In risky and other multiattribute choices, the process of choosing is well described by random walk or drift diffusion models in which evidence is accumulated over time to threshold. In strategic choices, level‐k and cognitive hierarchy models have been offered as accounts of the choice process, in which people simulate the choice processes of their opponents or partners. We recorded the eye movements in 2 × 2 symmetric games including dominance‐solvable games like prisoner's dilemma and asymmetric coordination games like stag hunt and hawk–dove. The evidence was most consistent with the accumulation of payoff differences over time: we found longer duration choices with more fixations when payoffs differences were more finely balanced, an emerging bias to gaze more at the payoffs for the action ultimately chosen, and that a simple count of transitions between payoffs—whether or not the comparison is strategically informative—was strongly associated with the final choice. The accumulator models do account for these strategic choice process measures, but the level‐k and cognitive hierarchy models do not. © 2015 The Authors. Journal of Behavioral Decision Making published by John Wiley & Sons Ltd.

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We use computational modeling to examine the ability of evidence accumulation models to produce the reaction time (RT) distributions and attentional biases found in behavioral and eye-tracking research. We focus on simulating RTs and attention in binary choice with particular emphasis on whether different models can predict the late onset bias (LOB), commonly found in eye movements during choice (sometimes called the gaze cascade). The first finding is that this bias is predicted by models even when attention is entirely random and independent of the choice process. This shows that the LOB is not evidence of a feedback loop between evidence accumulation and attention. Second, we examine models with a relative evidence decision rule and an absolute evidence rule. In the relative models a decision is made once the difference in evidence accumulated for 2 items reaches a threshold. In the absolute models, a decision is made once 1 item accumulates a certain amount of evidence, independently of how much is accumulated for a competitor. Our core result is simple—the existence of the late onset gaze bias to the option ultimately chosen, together with a positively skewed RT distribution means that the stopping rule must be relative not absolute. A large scale grid search of parameter space shows that absolute threshold models struggle to predict these phenomena even when incorporating evidence decay and assumptions of either mutual inhibition or feedforward inhibition.

Decision makers are often unable to choose between the options that they are offered. In these settings they typically defer their decision, that is, delay the decision to a later point in time or avoid the decision altogether. In this paper, we outline eight behavioral findings regarding the causes and consequences of choice deferral that cognitive theories of decision making should be able to capture. We show that these findings can be accounted for by a deferral-based time limit applied to existing sequential sampling models of preferential choice. Our approach to modeling deferral as a time limit in a sequential sampling model also makes a number of novel predictions regarding the interactions between choice probabilities, deferral probabilities, and decision times, and we confirm these predictions in an experiment. Choice deferral is a key feature of everyday decision making, and our paper illustrates how established theoretical approaches can be used to understand the cognitive underpinnings of this important behavioral phenomenon.