| Summary: | Recent work has
derived the optimal policy for two-alternative value-based decisions, in which
decision-makers compare the subjective expected reward of two alternatives.
Under specific task assumptions --- such as linear utility, linear cost of time
and constant processing noise --- the optimal policy is implemented by a
diffusion process in which parallel decision thresholds collapse over time as a
function of prior knowledge about average reward across trials. This policy
predicts that the decision dynamics of each trial are dominated by the
difference in value between alternatives and are insensitive to the magnitude
of the alternatives (i.e., their summed values). This prediction clashes with
empirical evidence showing magnitude-sensitivity even in the case of equal
alternatives, and with ecologically plausible accounts of decision making.
Previous work has shown that relaxing assumptions about linear utility or
linear time cost can give rise to optimal magnitude-sensitive policies. Here we
question the assumption of constant processing noise, in favour of
input-dependent noise. The neurally plausible assumption of input-dependent
noise during evidence accumulation has received strong support from previous
experimental and modelling work. We show that including input-dependent noise
in the evidence accumulation process results in a magnitude-sensitive optimal
policy for value-based decision-making, even in the case of a linear utility
function and a linear cost of time, for both single (i.e., isolated) choices
and sequences of choices in which decision-makers maximise reward rate.
Compared to explanations that rely on non-linear utility functions and/or
non-linear cost of time, our proposed account of magnitude-sensitive optimal
decision-making provides a parsimonious explanation that bridges the gap
between various task assumptions and between various types of decision
making.
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