Explaining Human Choice Probabilities with Simple Vector Representations

Abstract

We formalize human choice behavior in a probabilistic hide-and-seek task. In our geometric construction, vectors represent participant choice frequencies as well as probability matching and maximizing strategies. We measured choice behavior not just in the well-studied scenario of pursuing an objective (seeking), but also the rarely studied scenario of avoiding consequences (hiding). We used our geometric construction to define the avoidance counterpart of probability matching, probability antimatching, as a vector reflection across the uniform distribution. Decomposing the behavior of participants when they were seeking into matching and maximizing components, we could mathematically derive the analogous antimatching and minimizing strategies for hiding. Participants did change their choice frequencies between hiding and seeking conditions. In both cases, we found that a linear combination of just two vectors did an excellent job of fitting participant choice frequencies: matching + maximizing for seeking, antimatching + minimizing for hiding. We could account for diversity in participant strategy usage by varying the coefficients of the two relevant basis strategy vectors. We successfully applied this model in scenarios of up to 7 rooms. We conclude that an apparent diversity of human conduct in stochastic environments can, in some cases, be explained by varying the weighting of two principle strategies: whether to match/antimatch or maximize/minimize.