Clarifying the role of an unavailable distractor in human multiattribute choice
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eLife assessment
This study presents an important finding on the decoy effect in multiattribute economic choices in humans. It makes a compelling case for the conclusion that the distractor effect reported in previous articles was confounded with the additive utility difference between the available alternatives. Though the contribution is somewhat narrowly focused with respect to the phenomenon that it addresses - the distractor effect in risky choice, it is important for understanding this particular phenomenon. The main weakness is the complexity of the current manuscript.
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Abstract
Decisions between two economic goods can be swayed by a third unavailable ‘decoy’ alternative, which does not compete for choice, notoriously violating the principles of rational choice theory. Although decoy effects typically depend on the decoy’s position in a multiattribute choice space, recent studies using risky prospects (i.e., varying in reward and probability) reported a novel ‘positive’ decoy effect operating on a single value dimension: the higher the ‘expected value’ (EV) of an unavailable (distractor) prospect was, the easier the discrimination between two available target prospects became, especially when their expected-value difference was small. Here, we show that this unidimensional distractor effect affords alternative interpretations: it occurred because the distractor’s EV covaried positively with the subjective utility difference between the two targets. Looking beyond this covariation, we report a modest ‘negative’ distractor effect operating on subjective utility, as well as classic multiattribute decoy effects. A normatively meaningful model (selective integration), in which subjective utilities are shaped by intra-attribute information distortion, reproduces the multiattribute decoy effects, and as an epiphenomenon, the negative unidimensional distractor effect. These findings clarify the modulatory role of an unavailable distracting option, shedding fresh light on the mechanisms that govern multiattribute decisions.
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Author Response
Reviewer #2 (Public Review):
One other major concern I have regards the conclusion that the participants in these studies use an additive rather than a multiplicative rule to integrate the risk information. The additive rule is problematic in general because it fails to predict the reversal in the effect of probability on payoffs when the payoffs change sign. More specifically, increasing the probability of winning increases the probability of choosing an option when the payoff is positive, but the effect reverses when the payoff is negative. One needs to impose some pretty ad hoc assumptions to make the additive model account for this fundamental interaction between probability and payoff. Of course, the experiments reported here did not include negative payoffs, and so didn't run into this problem. In fact, when the …
Author Response
Reviewer #2 (Public Review):
One other major concern I have regards the conclusion that the participants in these studies use an additive rather than a multiplicative rule to integrate the risk information. The additive rule is problematic in general because it fails to predict the reversal in the effect of probability on payoffs when the payoffs change sign. More specifically, increasing the probability of winning increases the probability of choosing an option when the payoff is positive, but the effect reverses when the payoff is negative. One needs to impose some pretty ad hoc assumptions to make the additive model account for this fundamental interaction between probability and payoff. Of course, the experiments reported here did not include negative payoffs, and so didn't run into this problem. In fact, when the payoffs are positive, it is possible to transform the multiplicative model to an additive model by a log transform. This transformation is only possible for the simple type of gamble investigated in this manuscript - a single amount to win with some probability of winning, otherwise win or lose nothing. If the gambles involved more than one outcome, then the theorist needs to deal with a sum of products and the log transform is no longer possible. For these reasons I am very skeptical about the general application of a summation rule for probability and value in risk choice. The authors do address this issue to some extent. They point out the abundance of other research supporting a multiplicative rule, and they speculate that the additive rule may have occurred within the restrictions of this special situation. The latter discussion is a good start, but I suggest that the authors discuss this fundamental issue in more depth.
Thank you for this very insightful comment. We have now included more in-depth discussions about the decision rules (multiplicative vs. additive) in our Discussion, in which we have absorbed and reflected many of the insights offered by Reviewer #2.
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eLife assessment
This study presents an important finding on the decoy effect in multiattribute economic choices in humans. It makes a compelling case for the conclusion that the distractor effect reported in previous articles was confounded with the additive utility difference between the available alternatives. Though the contribution is somewhat narrowly focused with respect to the phenomenon that it addresses - the distractor effect in risky choice, it is important for understanding this particular phenomenon. The main weakness is the complexity of the current manuscript.
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Reviewer #1 (Public Review):
In this study, the authors investigate multi-attribute economic decisions in humans. More specifically, they investigate the impact of adding a decoy option to a binary choice, the effect of which has been debated in the previous literature with recent studies finding effects in different directions. By re-analyzing large datasets from some of these studies and by applying computational modeling to the data, the authors propose that a subjective encoding rule comparing attributes separately, and not computed as one multiplicative value, explains participants' behavior on different levels of granularity. Context effects were well captured by a selective integration model. The work has many positive features, including praising open science, the analysis of the potential confounds of previously used designs, …
Reviewer #1 (Public Review):
In this study, the authors investigate multi-attribute economic decisions in humans. More specifically, they investigate the impact of adding a decoy option to a binary choice, the effect of which has been debated in the previous literature with recent studies finding effects in different directions. By re-analyzing large datasets from some of these studies and by applying computational modeling to the data, the authors propose that a subjective encoding rule comparing attributes separately, and not computed as one multiplicative value, explains participants' behavior on different levels of granularity. Context effects were well captured by a selective integration model. The work has many positive features, including praising open science, the analysis of the potential confounds of previously used designs, and both quantitative and qualitative comparisons of several well-justified models.
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Reviewer #2 (Public Review):
Summary
This manuscript re-examines a distractor effect of decoy options on risky choice reported in previous research by re-analyzing data from previously published experiments that reported these effects. The previous studies reported that adding an unavailable decoy option to a choice set consisting of two available risky choices increased the discriminability between the two available risky choices, especially when the expected value difference between the two available risky options was small, by increasing the expected value of the unavailable distractor. The authors argue convincingly that the distractor effect is an artifact of two other confounding factors: one is that there is a covariance between the distractor's expected value and the subjective utility difference between the two targets; the …
Reviewer #2 (Public Review):
Summary
This manuscript re-examines a distractor effect of decoy options on risky choice reported in previous research by re-analyzing data from previously published experiments that reported these effects. The previous studies reported that adding an unavailable decoy option to a choice set consisting of two available risky choices increased the discriminability between the two available risky choices, especially when the expected value difference between the two available risky options was small, by increasing the expected value of the unavailable distractor. The authors argue convincingly that the distractor effect is an artifact of two other confounding factors: one is that there is a covariance between the distractor's expected value and the subjective utility difference between the two targets; the second is that the expected value of the distractor alternative could covary with its relative position in the reward-probability space, and its relative position in the multi-attribute space could induce a well-known context effect. The first alternative explanation was established by comparing binary choice with and without the distractor present and finding the same effect in binary choice without any distractor present. The second was established by showing that the distractor effect was most pronounced when it was close to the higher-value target in the multi-attribute space, inadvertently producing a previously well-known attraction effect. These results clarify the role that an unavailable distractor plays in decisions between two risk alternatives.
Evaluation
This is a very comprehensive and somewhat complex manuscript. It does a good job of detective work to get at the bottom of the distractor effect reported in previous articles (including this journal). It essentially contains two main sections. The first section is designed to establish the conclusion that the distractor effect is an artifact of a confounding variable, the additive utility difference between the two available choices, and generalized linear model analyses were used to make this point. The second section is designed to show that the distractor effect also covaries with a well-known context effect called the attraction effect, and they use mathematical modeling of choice and response time to understand this part. Different hypotheses about how the risk information was integrated tested by varying how the drift rate was calculated in a racing drift diffusion model for choice and response time. In particular, they contrasted a divisive expected value type of integration hypothesis with a selective attention type of additive utility hypothesis. They concluded from these mathematical modeling analyses that an additive utility model for integrating the risk information was used in these experiments to evaluate the risky gambles.
Strengths the manuscript makes a very compelling case for the conclusion that the distractor effect was confounded with the additive utility difference between the available alternatives. This was achieved comparing the binary choice results, with and without the distractor, and finding little or no difference between these two conditions. The manuscript is also commendable for its rigorous mathematical modeling of the context effect of the distractor on the binary choices when the distractor was present.
One weakness is that the contribution is somewhat narrowly focused with respect to the phenomenon that it addresses - the distractor effect in risky choice. However, I do think it is important for understanding this particular phenomenon. The other main weakness is the complexity of the manuscript. The manuscript is very long with numerous detailed statistical analyses and computational modeling analyses. Generally speaking, the authors did a good job describing and summarizing all these analyses, and they made effective use of figures to illustrate the ideas and conclusions. However, there are several spots that are somewhat difficult to follow (see specific comments), and the reader is pressed to think pretty hard and fairly long and with a lot of effort to absorb all the points.
One other major concern I have regards the conclusion that the participants in these studies use an additive rather than a multiplicative rule to integrate the risk information. The additive rule is problematic in general because it fails to predict the reversal in the effect of probability on payoffs when the payoffs change sign. More specifically, increasing the probability of winning increases the probability of choosing an option when the payoff is positive, but the effect reverses when the payoff is negative. One needs to impose some pretty ad hoc assumptions to make the additive model account for this fundamental interaction between probability and payoff. Of course, the experiments reported here did not include negative payoffs, and so didn't run into this problem. In fact, when the payoffs are positive, it is possible to transform the multiplicative model to an additive model by a log transform. This transformation is only possible for the simple type of gamble investigated in this manuscript - a single amount to win with some probability of winning, otherwise win or lose nothing. If the gambles involved more than one outcome, then the theorist needs to deal with a sum of products and the log transform is no longer possible. For these reasons I am very skeptical about the general application of a summation rule for probability and value in risk choice. The authors do address this issue to some extent. They point out the abundance of other research supporting a multiplicative rule, and they speculate that the additive rule may have occurred within the restrictions of this special situation. The latter discussion is a good start, but I suggest that the authors discuss this fundamental issue in more depth.
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Reviewer #3 (Public Review):
The authors re-analyze published datasets of value-based decision making with and without unavailable distractors, i.e., with ternary and binary choices. By setting the accuracy of binary choices as baseline, they show that a phantom distractor effect appears even without the presence of distractor. This result suggests that distractor effects could be partially explained by target-related covariation. They test how reward and probability are integrated under their datasets. The additive model wins over the multiplicative model in predicting both true and phantom distractor effects in binary choices. Then they test how multiple alternatives interfere with each other in ternary choices. They find that the model with the assumption of rank dominance wins over normalization models. They also replicate the …
Reviewer #3 (Public Review):
The authors re-analyze published datasets of value-based decision making with and without unavailable distractors, i.e., with ternary and binary choices. By setting the accuracy of binary choices as baseline, they show that a phantom distractor effect appears even without the presence of distractor. This result suggests that distractor effects could be partially explained by target-related covariation. They test how reward and probability are integrated under their datasets. The additive model wins over the multiplicative model in predicting both true and phantom distractor effects in binary choices. Then they test how multiple alternatives interfere with each other in ternary choices. They find that the model with the assumption of rank dominance wins over normalization models. They also replicate the correlation between individual-level decision noise and distractor-related parameters, which implies distractor effects can be emergent properties from a normative decision policy.
I see three strengths of this work.
First, the highlight of this work is that they explore the integration of the multi-attribute and multi-alternative information by bridging distinct distractor effects and providing a unified explanation. The result has a potential impact on a neuroscience topic that attracts a lot of attention in recent years-how the brain represents multiple features and items (e.g. Rigotti, Nature, 2013; Flesch et al., Neuron, 2022; Fusi et al., Curr. Opin. Neurobiol., 2016).
Second, the results of the trial-by-trial baseline approach warn that, due to the complexity of multi-attribute and multi-alternative problem, the studies of the effect should be designed and analyzed with care to prevent possible confounding factors from high dimensionality.
Third, besides static models that can only account for accuracy, the authors implement a dynamic accumulator frame to test all hypotheses. The dynamic accumulator models take into account both accuracy and reaction time. This approach strengthens their model comparison.
Overall, I think this paper is an impressive piece of work that clarifies the true effect of distractors by well-designed analysis and provides a model that bridges distinct distractor effects. Their analysis supports their claims.
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