Magnitude-sensitive reaction times reveal non-linear time costs in multi-alternative decision-making

Abstract

Optimality analysis of value-based decisions in binary and multi-alternative choice settings predicts that reaction times should be sensitive only to differences in stimulus magnitudes, but not to overall absolute stimulus magnitude. Yet experimental work in the binary case has shown magnitude sensitive reaction times, and theory shows that this can be explained by switching from linear to geometric time costs, but also by nonlinear subjective utility. Thus disentangling explanations for observed magnitude sensitive reaction times is difficult. Here for the first time we extend the theoretical analysis of geometric time-discounting to ternary choices, and present novel experimental evidence for magnitude-sensitivity in such decisions. We consider the optimal policies for all possible combinations of linear and geometric time costs, and linear and nonlinear utility; interestingly, geometric discounting emerges as the predominant explanation for magnitude sensitivity.

Magnitude-sensitivity: rethinking decision-making

“…while in other cases researchers derive optimal models of decision-making [57,97,100] for specific scenarios and then compare the optimal models to the descriptive accounts in order to highlight similarities and differences. A word of caution with regard to the concept of 'optimality': any model/rule implements optimality only under specific, limited, assumptions.…”

“…A word of caution with regard to the concept of 'optimality': any model/rule implements optimality only under specific, limited, assumptions. Therefore, these assumptions are often the matter of debate in research about optimal decision-making [25,33,34,57].…”

“…Recent work [100] has shown that, also in the multi-alternative case, magnitude-sensitivity is observed, but with surprising differences compared to the case of binary decisions [13,57]. Theory shows that, for multialternative decision-making, nonlinear subjective utility combined with linear time discounting induces only very weak magnitude-sensitivity; multiplicative time discounting instead predicts strong magnitude-sensitivity for both linear and nonlinear utility, in line with empirical evidence showing strongly magnitude-sensitive reaction times with three alternatives [57].…”

“…Recent work [100] has shown that, also in the multi-alternative case, magnitude-sensitivity is observed, but with surprising differences compared to the case of binary decisions [13,57]. Theory shows that, for multialternative decision-making, nonlinear subjective utility combined with linear time discounting induces only very weak magnitude-sensitivity; multiplicative time discounting instead predicts strong magnitude-sensitivity for both linear and nonlinear utility, in line with empirical evidence showing strongly magnitude-sensitive reaction times with three alternatives [57]. Overall, the multiplicative cost of time account assumes that magnitude-sensitivity is the signature of a common mechanism for decision-making that has evolved to directly optimise speed-value trade-offs and that, as a consequence, is observed even when there is no reward associated with a choice [e.g., in perceptual tasks, see 3,9,11,12] or in experiments for which the cost of time is controlled/minimised (e.g., when the experiment duration and number of trials are fixed).…”

“…Overall, the multiplicative cost of time account assumes that magnitude-sensitivity is the signature of a common mechanism for decision-making that has evolved to directly optimise speed-value trade-offs and that, as a consequence, is observed even when there is no reward associated with a choice [e.g., in perceptual tasks, see 3,9,11,12] or in experiments for which the cost of time is controlled/minimised (e.g., when the experiment duration and number of trials are fixed). That is, even though decision-makers perform a purely perceptual task, they perform it as if optimising a speed-value trade-off for value-based choices [34,57].…”