Combining additive representations on subsets into an overall representation

Many traditional conjoint representations of binary preferences are additively decomposable, or additive for short. An important generalization arises under rank-dependence, when additivity is restricted to cones with a fixed ranking of components from best to worst (comonotonicity), leading to configural weighting, rank-dependent utility, and rank- and sign-dependent utility (prospect theory). This paper provides a general result showing how additive representations on an arbitrary collection of comonotonic cones can be combined into one overall representation that applies to the union of all cones considered. The result is applied to a new paradigm for decision under uncertainty developed by Duncan Luce and others, which allows for violations of basic rationality properties such as the coalescing of events and other framing conditions. Through our result, a complete preference foundation of a number of new models by Luce and others can be obtained. We also show how additive representations on different full product sets can be combined into a representation on the union of these different product sets.     

A Representation Theorem for a Decision Theory With Conditionals

This paper investigates the role of conditionals in hypothetical reasoning and rational decision making. Its main result is a proof of a representation theorem for preferences defined on sets of sentences (and, in particular, conditional sentences), where an agent’s preference for one sentence over another is understood to be a preference for receiving the news conveyed by the former. The theorem shows that a rational preference ordering of conditional sentences determines probability and desirability representations of the agent’s degrees of belief and desire that satisfy, in the case of non-conditional sentences, the axioms of Jeffrey’s decision theory and, in the case of conditional sentences, Adams’ expression for the probabilities of conditionals. Furthermore, the probability representation is shown to be unique and the desirability representation unique up to positive linear transformation. This revised version was published online in June 2006 with corrections to the Cover Date.     

Simplified approaches for multicriteria decision making under uncertainty

The problem of uncertainty in the outcome of decisions has tended to be glossed over by many MCDM methods, with the exception of multiattribute utility theory (MAUT). MAUT does, however, require quite complicated preference elicitations and knowledge of the full multivariate distribution of outcomes. Results from a series of simulation studies indicate that the preference orderings of MAUT are only minimally changed when using a simple additive aggregation of marginal utilities, especially in relation to the natural imprecisions inherent in preference elicitation. It is shown in the simulations that by far the most critical aspect of multicriteria decision analysis under uncertainty is not the form of aggregation, but the correct elicitation of marginal utilities which properly represent decision maker preferences over gambles. We relate the results obtained here to other results on the approximation of distributions by three- or five-point discrete distributions, and suggest that the use of deterministic MCDM methods of any form (not necessarily value function techniques), applied to an extended formulation in which each criterion measure is repeated for three or five ‘scenarios’, can be justified.     

Inferring latent class lexicographic rules from choice data

A lexicographic rule orders multi-attribute alternatives in the same way as a dictionary orders words. Although no utility function can represent lexicographic preference over continuous, real-valued attributes, a constrained linear model suffices for representing such preferences over discrete attributes. We present an algorithm for inferring lexicographic structures from choice data. The primary difficulty in using such data is that it is seldom possible to obtain sufficient information to estimate individual-level preference functions. Instead, one needs to pool the data across latent clusters of individuals. We propose a method that identifies latent clusters of subjects, and estimates a lexicographic rule for each cluster. We describe an application of the method using data collected by a manufacturer of television sets. We compare the predictions of the model with those obtained from a finite-mixture, multinomial-logit model.     

Representation of subjective preferences under ambiguity

The objective of this paper is to show how potentially incomplete preferences of a decision maker (DM) on acts can be modelled formally in a subjective ambiguity perspective. We identify acts as functions from a state space Ω to bounded support (finitely additive) probabilities over a set X of prizes. Then, we characterize preferences over equibounded acts a which have a numerical representation by the family of functionals , where u is a cardinal utility on X (representing the risk attitude of the DM) and Π is a unique pointwise closed convex set of probabilities on all events in Ω (representing the ambiguity perceived by the DM). To this end, in addition to the usual independence and continuity assumptions, we add completeness and dominance for preferences restricted to constant acts; moreover, we consider two other properties (subjective monotonicity and coherence) related with the preferences of a DM who is not able, owing to his partial knowledge, to evaluate any event in Ω.     

Implications of the Dutch Book: Following Ramsey��s axioms

The Dutch Book Argument shows that an agent will lose surely in a gamble (a Dutch Book is made) if his degrees of belief do not satisfy the laws of the probability. Yet a question arises here: What does the Dutch Book imply? This paper firstly argues that there exists a utility function following Ramsey’s axioms. And then, it explicates the properties of the utility function and degree of belief respectively. The properties show that coherence in partial beliefs for Subjective Bayesianism means that the degree of belief, representing a belief ordering, satisfies the laws of probability, and that coherence in preferences means that the preferences are represented by expected utilities. A coherent belief ordering and a utility scale induce a coherent preference ordering; a coherent preference ordering induces a coherent belief ordering which can be uniquely represented by a degree-of-belief function. The preferences (values) and beliefs are both incoherent or disordered if a Dutch Book is made.     

A postulate-based analysis of comparative preference statements

There has been a growing interest in the study of preferences for their utility in solving problems related to decision making. Most of the preference representation languages developed in the literature are based on comparative preference statements since they offer a simple and intuitive way for expressing preferences. They can be further interpreted following different semantics, imparting a greater flexibility on how outcomes can be compared. So far the main objective has been to rank-order the set of outcomes given a set of comparative preference statements and one or several semantics. Tackling this problem from a different angle, we look into the behavioural aspects of the preference semantics and statements by attempting to formalise the intuition behind them using postulates studied in preference logics and non-monotonic reasoning. We select the postulates w.r.t. three criteria: coherence, syntax independence and inference. Thus, our analysis provides a means to determine those properties that are satisfied for a given preference semantics.     

Decomposition of multivariate utility functions in non-additive expected utility theory

In expected utility many results have been derived that give necessary and/or sufficient conditions for a multivariate utility function to be decomposable into lower-dimensional functions. In particular, multilinear, multiplicative and additive decompositions have been widely discussed. These utility functions can be more easily assessed in practical situations. In this paper we present a theory of decomposition in the context of nonadditive expected utility such as anticipated utility or Choquet expected utility. We show that many of the results used in conventional expected utility carry over to these more general frameworks. If preferences over lotteries depend only on the marginal probability distributions, then in expected utility the utility function is additively decomposable. We show that in anticipated utility the marginality condition implies not only that the utility function is additively decomposable but also that the distortion function is the identity function. We further demonstrate that a decision maker who is bivariate risk neutral has a utility function that is additively decomposable and a distortion function q for which q(½) = ½.     

Folded additive structures: A nonpolynomial model of some factorial interactions

A nonpolynomial measurement model for representing nonadditive compositions of stimulus dimensions is presented. This representation, which is referred to as a folded additive structure, permits the decomposition of a behavioral ordering into independent factors in some of the cases where the behavior itself does not directly reflect this independence. Psychologically, this representation corresponds to a model of behavior which assumes that (1) the effect stimulus attributes have on behavior is mediated by a single relevent psychological dimension, (2) the behavioral ordering is single-peaked over this mediating dimension and (3) the mediating dimension has a conjoint additive ordering over a set of relevent stimulus dimensions. Necessary and sufficient tests for folded additive structures are given. In addition, five psychological theories which make these assumptions are discussed.     

The Causal Structure of Utility Conditionals

The psychology of reasoning is increasingly considering agents' values and preferences, achieving greater integration with judgment and decision making, social cognition, and moral reasoning. Some of this research investigates utility conditionals, ‘‘if p then q’’ statements where the realization of p or q or both is valued by some agents. Various approaches to utility conditionals share the assumption that reasoners make inferences from utility conditionals based on the comparison between the utility of p and the expected utility of q. This article introduces a new parameter in this analysis, the underlying causal structure of the conditional. Four experiments showed that causal structure moderated utility‐informed conditional reasoning. These inferences were strongly invited when the underlying structure of the conditional was causal, and significantly less so when the underlying structure of the conditional was diagnostic. This asymmetry was only observed for conditionals in which the utility of q was clear, and disappeared when the utility of q was unclear. Thus, an adequate account of utility‐informed inferences conditional reasoning requires three components: utility, probability, and causal structure.     

Violation of the transitivity axiom may explain why, in empirical studies, a significant number of subjects violate GARP

Most papers using experimental data find that a significant number of agents are not utility function maximizers. Using three experimental datasets, we provide empirical evidence that these violations of utility function maximizing behavior are simply generated by a violation of the preference transitivity axiom. Moreover, we find that 97% of agents’ behavior is consistent with maximization of a generalized utility function called a variable intervals function (which corresponds to a numerical representation of complete-acyclic preferences).     

Basic psychological needs and neurophysiological responsiveness to decisional conflict: an event-related potential study of integrative self processes

Fulfillment of the basic psychological needs for competence, relatedness, and autonomy is believed to facilitate people’s integrative tendencies to process psychological conflicts and develop a coherent sense of self. The present study therefore used event-related potentials (ERPs) to examine the relation between need fulfillment and the amplitude of conflict negativity (CN), a neurophysiological measure of conflict during personal decision making. Participants completed a decision-making task in which they made a series of forced choices according to their personal preferences. Three types of decision-making situations were created on the basis of participants’ unique preference ratings, which were obtained prior to ERP recording: low-conflict situations (choosing between an attractive and an unattractive option), high-conflict approach-approach situations (choosing between two similarly attractive options), and high-conflict avoidance-avoidance situations (choosing between two similarly unattractive options). As expected, CN amplitudes were larger in high- relative to low-conflict situations, and source localization analyses suggested that the anterior cingulate cortex was the generating structure of the CN. Most importantly, people reporting higher need fulfillment exhibited larger CN amplitudes in avoidance–avoidance situations relative to low-conflict situations; to a lesser extent, they also exhibited larger CN amplitudes in approach–approach situations relative to low-conflict situations. By contrast, people reporting lower need fulfillment exhibited CN amplitudes that poorly discriminated the three decision situations. These results suggest that need fulfillment may promote self-coherent functioning by increasing people’s receptivity to and processing of events that challenge their abilities to make efficient, self-congruent choices.     

Accounting for Time Preference in Management Decisions: An Application to Invasive Species

Managers of invasive species seek to prevent and mitigate their impact, which vary in the time horizon over which they are realized. Likewise, stakeholders vary in the time horizons they consider relevant. Agricultural impacts might reasonably be considered over two or three decades, although ecologists typically consider environmental impacts over much longer time frames. Although time preference plays a critical role in decision making, it has largely been ignored in multicriteria analyses. In this study, we examine how time has been treated in previous decision analyses of invasive species management, focusing on the differences between multicriteria and economic cost–benefit analyses. We then outline a method for incorporating time preference information into multicriteria decision analyses to ensure that criteria weights remain a faithful representation of the decision maker's preferences. To illustrate how time preference can be elicited for invasive species problems involving both monetary and nonmonetary consequences, we describe a small empirical study we conducted with a small group of experts and managers. By outlining a way to consider time preference information in multicriteria analyses of invasive species management, we hope to facilitate better decision making that is reflective of the decision maker's true preferences. Copyright © 2013 John Wiley & Sons, Ltd.     

An eye-tracking investigation into readers' sensitivity to actual versus expected utility in the comprehension of conditionals

The successful comprehension of a utility conditional (i.e., an “if p, then q” statement where p and/or q is valued by one or more agents) requires the construction of a mental representation of the situation described by that conditional and integration of this representation with prior context. In an eye-tracking experiment, we examined the time course of integrating conditional utility information into the broader discourse model. Specifically, the experiment determined whether readers were sensitive, during rapid heuristic processing, to the congruency between the utility of the consequent clause of a conditional (positive or negative) and a reader's subjective expectations based on prior context. On a number of eye-tracking measures we found that readers were sensitive to conditional utility—conditionals for which the consequent utility mismatched the utility that would be anticipated on the basis of prior context resulted in processing disruption. Crucially, this sensitivity emerged on measures that are accepted to indicate early processing within the language comprehension system and suggests that the evaluation of a conditional's utility informs the early stages of conditional processing.     

Eye movements reveal the time-course of anticipating behaviour based on complex, conflicting desires

The time-course of representing others’ perspectives is inconclusive across the currently available models of ToM processing. We report two visual-world studies investigating how knowledge about a character’s basic preferences (e.g. Tom’s favourite colour is pink) and higher-order desires (his wish to keep this preference secret) compete to influence online expectations about subsequent behaviour. Participants’ eye movements around a visual scene were tracked while they listened to auditory narratives. While clear differences in anticipatory visual biases emerged between conditions in Experiment 1, post-hoc analyses testing the strength of the relevant biases suggested a discrepancy in the time-course of predicting appropriate referents within the different contexts. Specifically, predictions to the target emerged very early when there was no conflict between the character’s basic preferences and higher-order desires, but appeared to be relatively delayed when comprehenders were provided with conflicting information about that character’s desire to keep a secret. However, a second experiment demonstrated that this apparent ‘cognitive cost’ in inferring behaviour based on higher-order desires was in fact driven by low-level features between the context sentence and visual scene. Taken together, these results suggest that healthy adults are able to make complex higher-order ToM inferences without the need to call on costly cognitive processes. Results are discussed relative to previous accounts of ToM and language processing.     

Decision theoretic foundations for axioms of rational preference

Rationality postulates for preferences are developed from two basic decision theoretic principles, namely: (1) the logic of preference is determined by paradigmatic cases in which preferences are choice-guiding, and (2) excessive comparison costs should be avoided. It is shown how the logical requirements on preferences depend on the structure of comparison costs. The preference postulates necessary for choice guidance in a single decision problem are much weaker than completeness and transitivity. Stronger postulates, such as completeness and transitivity, can be derived under the further assumption that the original preference relation should also be capable of guiding choice after any restriction of the original set of alternatives.     

Evolutionary preference/utility functions: A dynamic perspective

The collection of repeated measures in psychological research is one of the most common data collection formats employed in survey and experimental research. The behavioral decision theory literature documents the existence of the dynamic evolution of preferences that occur over time and experience due to learning, exposure to additional information, fatigue, cognitive storage limitations, etc. We introduce a Bayesian dynamic linear methodology employing an empirical Bayes estimation framework that permits the detection and modeling of such potential changes to the underlying preference utility structure of the respondent. An illustration of revealed stated preference analysis (i.e., conjoint analysis) is given involving students’ preferences for apartments and their underlying attributes and features. We also present the results of several simulations demonstrating the ability of the proposed procedure to recover a variety of different sources of dynamics that may surface with preference elicitation over repeated sequential measurement. Finally, directions for future research are discussed.The authors wish to acknowledge and thank the Editor, the Associate Editor, and two anonymous reviewers for their constructive and insightful comments. Duncan K.H. Fong’s work was sponsored in part by a research grant from the Smeal College.This revised article was published online in August 2005 with the PDF paginated correctly.     

Interactions between conditioned and unconditioned flavor preferences

Five experiments investigated how rats' conditioned preferences or aversions for aqueous odors paired with sucrose or salt are affected by their unconditioned response to those tastes. Rats preferred an odor paired with 30% sucrose over an odor paired with 5% sucrose when both were presented in 5% sucrose, but they showed no preference or, if thirsty, showed the reverse preference, when the odors were presented in 30% sucrose. These changes in conditioned preference corresponded to changes in the rats' unconditioned preference for the accompanying sucrose solution. Rats' conditioned aversions for odors paired with salt showed a similar dependence on their reaction to the accompanying salt solution. The results were interpreted as showing that conditioned and unconditioned flavor preferences combine additively, as if mediated by the same sensory representation.