This paper formalizes human choice behavior in a probabilistic hide-and-seek task. Using geometric construction, vectors represent both participant choice frequencies and strategies of probability matching and maximizing.
We measured choice behavior in both the well-studied scenario of pursuing an objective (seeking) and the less studied scenario of avoiding consequences (hiding). We defined the avoidance counterpart of probability matching as probability antimatching, represented by a vector reflection across the uniform distribution.
By decomposing the behavior of participants in seeking into matching and maximizing components, we mathematically derived analogous antimatching and minimizing strategies for hiding. Participants exhibited changes in choice frequencies between hiding and seeking conditions.
In both scenarios, a linear combination of two vectors effectively fit participant choice frequencies: matching + maximizing for seeking and antimatching + minimizing for hiding. We accounted for diversity in strategy usage by varying the coefficients of the two relevant basis strategy vectors.
Our model was successfully applied in scenarios involving up to 7 rooms. We conclude that the apparent diversity in human conduct in stochastic environments can sometimes be explained by varying the weighting of two principal strategies: whether to match/antimatch or maximize/minimize.
Blogger's Review: This paper offers an innovative geometric approach to unraveling the underlying logic of human choice behavior in complex environments. The simplicity and effectiveness of the proposed model provide significant theoretical and practical implications, particularly in the fields of psychology and behavioral economics, potentially offering new perspectives for future research.