Vector model explains human choice with just two strategies

A new paper by Peter A.V. DiBerardino and Britt Anderson (arXiv:2511.03643) proposes a geometric model that explains human choice probabilities in stochastic environments using simple vector representations. The researchers formalized behavior in a probabilistic hide-and-seek task, where participants either seek (pursue an objective) or hide (avoid detection). They constructed vectors representing individual choice frequencies alongside theoretical strategies like probability matching (choosing options proportional to their true probabilities) and maximizing (always picking the highest-probability option). For the hiding condition, they defined a novel counterpart called probability antimatching by reflecting the matching vector across the uniform distribution. This geometric approach allowed them to decompose seeking behavior into matching and maximizing components, then mathematically derive the analogous antimatching and minimizing strategies for hiding.

Experiments showed that participants systematically changed their choice frequencies between hiding and seeking conditions. Crucially, a linear combination of just two basis strategy vectors—matching plus maximizing for seeking, antimatching plus minimizing for hiding—provided an excellent fit to observed participant behavior across scenarios with up to 7 rooms. Individual differences in strategy usage were captured by varying the coefficients of these two vectors. The authors conclude that much of the apparent diversity in human decision-making under uncertainty can be explained by a simple weighting of two fundamental strategies: whether to match (or antimatch) probabilities or to maximize (or minimize) outcomes. This work bridges cognitive science and AI, offering a parsimonious mathematical framework for understanding choice behavior in adversarial or uncertain environments.