Explaining Human Choice Probabilities with Simple Vector Representations

2025-11-05

AI Summary

This study investigates why humans prefer suboptimal “frequency matching”—selecting options with probabilities approximating their target occurrence frequencies—in stochastic reward environments. Method: Using a “hide-and-seek” behavioral experiment, we construct a vector representation model based on choice-frequency histograms and formally propose and characterize “probability inverse matching”—a strategy implemented via vector reflection. Contribution/Results: We demonstrate that only two orthogonal basis strategies—frequency matching versus inverse matching (exploratory responses), and reward maximization versus minimization (exploitative responses)—suffice to unify individual choice patterns across varying numbers of rooms and opponent distributions. A mixture model combining these strategies significantly improves behavioral prediction accuracy. Our findings reveal that human decision-making in such environments can be effectively captured within a low-dimensional strategy space, providing a concise, computationally tractable framework for understanding the cognitive mechanisms underlying adaptive decision-making.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Humans and AI: Learning Human Values and Preferences
• Machine Learning: Learning Preferences or Rankings

Application Category

• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Economics, Online Markets and Human Computation: Social networks and social learning
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Modeling human choice probabilities using vector representations of frequency histograms
• Explaining suboptimal probability matching behavior in stochastic reward environments
• Identifying basis policies that capture human choice patterns across varying complexities

Innovation

• Vector representation models human choice probabilities
• Two basis policies: matching/antimatching and maximizing/minimizing
• Mixture of policies captures human stochastic choice patterns