Testing mixture models of transitive preference: comment on Regenwetter, Dana, and Davis-Stober (2011)

This article contrasts 2 approaches to analyzing transitivity of preference and other behavioral properties in choice data. The approach of Regenwetter, Dana, and Davis-Stober (see record 2011-00732-003) assumes that on each choice, a decision maker samples randomly from a mixture of preference orders to determine whether A is preferred to B. In contrast, Birnbaum and Gutierrez (2007) assumed that within each block of trials, the decision maker has a true set of preferences and that random errors generate variability of response. In this latter approach, preferences are allowed to differ between people; within-person, they might differ between repetition blocks. Both approaches allow mixtures of preferences, both assume a type of independence, and both yield statistical tests. They differ with respect to the locus of independence in the data. The approaches also differ in the criterion for assessing the success of the models. Regenwetter et al. fitted only marginal choice proportions and assumed that choices are independent, which means that a mixture cannot be identified from the data. Birnbaum and Gutierrez fitted choice combinations with replications; their approach allows estimation of the probabilities in the mixture. It is suggested that researchers should separate tests of the stochastic model from the test of transitivity. Evidence testing independence and stationarity assumptions is presented. Available data appear to fit the assumption that errors are independent better than they fit the assumption that choices are independent.     

Robustness of Additive Value Function Methods in MCDM

A simulation model is constructed of choice between a discrete number of non-dominated alternatives. The long-run goals of the decision maker are assumed to be consistent with a hypothetical preference structure which satisfies assumptions of completeness, transitivity and additive independence for an ideal set of criteria. The use of additive value functions to aid the decision maker in this choice is simulated for a variety of contexts and under a number of non-idealities such as the omission of criteria, confounding of criteria and inconsistent responses. It is found that ideal preference orderings are well identified by additive value functions provided that the non-idealities are moderate and that sufficient effort is put into modelling changing marginal values for different levels of performance. One of the potentially most sensitive areas is that of shifts in the decision maker's reference points as a result of the types of preference information asked.     

Variation of Preference Inconsistency When Applying Ratio and Interval Scale Pairwise Comparisons

Several studies on numerical rating in discrete choice problems address the tendency of inconsistencies in decision makers' measured preferences. This is partly due to true inconsistencies in preferences or the decision makers' uncertainty on what he or she really wants. This uncertainty may be reflected in the elicited preferences in different ways depending on the questions asked and methods used in deriving the preferences for alternatives. Some part of the inconsistency is due to only having a discrete set of possible judgments. This study examined the variation of preference inconsistency when applying different pairwise preference elicitation techniques in a five‐item discrete choice problem. The study data comprised preferences of five career alternatives elicited applying interval scale and numerically and verbally anchored ratio scale pairwise comparisons. Statistical regression technique was used to analyse the differences of inconsistencies between the tested methods. The resulting relative residual variances showed that the interval ratio scale comparison technique provided the greatest variation of inconsistencies between respondents, thus being the most sensitive to inconsistency in preferences. The numeric ratio scale comparison gave the most uniform preferences between the respondents. The verbal ratio scale comparison performed between the latter two when relative residual variances were considered. However, the verbal ratio scale comparison had weaker ability to differentiate the alternatives. The results indicated that the decision recommendation may not be sensitive to the selection between these preference elicitation methods in this kind of five‐item discrete choice problem. The numeric ratio scale comparison technique seemed to be the most suitable method to reveal the decision makers' true preferences. However, to confirm this result, more studying will be needed, with an attention paid to users' comprehension and learning in the course of the experiment. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Modelling intransitive preferences: A random-effects approach

Current models for individual-level paired comparison data are based on the three assumptions that (1) pairwise judgments are independent, (2) the utility of an item remains invariant across trials, and (3) pair-specific variability can account for intransitive choice behaviour. All three assumptions seem strong and likely to be violated in empirical applications. This paper introduces a new framework for the analysis of paired comparison data which relaxes these three assumptions and considers the utilities associated with the same item across trials to be neither independent nor identical, but related. The proposed approach provides new insights about the reliability and consistency of paired comparison judgments and can account for systematic violations of transitivity. An application, based on a replication of Tversky's [(1969). Intransitivity of preference. Psychological Review, 76, 31-48] gamble study, illustrates the usefulness of the new approach in modelling both transitive and intransitive preferences.     

TRANSITIVITY OF ODOR PREFERENCES: CONSTANT AND PARTICULARITIES IN HEDONIC PERCEPTION

Transitivity of preferences has been investigated for a long time in decision‐making. In the field of perception, the pleasantness of odors raises several questions related to individual versus cultural or universal preferences and the existence of a classification in a delimited hedonic space. The aim of this study was to test transitivity in olfactory hedonicity using a first panel of 10 mixed odors and a second panel of 10 odors from a delimited floral category. Data were collected by paired comparisons in a two‐alternative forced choice. Results in both panels showed a strong transitivity for each participant leading to a linear range of 10 odors classified by preference. However, ranges varied from one participant to another and the mean preferences of the group did not allow one to infer individual's hedonic classification of odors. Moreover, the individual classification appeared stable over time and undisturbed by odorant distractors. These findings suggest that humans have considerable ability to classify odors hedonically as a model of individual preferences in a sensory space usually considered to be more involved in affective/emotional states than in cognitive performances.     

Sensation Seeking and Need for Achievement Among Study-Abroad Students

Abstract

A constitutional decision rule is the criterion of agreement that the collectivity designates as necessary to achieve binding decisions. Ostrom and Ostrom's (1977) individual calculus model specifies that groups consider two types of costs in choosing a constitutional decision rule: decision-making costs (time, money and effort invested in the decision-making process) and deprivation costs (the extent to which each participant is disadvantaged by an unfavorable decision). Deprivation costs and decision-making costs were manipulated, and preferences for decision rules were observed in this study of 420 American college students. The results partially supported the Ostrom and Ostrom model: Decision-making costs were related to constitutional choice; deprivation costs were not so related. A very large preference was found for majority rule and elected leader rule. In general, subjects did not respond strongly to the desires for efficiency or for individual gain that were proposed by the calculus model.     

Money Pumps,Incompleteness, and Indeterminacy

In an alleged counter‐example to the completeness of rational preferences, a career as a clarinettist is compared with a career in law. It seems reasonable to neither want to judge that the law career is at least as preferred as the clarinet career nor want to judge that the clarinet career is at least as preferred as the law career. The two standard interpretations of examples of this kind are, first, that the examples show that preferences are rationally permitted to be incomplete and, second, that the examples show that preferences are rationally permitted to be indeterminate. In this paper, I shall argue that the difference between these interpretations is crucial for the money‐pump argument for transitivity, which is the standard argument that rational preferences are transitive. I shall argue that the money‐pump argument for transitivity fails if preferences are rationally permitted to be incomplete but that it works if preferences are rationally permitted to be indeterminate and rationally required to be complete.     

Reference-dependent utility with shifting reference points and incomplete preferences

Many empirical studies have shown that people's preferences are reference-dependent. Previous theoretical studies of reference-dependence assumed that the reference point was fixed and then imposed the usual assumptions of decision theory, in particular completeness of preferences. This paper gives preference foundations for additive reference-dependent utility when the reference point varies across decisions and is one of the options in the decision maker's opportunity set. This decision situation is common, for example because usually the retention of the status quo is an available option, but is difficult to handle axiomatically because it implies incompleteness of preferences. The results of this paper provide tools to extend existing theories of reference-dependent preferences, such as prospect theory, to new and empirically important decision contexts.     

Information Processing Strategies in Riskless Preference Reversals: The Prominence Effect

A preference reversal occurs whenever an individual prefers one alternative to another in one response mode (e.g., choice) but shows the opposite preference order in another response mode (e.g., attractiveness ratings, matching). In previous studies of riskless multiattribute preferences the most common reversal pattern involves a prominence effect: The more important attribute has a greater influence in choices than in matching judgments. Previous research has suggested that the prominence effect can be accounted for by the strategy compatibility principle, which states that response tasks can evoke different decision strategies and these strategies determine the relative impact of the various attributes. This article attempts to establish the mediating role of decision processes in determining the occurrence and pattern of riskless preference reversals. In a process tracing experiment we replicate previous findings of a prominence effect in riskless two-attribute preferences. In addition, there are clear differences in process between response modes, and these differences are consistent with previous explanations of riskless preference reversals. Finally, we are able to predict subject level differences in choice preferences and choice versus matching reversals using measures of information search.     

Stochastic transitivity and the unidimensional control of choice

A concurrent-chains paradigm was used to test three models of preference for schedules of reinforcement. Each model assumes choice to be a monotonic function of values on a single dimension (“simple scalability”). For choices involving variable-interval and fixed-interval schedules, this dimension is assumed to be an harmonic average of the interreinforcement intervals; for choices involving fixedinterval and fixed-ratio schedules, the dimension is the time to reinforcement irrespective of response rate; for choices involving different combinations of rate and duration of reinforcement, the dimension is the rate of “reinforcement-time”, or the product of the two parameters. Each model implies a strong form of transitivity (“functional equivalence”), which held for half the subjects (that half exclusively sensitive to the reinforcement variable specified by the model). An alternative unidimensional model which implies a weaker form of transitivity (“weak binary utility model”) was consistent with the preferences of all subjects. This model states that a single factor controls the direction of preferences but not necessarily the exact choice probability, as simple scalability assumes.     

Emotions within reason: Resolving conflicts in risk preference

This research focused on differential effects of emotional and rational preferences in decision making and how people resolve conflicting risk preferences caused by inconsistency between their emotional reactions to and rational assessment of a risk problem. In addition, effects of the framing of choice outcomes on emotional, rational, and overall risk preferences were examined. Adopting a within-subjects design, Study 1 showed that the emotional choice preference was often the opposite of the rational choice preference and was more risk-seeking than the rational preference. The overall favourability rating for a chosen option was significantly higher when the emotional choice and rational choice were the same than when they were opposed. Emotional preferences were significantly more susceptible than rational preferences to the hedonic tone of risky choice framing. The overall preference was a compromise of the conflicting emotional and rational preferences in some risk domains, and resembled either the emotional preference or the rational preference in other risk domains. Study 2, using a between-subjects manipulation, further confirmed that emotional preference and rational preference had differential effects on risky choice.     

Robust interactive decision-analysis (RID): Behavioral results and implications

We have proposed a novel interactive procedure for performing decision analysis, called Robust Interactive Decision Analysis (RID), which permits a decision maker (DM) to voluntarily and interactively express strong (viz, sure) binary preferences for actions, partial decision functions, and full decision functions, and only imprecise probability and utility function assessments. These serve as INPUTS TO operators to prune the state probability space and decision space until an optimal choice strategy is obtained. The viability of the RID approach depends on a DM's ability to provide such information consistently and meaningfully. On a limited scale we experimentally investigate the behavioral implications of the RID method in order to ascertain its potential operational feasibility and viability. More specifically, we examine whether a DM can (1) express strong preferences between pairs of vectors of unconditional and conditional payoffs or utilities consistently; (2) provide imprecise (ordinal and interval) state probabilities that are individually as well as mutually consistent with the state probabilities imputed from the expressed strong preferences. The results show that a DM can provide strong individually and mutually consistent preference and ordinal probability information. Moreover, most individuals also appear to be able to provide interval probabilities that are individually and mutually consistent with their strong preference inputs. However, the several violations observed, our small sample size, and the limited scope of our investigation suggest that further experimentation is needed to determine whether and/or how such inputs should be elicited. Overall, the results indicate that the RID method is behaviorally viable.     

Help or hinder? When recommendation signage expands consideration sets and heightens decision difficulty

This research examines whether recommendation signage helps or hinders the consumer when faced with choosing from large product assortments. In spite of frequent usage and retailer intuition suggesting that providing recommendation signs (e.g., “Best Seller,” “Award Winner”) should help consumers in the choice process, we propose that signs can hinder choice for consumers with more developed preferences by adding to the complexity and difficulty of the decision process. In three experiments using horizontally differentiated products in multiple categories, we provide evidence that recommendation signs create preference conflict for consumers with more developed preferences, leading these consumers to form larger consideration sets and ultimately experience more difficulty from the decision-making process. In addition, we show that these effects are mitigated for consumers with less developed preferences and when the choice is from a small assortment. The results suggest that recommendation signage may not be an effective tool for aiding choice from large assortments; instead signage can exacerbate the difficulties associated with having too many choices, with implications on purchase quantity.     

Choice/Matching Preference Reversals in Groups: Consensus Processes and Justification-Based Reasoning

Individual preferences can vary significantly by the mode in which they are elicited. Thus, the seemingly benign procedural issue of elicitation mode (i.e., choice, buying price, rating, matching) could have a profound effect on group decisions, although elicitation mode has not been much studied as a group procedural variable. Individual preferences differ by elicitation mode when the elicitation contexts differentially emphasize particular aspects of the decision. Emphasis on explainability, for example, may produce decisions that are based only on a few, important, attributes. Because group consensus processes also can encourage particular reasoning strategies, grouping may interact with elicitation mode; that is, group consensus processes may moderate or exacerbate preference reversals. The present study explored a particular elicitation effect, choice versus matching preference reversals, for decisions with both low and high social significance. The results confirmed both that elicitation mode can affect group decisions and that group consensus processes moderate choice/matching preference reversals. Further, evidence from both preference measures and rating scales suggested that the moderation was due to an increase in easily defended, justifiable decisions. Social significance did not affect individual or group decisions, but decreased members′ post group commitment to the group decision. These results have implications both for group decision making and for the study of the role of explanation-based strategies in preference formation.     

Preference-based belief revision for rule-based agents

Agents which perform inferences on the basis of unreliable information need an ability to revise their beliefs if they discover an inconsistency. Such a belief revision algorithm ideally should be rational, should respect any preference ordering over the agent’s beliefs (removing less preferred beliefs where possible) and should be fast. However, while standard approaches to rational belief revision for classical reasoners allow preferences to be taken into account, they typically have quite high complexity. In this paper, we consider belief revision for agents which reason in a simpler logic than full first-order logic, namely rule-based reasoners. We show that it is possible to define a contraction operation for rule-based reasoners, which we call McAllester contraction, which satisfies all the basic Alchourrón, Gärdenfors and Makinson (AGM) postulates for contraction (apart from the recovery postulate) and at the same time can be computed in polynomial time. We prove a representation theorem for McAllester contraction with respect to the basic AGM postulates (minus recovery), and two additional postulates. We then show that our contraction operation removes a set of beliefs which is least preferred, with respect to a natural interpretation of preference. Finally, we show how McAllester contraction can be used to define a revision operation which is also polynomial time, and prove a representation theorem for the revision operation.     

Making a good decision: value from fit

The classic answer to what makes a decision good concerns outcomes. A good decision has high outcome benefits (it is worthwhile) and low outcome costs (it is worth it). I propose that, independent of outcomes or value from worth, people experience a regulatory fit when they use goal pursuit means that fit their regulatory orientation, and this regulatory fit increases the value of what they are doing. The following postulates of this value from fit proposal are examined: (a) People will be more inclined toward goal means that have higher regulatory fit, (b) people's motivation during goal pursuit will be stronger when regulatory fit is higher, (c) people's (prospective) feelings about a choice they might make will be more positive for a desirable choice and more negative for an undesirable choice when regulatory fit is higher, (d) people's (retrospective) evaluations of past decisions or goal pursuits will be more positive when regulatory fit was higher, and (e) people will assign higher value to an object that was chosen with higher regulatory fit. Studies testing each of these postulates support the value-from-fit proposal. How value from fit can enhance or diminish the value of goal pursuits and the quality of life itself is discussed.