# One and Done? Optimal Decisions from Very Few Samples

- Edward Vul,
*Massachusetts Institute of Technology*
- Noah Goodman,
*Massachusetts Institute of Technology*
- Thomas Griffiths,
*UC Berkeley*
- Joshua Tenenbaum,
*Massachusetts Institute of Technology*

## Abstract

In many situations human behavior approximates that of a Bayesian
ideal observer, suggesting that, at some level, cognition can be described as
Bayesian inference. However, a number of findings have highlighted an intriguing
mismatch between human behavior and that predicted by Bayesian inference: people
often appear to make judgments based on a few samples from a probability
distribution, rather than the full distribution. Although sample-based
approximations are a common implementation of Bayesian inference, the very
limited number of samples used by humans seems to be insufficient to approximate
the required probability distributions. Here we consider this discrepancy in the
broader framework of statistical decision theory, and ask: if people were making
decisions based on samples, but samples were costly, how many samples should
people use? We find that under reasonable assumptions about how long it takes to
produce a sample, locally suboptimal decisions based on few samples are globally
optimal. These results reconcile a large body of work showing sampling, or
probability-matching, behavior with the hypothesis that human cognition is well
described as Bayesian inference, and suggest promising future directions for
studies of resource-constrained cognition.

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