Geometric representations of evidence in models of decision-making

Traditionally, models of the decision-making process have focused on the case where a decision-maker must choose between two alternatives. The most successful of these, sequential sampling models, have been extended from the binary case to account for choices and response times between multiple alternatives. In this paper, I present a geometric representation of diffusion and accumulator models of multiple-choice decisions, and show how these can be analyzed as Markov processes on lattices. I then introduce psychological relationships between choice alternatives and show how this impacts the sequential sampling process. I conclude with two examples showing how one can predict distributions of responses on a continuum as well as response times by incorporating psychological representations into a multi-dimensional random walk diffusion process.