Revisiting the connection between Luce’s Choice Axiom and Signal Detection Theory: Application to visual memory

In many decision tasks, we have a set of alternative choices and are faced with the problem of how to use our latent beliefs and preferences about each alternative to make a single choice. Cognitive and decision models typically presume that beliefs and preferences are distilled to a scalar latent strength for each alternative, but it is also critical to model how people use these latent strengths to choose a single alternative. Most models follow one of two traditions toestablish this link. Modern psychophysics and memory researchers make use of signal detection theory, assuming that latent strengths are perturbed by noise, and the highest resulting signal is selected. By contrast, many modern decision theoretic modeling and machine learning approaches use the softmax function (which is based on Luce’s choice axiom; Luce, 1959) to give some weight to non-maximal-strength alternatives. Despite the prominence of these two theories of choice, current approaches rarely address the connection between them, and the choice of one or the other appears more motivated by the tradition in the relevant literature than by theoretical or empirical reasons to prefer one theory to the other. The goal of the current work is to revisit this topic by elucidating which of these two models provides a better characterization of latent processes in m-alternative decision tasks, with a particular focus on memory tasks. In a set of visual memory experiments, we show that, within the same experimental design, the softmax parameter β varies across m-alternatives, whereas the parameter d′ of the signal-detection model is stable. Together, our findings indicate that replacing softmax with signal-detection link models would yield more generalizable predictions across changes in task structure. More ambitiously, the invariance of signal detection model parameters acrossdifferent tasks suggests that the parametric assumptions of these models may be more than just a mathematical convenience, but reflect something real about human decision-making.