When expectation-maximization-based theories work or do not work: An eye-tracking study of the discrepancy between everyone and every one

Mainstream theorists in risky decision-making have developed various expectation-maximization-based theories with the ambitious goal of capturing everyone's choices. However, ample evidence has revealed that these theories could not capture every individual's ("every one's") actual risky choice as descriptive theories. Substantial research has demonstrated that people do not follow the logical process suggested by expectation-maximization-based theories when making risky choices but rather rely on simplifying heuristics. From our perspective, the possible reason why mainstream decision theorists did not abandon the framework of expectation is that these theorists never doubted the validity of the expectation rule as a descriptive rule in describing decision-making under risk. We believe that expectation-maximization-based theories may capture risky choices when individuals make decisions for everyone. However, whether these theories could capture risky choices when individuals make decisions for themselves cannot be taken for granted. We thus used an eye-tracking technique to explore whether a theory for everyone would work well for every one. A total of 52 college students participated in the experiment. Three risky choice tasks were conducted in the present study: a D-everyone task, a D-multiple task, and a D- single task. In the D-everyone task, participants were asked to choose the more optimal option out of two options under the assumption that their selection would be the final decision for everyone who was facing the same choice-that is, everyone would be subject to the same choice but could receive different outcomes. In the D-multiple task, participants were asked to choose between the two options under the assumption that their selection would be applied a total of 100 times. In the D-single task, participants were asked to choose between the two options under the assumption that their selection would be applied only once to themselves. The participants' eye movements were recorded while they performed the tasks. Behavioral results revealed that, compared with the D-single task, participants selected more choices correctly predicted by EV and EU theories, and took a longer time to make a decision in the D- everyone and D-multiple tasks. Furthermore, eye movement measurements revealed the following. ( 1) The scanpath patterns of the D- everyone task and D- multiple task were similar but different from those of the D-single task. (2) The depth of information acquisition and the level of complexity of information processing in the D-everyone task and D-multiple task was higher than that in the D-single task. ( 3) The direction of information search in the D-everyone task and D-multiple task was more alternative-based than that in the D- single task. (4) The eye-tracking measures mediated the relationship between the task and the EV-consistent choice. In summary, behavioral and eye movement results supported our hypotheses that participants were likely to follow an expectation strategy in the D- everyone and D-multiple tasks, whereas they were likely to follow a heuristic/nonexpectation strategy in the D-single task. We found that expectation-maximization-based theories could capture the choice of an individual when making decisions for everyone and for self in a multiple- play condition but could not capture the choice of an individual when making decisions for self in a single-play condition. The evidence for the discrepancy between everyone and every one, which was first reported in our study, implied that the possible reason why expectation-maximization- based theories do not work is that a default compatibility between the full set (everyone) and the subset (every one) does not exist. Our findings contribute to an improved understanding of the boundaries of expectation-maximization-based theories and those of heuristic/non- expectation models. Our findings may also shed light on the general issue of the classification of risky decision-making theories.