The even-swap method builds the dominance relations between alternatives based on trade-offs between criteria. This dominance relation is affected by the order (i.e., the decision path) in which decision makers put alternatives and criteria into trade-offs. Such a phenomenon is referred to as path dependence. Although some psychological factors contributing to path dependence have been identified, studies on the causes and conditions that lead to path dependence are still lacking, making it difficult to quantify the influence of decision path on dominance relations. This paper reveals that the trade-off process in the even-swap method resembles the matching process used to generate indifference curves. Inspired by this finding, indifference curves are used to analyze the trade-off process and obtain trade-off curves. Based on these trade-off curves, a mathematical definition of path dependence is proposed, which serves as the occurrence condition of path dependence in the even-swap method. A sensitivity analysis is conducted to examine the effects of risk attitude, loss attitude, and inconsistent reference points on path dependence. The results reveal two interdependent necessary conditions for path dependence: (1) the presence of kinks in the utility function and (2) the use of inconsistent reference points across trade-offs. Furthermore, path dependence is found to be more likely when both evaluation distances are less than 1 and evaluation gap ratios approach 1. Finally, two practical insights are provided to help avoid path dependence. Funding: This research was supported by the Sichuan Science and Technology Program [Grants 2025NSFSC1961, 2025NSFJQ0072], the National Natural Science Foundation of China [Grants 72171158, 72371173], and the Team Development Program at Sichuan University.

Determining one-dimensional utility functions for each objective in multiattribute utility theory takes time and effort from decision makers. They must consider including a decreasing or increasing marginal utility and/or their relative risk attitude, resulting in a nonlinear shape. This assessment is prone to errors and distortions. We analyze to what extent a linear transformation of one-dimensional utility functions compromises the quality of the decision. Therefore, we examine the impact of one-dimensional utility functions on the final ranking of alternatives in practice, focusing on three aspects: the use of (non)linear utility functions, their impact on the ranking of alternatives, and the stability of best alternatives concerning utility differences of alternatives assuming linear transformation. We examine 2,536 carefully modeled personal decisions analyzed by students with the decision support tool Entscheidungsnavi. Our results show that 95.9% of the participants used at least one nonlinear utility function in their decision, and 76.4% of all objectives were evaluated with nonlinear utility functions. Simplifying preference-accurate utility functions with linearization led to a rank reversal of the best alternative in 15.5% of the decisions. The top-three set of alternatives changed in 14% of the decisions. In 98.8% of the decisions, the best alternative could be found in the top three alternatives ranked under linearity. Based on our results, we recommend determining the utility functions preference-accurately using (non)linearity to model the decision as precisely as possible, especially for important decisions. However, no rank reversal for the best alternative was detected in our data set from an absolute utility difference greater than 0.27 between the best and second best alternatives under linearity. In these cases, assuming linear utility functions is useful if decision makers want to save time and effort. Supplemental Material: The online appendix is available at https://doi.org/10.1287/deca.2024.0317 .

Prior studies suggest that large language models (LLMs) act prosocially in simplified game-theoretic settings, but whether such behavior reflects stable objectives or context-driven patterns is unclear. We test whether LLMs exhibit fairness when choices follow complex tasks or take place in more complex decision environments. We hypothesize that problem complexity and mathematical prompts increase the LLM’s weight on prioritizing self-interests by activating responses geared toward calculation and rationality. We operationalize our theory using a quantal response framework and conducted a series of experiments with GPT-4, GPT-4o, and o3-mini as decision makers to test our hypotheses. In Study 1, models played Dictator and Ultimatum games following a series of unrelated problems that varied in context and difficulty. Study 2 was a sequential supply chain game that mirrors key aspects of the Ultimatum game regarding fairness concerns, but with added complexity. In Study 1, simple prompts produced nearly equal splits, because of fairness norms and preference for equity. However, complex math prompts invoked rational profit maximization logic to reduce allocation offers. In the pricing game, the models prioritized self-interested pricing but differed in decision execution. GPT-4 and GPT-4o selected lower prices because of random errors and heuristic responses rather than fairness concerns. In contrast, o3-mini consistently derived the profit-maximizing solution. Fairness in LLM responses is context sensitive and often suppressed by task characteristics that trigger goal-directed responses. Thus, researchers and developers must assess social preferences in more complex scenarios. Moreover, our research shows that utility-based models that incorporate bounded rationality and fairness capture core patterns in LLM behavior and yield testable predictions, supported by both choice data and model-generated text. History: This paper has been accepted for the Decision Analysis Special Issue on the Implications of Advances in Artificial Intelligence for Decision Analysis. Funding: The authors also acknowledge the financial support of UNSW Business School and the National Natural Science Foundation of China [Grant 72403226]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/deca.2025.0396 .

This paper explores the efficacy of generative artificial intelligence (GenAI) for value-focused thinking, specifically the ability to generate high-quality sets of objectives for organizational or policy decisions. Overall, we find that most of the GenAI objectives are viable individually, but the sets as a whole are highly flawed. They often include nonessential considerations, omitting important ones. In addition, they are redundant and nondecomposable, often because of a tendency to include means objectives even when explicitly instructed not to. However, the sets of objectives can be improved by implementing best practices in prompting and with decision analysis (DA) expertise. The results provide further evidence of the importance of a human in the loop; in this case, GenAI tools are helpful for brainstorming objectives, but an expert with a background in decision analysis is needed before the results are used to support decision making. To facilitate this, a four-step approach incorporating the relative strengths of both GenAI and decision analysts is presented and demonstrated. History: This paper has been accepted for the Decision Analysis Special Issue on the Implications of Advances in Artificial Intelligence for Decision Analysis. Supplemental Material: The online appendix is available at https://doi.org/10.1287/deca.2025.0387 .

Proof in financial economics reveals how investors (incoming buyers) in a rationally priced market perceive a higher expected utility investment when the payoff from the risky asset has higher variance. The asset’s lower market price more than compensates for its higher risk. Because better information tends to reduce payoff variance, investors can prefer that markets be less informed—that is the paradox. The obvious retort is that less information can mean ill-informed prices and investments, and consequent losses. To grow wealth, investors prefer that the market is sufficiently well informed to allow accurate parameter estimation but not so well informed that there is little remaining payoff variance and hence no attractive investment opportunity. The “ideal investment” is a bet on a fair coin, because the probability of winning is not only “known,” it is known to be 0.5, leaving the payoff from the bet with maximum possible variance.

This research considers Bayesian decision-analytic approaches toward the traversal of an uncertain graph. Namely, a traveler progresses over a graph in which rewards are gained upon a node’s first visit, and costs are incurred for every edge traversal. The traveler knows the graph’s adjacency matrix and the starting position but does not know the rewards and costs. The traveler is a Bayesian who encodes his beliefs about these values using a Gaussian process prior and who seeks to maximize his expected utility over these beliefs. Adopting a decision-analytic perspective, we develop sequential decision-making solution strategies for this coupled information-collection and network-routing problem. We show that the problem is NP-hard and derive properties of the optimal walk. These properties provide heuristics for the traveler’s problem that balance exploration and exploitation. We provide a practical case study focused on the use of unmanned aerial systems for public safety and empirically study policy performance in myriad Erdös–Rényi settings. Funding: This work was supported by the Office of Naval Research [Grant 6000012277] and the Air Force Office of Scientific Research [Grant 21RT0867].

Classic risk sharing results determine the optimal share of each member in a group that faces a present deal by maximizing the sum of expected utilities of the group members. For decision-makers with exponential utility functions, this formulation is equivalent to maximizing the sum of certain equivalents of the group members. This paper investigates the effects of time preference and different (but constant) risk tolerances among the group members on the individual shares when the payoff is received at a future time period. The analysis first defines several concepts: (i) a group future risk tolerance to be used for valuing the certain equivalent of future payoffs, (ii) a group time preference compounding factor that takes into account the time preference of individuals in the group, and (iii) a group present risk tolerance with time preference by which the partnership should operate for the discounted value of future deals. The results show that if the individuals in a group have the same time preference, then the classic risk sharing results still apply. However, when individuals have different time preferences, then the optimal shares of the individuals are modified by two components; the first depends on the ratio of the individual time preference compounding factor to the group time preference compounding factor, and the second depends on the surety of the deal multiplied by the group future risk tolerance. Several examples illustrate the results.

Crises faced by regional or national governments are usually caused by either natural or human disasters or by the actions of terrorists or other nations. Decision making in the face of a crisis is difficult because the context typically is complex, and decision makers often have insufficient time or information to thoughtfully make decisions that will manage the crisis well. As a result, they often rely on brief discussions and past experiences that omit key dimensions of the crisis, which results in selection of an inferior response alternative. This article describes concepts and procedures to guide the initial phases of planning for crises so that if and when a crisis occurs, a proactively developed framework provides a sound foundation for quickly structuring decisions and implementing more detailed analyses in advance of taking specific crisis-response actions. Case-study examples are used to illustrate three main elements of our suggested approach: identifying the main dimensions of the decisions to be faced, articulating the objectives that are to be achieved, and generating a set of potentially desirable alternatives to best achieve these objectives. Although the decision analysis and behavioral science methods that we rely on are not novel, proactive structuring of crisis decisions that likely will need to be made quickly has been given only limited attention by analysts and decision makers. Improved recognition of the importance of decision-focused proactive planning should result in better decisions when a crisis occurs, leading to a reduction in the adverse consequences for countries and their citizens. Funding: This work was supported by Ben Delo and Longview Philanthropy.

Anchoring bias refers to the human tendency to rely heavily on an initial piece of information when making judgments. This bias has significant implications for decision analysis methods that rely on human judgments. This study examines the influence of anchoring bias in the value function elicitation step of the multiattribute value theory, specifically within the midvalue splitting procedure. We hypothesize that the starting point provided by the analyst during elicitation creates a bias in decision makers’ judgments, leading to distorted value functions and ultimately affecting decision outcomes. We also hypothesize that counter-anchoring and avoiding the use of anchors mitigate the effect of anchoring bias. To test the hypotheses, we designed an experiment and collected data from 320 subjects. The findings show that the starting point in the midvalue splitting procedure could change the attribute-specific value functions and, consequently, the overall value of the alternatives. Additionally, two debiasing strategies, counter-anchoring and avoiding the use of anchors, were found to be effective in reducing the effect of anchoring bias. The implications of this study can extend to other structured value function elicitation methods. Supplemental Material: The online appendix is available at https://doi.org/10.1287/deca.2024.0308 .

Many practitioners consider decision analysis as a sociotechnical discipline, with probability, utility, and trade-offs as the core components of a model that enables an accountable decision maker experiencing a sense of unease about the present to explore different assumptions about the future and develop a plan about the way forward for the organization. The decision analyst acts as a process consultant, working with the decision maker and key players as a problem solver and applying any of five structural and five content ingredients of decision analysis in building a requisite model that is sufficient in form and content to resolve the problem while acting as a transitional object, which holds and contains the decision maker’s unease and anxiety about the future. Ten social skills that enable the decision analyst to serve as a process consultant are explained. Six case studies representing problem types for evaluating options, allocating resources, bargaining and negotiating, choosing and deciding, managing risk, and revising opinion demonstrate the many ways that their acting as a transitional object enables exploring the future. Funding: This work was supported by Facilitations Ltd.