior ratings created significant bias in individual rating behavior, and positive and negative social influences created asymmetric herding effects. Whereas negative social influence inspired users to correct manipulated ratings, positive social influence increased the likelihood of positive ratings by 32% and created accumulating positive herding that increased final ratings by 25% on average. This positive herding was topic-dependent and affected by whether individuals were viewing the opinions of friends or enemies. A mixture of changing opinion and greater turnout under both manipulations together with a natural tendency to up-vote on the site combined to create the herding effects. Such findings will help interpret collective judgment accurately and avoid social influence bias in collective intelligence in the future.

We formulate and carry out an analytical treatment of a single-period portfolio choice model featuring a reference point in wealth, S-shaped utility (value) functions with loss aversion, and probability weighting under Kahneman and Tversky's cumulative prospect theory (CPT). We introduce a new measure of loss aversion for large payoffs, called the large-loss aversion degree (LLAD), and show that it is a critical determinant of the well-posedness of the model. The sensitivity of the CPT value function with respect to the stock allocation is then investigated, which, as a by-product, demonstrates that this function is neither concave nor convex. We finally derive optimal solutions explicitly for the cases in which the reference point is the risk-free return and those in which it is not (while the utility function is piecewise linear), and we employ these results to investigate comparative statics of optimal risky exposures with respect to the reference point, the LLAD, and the curvature of the probability weighting. This paper was accepted by Wei Xiong, finance.

Agrowing body of qualitative evidence shows that loss aversion, a phenomenon formalized in prospect theory, can explain a variety of field and experimental data. Quantifications of loss aversion are, however, hindered by the absence of a general preference-based method to elicit the utility for gains and losses simultaneously. This paper proposes such a method and uses it to measure loss aversion in an experimental study without making any parametric assumptions. Thus, it is the first to obtain a parameter-free elicitation of prospect theory's utility function on the whole domain. Our method also provides an efficient way to elicit utility midpoints, which are important in axiomatizations of utility. Several definitions of loss aversion have been put forward in the literature. According to most definitions we find strong evidence of loss aversion, at both the aggregate and the individual level. The degree of loss aversion varies with the definition used, which underlines the need for a commonly accepted definition of loss aversion.

This paper investigates the capacity investment decision of a supplier who solicits private forecast information from a manufacturer. To ensure abundant supply, the manufacturer has an incentive to inflate her forecast in a costless, nonbinding, and nonverifiable type of communication known as \"cheap talk.\" According to standard game theory, parties do not cooperate and the only equilibrium is uninformative-the manufacturer's report is independent of her forecast and the supplier does not use the report to determine capacity. However, we observe in controlled laboratory experiments that parties cooperate even in the absence of reputation-building mechanisms and complex contracts. We argue that the underlying reason for cooperation is trust and trustworthiness. The extant literature on forecast sharing and supply chain coordination implicitly assumes that supply chain members either absolutely trust each other and cooperate when sharing forecast information, or do not trust each other at all. Contrary to this all-or-nothing view, we determine that a continuum exists between these two extremes. In addition, we determine (i) when trust is important in forecast information sharing, (ii) how trust is affected by changes in the supply chain environment, and (iii) how trust affects related operational decisions. To explain and better understand the observed behavioral regularities, we also develop an analytical model of trust to incorporate both pecuniary and nonpecuniary incentives in the game-theoretic analysis of cheap-talk forecast communication. The model identifies and quantifies how trust and trustworthiness induce effective cheap-talk forecast sharing under the wholesale price contract. We also determine the impact of repeated interactions and information feedback on trust and cooperation in forecast sharing. We conclude with a discussion on the implications of our results for developing effective forecast management policies. This paper was accepted by Ananth Iyer, operations and supply chain management.

Reference-dependent preferences have been well accepted in decision sciences, experimental economics, behavioral finance, and marketing. However, we still know very little about how decision makers form and update their reference points given a sequence of information. Our paper provides some novel experiments in a financial context to advance the understanding of reference-point formation over time. Our subjects' reference price is best described as a combination of the first and the last price of the time series, with intermediate prices receiving smaller and nondecaying weights. Hence, reference prices are not recursive. We provide a parsimonious formula to predict the reference points, which we test out-of-sample. The fit of the model is reasonably good. This paper was accepted by George Wu, decision analysis.

This paper deals with a basic issue: How does one approach the problem of designing the \"right\" objective for a given resource allocation problem? The notion of what is right can be fairly nebulous; we consider two issues that we see as key: efficiency and fairness. We approach the problem of designing objectives that account for the natural tension between efficiency and fairness in the context of a framework that captures a number of resource allocation problems of interest to managers. More precisely, we consider a rich family of objectives that have been well studied in the literature for their fairness properties. We deal with the problem of selecting the appropriate objective from this family. We characterize the trade-off achieved between efficiency and fairness as one selects different objectives and develop several concrete managerial prescriptions for the selection problem based on this trade-off. Finally, we demonstrate the value of our framework in a case study that considers air traffic management. This paper was accepted by Yossi Aviv, operations management.

Prospect theory is currently the main descriptive theory of decision under uncertainty. It generalizes expected utility by introducing nonlinear decision weighting and loss aversion. A difficulty in the study of multiattribute utility under prospect theory is to determine when an attribute yields a gain or a loss. One possibility, adopted in the theoretical literature on multiattribute utility under prospect theory, is to assume that a decision maker determines whether the complete outcome is a gain or a loss. In this holistic evaluation , decision weighting and loss aversion are general and attribute-independent. Another possibility, more common in the empirical literature, is to assume that a decision maker has a reference point for each attribute. We give preference foundations for this attribute-specific evaluation where decision weighting and loss aversion are depending on the attributes.

This paper reports on the results of an experimental elicitation at the individual level of all prospect theory components (i.e., utility, loss aversion, and weighting functions) in two decision contexts: situations where alternatives are described as probability distributions and situations where the decision maker must experience unknown probability distributions through sampling before choice. For description-based decisions, our results are fully consistent with prospect theory's empirical findings under risk. Furthermore, no significant differences are detected across contexts as regards utility and loss aversion. Whereas decision weights exhibit similar qualitative properties across contexts typically found under prospect theory, our data suggest that, for gains at least, the subjective treatment of uncertainty in experience-based and description-based decisions is significantly different. More specifically, we observe a less pronounced overweighting of small probabilities and a more pronounced underweighting of moderate and high probabilities for experience-based decisions. On the contrary, for losses, no significant differences were observed in the evaluation of prospects across contexts. This paper was accepted by George Wu, decision analysis.