Unchosen Alternatives Research Articles

On Optimal Scheduling

We consider a decision-maker sequentially choosing among alternatives when periodic payoffs depend on both chosen and unchosen alternatives in that period. We show that when flow payoffs are the sum or product of payoffs from chosen and unchosen alternatives, the optimal policy is an index policy. We characterize key properties of the optimal dynamics and present an algorithm for computing the indices explicitly. Furthermore, we use the results to generalize Weitzman’s (1979) classic “Pandora’s boxes” problem to allow for complementarities. We illustrate the framework’s usefulness through applications, including decision problems with disappearing alternatives, repeated bargaining, dynamic supervision, and dynamic occupational choice. (JEL C78, D82, M11)

Discrete choice modeling with anonymized data

This paper presents an approach to estimate mode-choice models from spatially anonymized revealed preference travel survey data. We propose an algorithm to find a feasible sequence of activity locations for each individual that minimizes the maximum error of each trip’s Euclidean distance within the activity chain. The synthetic activity locations are then used to create unchosen alternatives within the choice set for each individual. This is followed by the mode-choice model estimation. We test our approach on three large-scale travel surveys conducted in Switzerland, Île-de-France, and São Paulo. We find that our methodological approach can reconstruct activity locations that accurately match trip Euclidean distances but with location errors that still provide location protection. The discrete mode-choice models estimated on the synthetic locations perform similarly, in terms of goodness of fit and prediction, to the ones obtained from the observed activity locations.

Joint modelling of choice and rating data: Theory and examples

In many cases, ordinal data, for example rating objects on a scale from 1 to 5, is observed only for those objects that have been chosen from a set of discrete alternatives, with no ratings for unchosen objects. An example is customer ratings of goods sold by online retailers. The joint modelling of choice and rating is made difficult by the missing ratings for unchosen alternatives. A method of jointly modelling choice and rating data termed a choice-ordered logit (COL) model is presented. Two types of COL model are defined: two-step, which places a positive probability on the chosen alternative not having the highest rating, and one-step, where the highest rated alternative is always chosen. Three case studies exemplifying the use of COL models are given. One uses simulated data and two use data from discrete choice experiments. It is shown that COL models can produce robust estimates. Two-step models provided a better fit than one-step, and most participants seemed to use two-step decision-making. However, a sizeable minority used one-step decision-making in one case study. It is argued that COL models have benefits over standard approaches, in particular adding information on strength-of-preference to discrete choices.

Abstract inference of unchosen option values.

Reinforcement learning research has pursued a persistent question: Does reward feedback prompt inferences that transcend simple associations? Reversal learning data suggest an affirmative answer: When the positive stimulus (S+) becomes the negative stimulus (S-), trained humans rapidly switch to choosing the former S-. The operations supporting such inferences remain ambiguous. Do participants identify transitions between stimulus-specific contexts (i.e., A+B- and A-B+), or deduce values by learning the abstract contingency structure? Across two experiments, we probed humans' use of abstract rules to infer the values of unchosen alternatives. In Experiment 1, 37 participants attempted a task that originally demonstrated monkeys' difficulty with this form of inference. We presented modified discrimination problems in which the initially chosen stimulus (abstract inference group) or unchosen stimulus (control group) was replaced with a novel stimulus of identical status on Trial 2. In the abstract inference condition, accurate performance can be achieved by applying the consistent contingency structure (but not memory of stimulus-specific reward associations) to infer to the unchosen stimulus' value. The abstract inference group learned to make accurate choices, but only after committing substantially more errors than were observed among control participants-suggesting that unchosen value inferences are infrequently drawn in standard discrimination scenarios. In Experiment 2, 17 participants completed abstract inference problems that had been modified to be suitable for fMRI investigations. Behavioral results both corroborated the Experiment 1 trends and further revealed marked individual differences in explicit awareness of the novel stimulus values.

The mnemonic effect of choice.

Making choices during encoding leads to superior memory compared with having the same choices made for you. Evidence also suggests that chosen items might be more memorable than unchosen alternatives. In prior experiments, an incidental memory advantage was found for chosen over unchosen items when participants chose which one of two words would be more useful to a situation. However, it remains uncertain whether this mnemonic benefit is due to the act of choosing or to a better "fit" of chosen items to the encoding situation (congruity). In the present research, we conducted two experiments to dissociate choice and congruity effects. In both experiments, we manipulated choice and congruity and showed mnemonic benefits for chosen words over unchosen words and for congruent words over incongruent words, but these effects did not interact. There is apparently a unique mnemonic benefit for chosen words that cannot be explained by their "fit" to the encoding task.

A refinement of the uncovered set in tournaments

We introduce a new solution for tournaments called the unsurpassed set. This solution lies between the uncovered set and the Copeland winner set. We show that this solution is more decisive than the uncovered set in discriminating among alternatives, and avoids a deficiency of the Copeland winner set. Moreover, the unsurpassed set is more sensitive than the uncovered set but less sensitive than the Copeland winner set to the reinforcement of the chosen alternatives. Besides, it turns out that this solution violates the other standard properties including independence of unchosen alternatives, stability, composition consistency and indempotency.

ESTIMATING MULTINOMIAL LOGIT MODELS WITH SAMPLES OF ALTERNATIVES.

This comment reconsiders advice offered by Bruch and Mare regarding sampling choice sets in conditional logistic regression models of residential mobility. Contradicting Bruch and Mare's advice, past econometric research shows that no statistical correction is needed when using simple random sampling of unchosen alternatives to pare down respondents' choice sets. Using data on stated residential preferences contained in the Los Angeles portion of the Multi-City Study of Urban Inequality, it is shown that following Bruch and Mare's advice-to implement a statistical correction for simple random choice set sampling-leads to biased coefficient estimates. This bias is all but eliminated if the sampling correction is omitted.

Context-dependent choice as explained by foraging theory

An agent makes consumption choices in multiple periods. Choice objects vary in type and quality; objects of the same type are inter-temporal substitutes. The current choice set is informative about the distribution over future choice sets. Thus, the presence of unchosen alternatives may rationally alter the agent's choice. Under some simple assumptions, the optimal policy exhibits context-dependent choice behavior, such as the decoy effect and choice overload.

Modeling purchases of new cars: an analysis of the 2014 French market

This paper analyzes and compares different policy scenarios as well as discusses price elasticities and willingness to pay and to accept using revealed preference (RP) data from the French new-car market in 2014 by means of a cross-nested logit (CNL) model. We focus particularly on electric and hybrid vehicles. We use interactions between the cost (both fixed and running costs) and the household income to analyze the sensitivity towards different policy scenarios per income level. Results show that the willingness to pay and to accept obtained in our study is consistent with the real-market conditions. We also find that the most effective scenario to increase the market shares of new sold electric vehicles is that of a major technological advance such as a decrease in price due to cheaper manufacturing costs and an increase in driving range, rather than a policy-based scenario. In addition, the market segment that has more potential to increase the market shares of electric vehicle purchase is the middle-income level. In the paper, we discuss how to overcome the difficulties of working with revealed preference data, and propose multiple imputations to impute the attributes of the unchosen alternatives, by drawing from their empirical distributions.

On the structure of stable tournament solutions

A fundamental property of choice functions is stability, which, loosely speaking, prescribes that choice sets are invariant under adding and removing unchosen alternatives. We provide several structural insights that improve our understanding of stable choice functions. In particular, (i) we show that every stable choice function is generated by a unique simple choice function, which never excludes more than one alternative, (ii) we completely characterize which simple choice functions give rise to stable choice functions, and (iii) we prove a strong relationship between stability and a new property of tournament solutions called local reversal symmetry. Based on these findings, we provide the first concrete tournament---consisting of 24 alternatives---in which the tournament equilibrium set fails to be stable. Furthermore, we prove that there is no more discriminating stable tournament solution than the bipartisan set and that the bipartisan set is the unique most discriminating tournament solution which satisfies standard properties proposed in the literature.

Counterfactual comparison modulates fairness consideration in the mini-ultimatum game: an event-related potentials study.

Existing literature on the mini-ultimatum game indicates that counterfactual comparison between chosen and unchosen alternatives is of great importance for individual's fairness consideration. However, it is still unclear how counterfactual comparison influences the electrophysiological responses to unfair chosen offers. In conjunction with event-related potentials' (ERPs) technique, the current study aimed to explore the issue by employing a modified version of the mini-ultimatum game where a fixed set of two alternatives (unfair offer vs. fair alternative, unfair vs. hyperfair alternative, unfair offer vs. hyperunfair alternative) was presented before the chosen offer. The behavioral results showed that participants were more likely to accept unfair chosen offers when the unchosen alternative was hyperunfair than when the unchosen alternative was fair or hyperfair. The ERPs results showed that the feedback-related negativity (FRN) elicited by unfair chosen offers was insensitive to the type of unchosen alternative when correcting for possible overlap with other components. In contrast, unfair chosen offers elicited larger P300 amplitudes when the unchosen alternative was hyperunfair than when the unchosen alternative was fair or hyperfair. These findings suggest that counterfactual comparison may take effect at later stages of fairness consideration as reflected by the P300.

Learning about unchosen alternatives: When does curiosity overcome regret avoidance?

Much of the research on emotions and decision making has focused on how desire to avoid regret influences choices and post-decision information search. Recently van Dijk and Zeelenberg (2007) demonstrated that under certain circumstances individuals will seek out information about an alternative even though this information may induce regret about a previous decision. In two experiments, we extend this finding and show that curiosity is least likely to affect information seeking when the initial choice is made from fewer alternatives (a regret-inducing “near miss”) and the outcome of the choice is negative.

The Importance of Foregone Options: Generalizing Social Comparisons in Sequential-Move Games

Recent experimental evidence supports the influence of a player's unchosen alternatives on other agent's actions. This paper examines a tractable theoretical model of reference-dependent preferences in which individuals compare other players' chosen action with respect to their unchosen alternatives. We analyze the equilibrium prediction in complete information sequential-move games, and compare it with that of standard games where players are not concerned about unchosen alternatives. We show that, without relying on interpersonal payoff comparisons (i.e., with strictly individualistic preferences), our model predicts higher cooperation among the players than standard game-theoretic models. In addition, our framework embodies different models from the literature on social status acquisition and intentions-based reciprocity as special cases. Finally, we confirm our results in three economic applications: the ultimatum bargaining game, the labor market gift exchange game, and the sequential public good game.

Modelling airport and airline choice behaviour with the use of stated preference survey data

The majority of studies of air travel choice behavior make use of revealed preference (RP) data, generally in the form of survey data collected from departing passengers. While the use of RP data has certain methodological advantages over the use of stated preference (SP) data, major issues arise because of the often low quality of the data relating to the un-chosen alternatives, in terms of explanatory variables as well as availability. As such, studies using RP survey data often fail to recover a meaningful fare coefficient, and are generally not able to offer a treatment of the effects of airline allegiance. In this paper, we make use of SP data for airport and airline choice collected in the US in 2001. The analysis retrieves significant effects relating to factors such as airfare, access time, flight time and airline and airport allegiance, illustrating the advantages of SP data in this context. Additionally, the analysis explores the use of non-linear transforms of the explanatory variables, as well as the treatment of continuous variations in choice behavior across respondents.

Individual differences in the response to forgone payoffs: an examination of high functioning drug abusers

This study evaluates the effect of forgone payoffs in decision-making tasks used for studying individual differences. We investigate whether the disclosure of forgone payoffs (defined as payoffs associated with un-chosen alternatives) has selective effects for drug abusers. Evidence suggests that drug abusers are hypersensitive to signals of positive reward. Accordingly, because the forgone payoffs of risky high-variability options include rewarding outcomes, this may create a distraction and lead drug abusers to make more risky choices. In a controlled experiment, we examined the behavior of high-functioning drug abusers and healthy controls using the Iowa gambling task. The results showed that in a forgone payoff condition, drug abusers made more risky choices. The results demonstrate that adding information about forgone payoffs can be useful for studying individual differences, and that studying individual differences can be valuable in evaluating the effects of forgone payoffs. Copyright © 2005 John Wiley & Sons, Ltd.

Value in the guise of regret

According to a widely accepted philosophical model, agent‐regret is practically significant and appropriate when the agent committed a mistake, or she faced a conflict of obligations. I argue that this account misunderstands moral phenomenology because it does not adequately characterize the object of agent‐regret. I suggest that the object of agent‐regret should be defined in terms of valuable unchosen alternatives supported by reasons. This model captures the phenomenological varieties of regret and explains its practical significance for the agent. My contention is that agent‐regret is a mode of valuing: a way in which the agent expresses and confers value.

Explaining Context Effects on Choice Using a Model of Comparative Judgment

Context effects refer to the shifts in shares when another alternative is introduced in the choice set. The alternative can be asymmetrically dominated, asymmetrically dominating, totally dominated, or totally dominating. We developed a theoretically derived model based on the shifts in attribute valuation as a potential explanation for all context effects. First, the model is tested using data from previously published studies. As predicted, the results showed a high correlation between shifts in valuation and changes in the choice shares. The model is also tested using 2 studies that extend the design of the choice sets to include better alternatives in a search context and the removal of an alternative. The strong relation justifies the case for comparative valuation as an underlying mechanism for context effects. Assuming this valuation, the article illustrates how the framework can be used to develop new product strategies taking into account the values of the unchosen alternatives.

A Regret Theory Approach to Assessing Consumer Satisfaction

Because consumer satisfaction is an important determinant of brandloyalty and word-of-mouth communications, it has been widely studied inthe marketing literature. Much of this literature follows theexpectancy-disconfirmation paradigm, which posits satisfaction to be afunction of the positive or negative disconfirmation of one'sexpectations about the chosen brand. This article proposes a richermodel of consumer satisfaction that incorporates effects ofexpectations about the options not ultimately chosen from theconsideration set. Specifically, we posit that the expectations aboutthe unchosen alternatives affect satisfaction with one's choice whenthat choice does not meet the expectations but will have little effectwhen the choice meets expectations. A series of experimental studiesprovide support for this approach.

Protecting the self from the negative consequences of risky decisions.

Three experiments tested the idea that a motive to protect self-esteem (SE) from the threat of regret can influence decision making. Threat to SE was manipulated by varying whether people expected to know the outcome of their decisions. Study 1 showed that when Ss expected feedback about their decisions, only Ss low in SE made regret-minimizing choices. Study 2 showed that when Ss did not expect to know the outcome of their decisions, SE differences in choice strategies disappeared. Study 3 manipulated expectations about feedback on chosen and unchosen alternatives and showed that the more feedback that was expected, the more likely low but not high SE Ss were to make regret-minimizing choices. These studies suggest that people base decisions not only on objective attributes of choice alternatives, but also on the damage to SE that is perceived to result from a poor-decision outcome.

A rule-based calibration method for models with multiple rank-ordered choices

A model of multiple-ranked shopping center destination choice was developed using a rule-based expert systems format. The motivation behind this approach was twofold. First, this model avoids the need to collect data regarding unchosen alternatives that the consumer faces, as is typically required by ranked or “exploded” multinomial logit or probit models. The rule-based model requires only a random sample of decision makers where their actual stated preference are observed. The second motivation is to avoid misallocation of demand to alternatives, as is often the case with conventional models that ignore ranked data. This model is also different from others since all of the observed data are chosen alternatives but chosen with unknown frequency. The model that was developed is based on fuzzily defined clusters of survey respondents that make similar-ranked choices for similar reasons. Once clusters are defined through conventional cluster analysis, rules are created to classify respondents into the groups. No parameters are estimated by this method, but the overall meaning of the rules can be discerned through sensitivity analysis where variables are selectively changed and forecast results are recorded. Calibration of the model was based on a sample of 813 home-based shoppers in St. Catharines, Ontario. It was found that about 50 rules were needed in order to correctly predict the top three-ranked choices with accuracy levels in the mid 70% range. Sensitivity analysis indicated that the model was making sensible predictions, given changes in the input data.