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.