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When facing many options, we narrow down our focus to very few of them.Although behaviors like this can be a sign of heuristics, they can actually beoptimal under limited cognitive resources. Here we study the problem of how tooptimally allocate limited sampling time to multiple options, modelled asaccumulators of noisy evidence, to determine the most profitable one. We showthat the effective sampling capacity of an agent increases with both availabletime and the discriminability of the options, and optimal policies undergo asharp transition as a function of it. For small capacity, it is best toallocate time evenly to exactly five options and to ignore all the others,regardless of the prior distribution of rewards. For large capacities, theoptimal number of sampled accumulators grows sub-linearly, closely following apower law for a wide variety of priors. We find that allocating equal times tothe sampled accumulators is better than using uneven time allocations. Our workhighlights that multi-alternative decisions are endowed with breadth-depthtradeoffs, demonstrates how their optimal solutions depend on the amount oflimited resources and the variability of the environment, and shows thatnarrowing down to a handful of options is always optimal for small capacities.

Optimal allocation of finite sampling capacity in accumulator models of multi-alternative decision making