‘a bird in the hand is worth two in the bush (and so two in the hand are worth four in the bush)’) then optimal decision-making looks quite different-in particular, the theory predicts that decision-making should be sensitive to the absolute magnitude of the opportunities, such as coin pile sizes, under consideration, in a way that the optimal perceptual mechanisms are not. which light is brighter?) But, crucially, these analyses assume that the cost of time is linear-when the more usual assumption is made that time discounts multiplicatively ( e.g. which pile of coins would you like?) suggests that the optimal rules correspond to simple mechanisms also known to be optimal for perceptual decisions ( e.g. 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.Īnalysis of decisions based on option value ( e.g. 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, in both humans and slime moulds. Thus disentangling explanations for observed magnitude sensitive reaction times is difficult. 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 multiplicative time costs, but also by nonlinear subjective utility. 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.
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