A geometric framework for modeling dynamic decisions among arbitrarily many alternatives

Abstract

Multiple-choice and continuous-response tasks pose a number of challenges for models of the decision process, from empirical challenges like context effects to computational demands imposed by choice sets with a large number of outcomes. This paper develops a general framework for constructing models of the cognitive processes underlying both inferential and preferential choice among any arbitrarily large number of alternatives. This geometric approach represents the alternatives in a choice set along with a decision maker’s beliefs or preferences in a “decision space,” simultaneously capturing the support for different alternatives along with the similarity relations between the alternatives in the choice set. Support for the alternatives (represented as vectors) shifts over time according to the dynamics of the belief / preference state (represented as a point) until a stopping rule is met (state crosses a hyperplane) and the corresponding selection is made. This paper presents stopping rules that guarantee optimality in multi-alternative inferential choice, minimizing response time for a desired level of accuracy, as well as methods for constructing the decision space, which can result in context effects when applied to preferential choice.