Explaining Human Choice Probabilities with Simple Vector Representations

TL;DR

This paper introduces a simple vector-based model explaining human choice behavior in stochastic environments, capturing matching, antimatching, maximizing, and minimizing strategies with minimal assumptions.

Contribution

It proposes a novel vector reflection model for antimatching and demonstrates that human choices can be explained by a mixture of basic policies using simple vector operations.

Findings

A vector reflection model accounts for antimatching behavior.

Two basis policies—matching/antimatching and maximizing/minimizing—sufficiently explain choices.

Human strategies can be constructed from relative frequency memory and simple operations.

Abstract

When people pursue rewards in stochastic environments, they often match their choice frequencies to the observed target frequencies, even when this policy is demonstrably sub-optimal. We used a ``hide and seek'' task to evaluate this behavior under conditions where pursuit (seeking) could be toggled to avoidance (hiding), while leaving the probability distribution fixed, or varying complexity by changing the number of possible choices. We developed a model for participant choice built from choice frequency histograms treated as vectors. We posited the existence of a probability antimatching strategy for avoidance (hiding) rounds, and formalized this as a vector reflection of probability matching. We found that only two basis policies: matching/antimatching and maximizing/minimizing were sufficient to account for participant choices across a range of room numbers and opponent probability distributions. This schema requires only that people have the ability to remember the relative frequency of the different outcomes. With this knowledge simple operations can construct the maximizing and minimizing policies as well as matching and antimatching strategies. A mixture of these two policies captures human choice patterns in a stochastic environment.