A Mechanism for Value-Sensitive Decision-Making
Decision-making dynamics on the unit simplex with vertex corresponding to a fully uncommitted decision-maker (), vertex to a decision-maker fully committed to alternative (, and vertex ) to a decision-maker fully committed to alternative ().
When the accumulator for alternative or ( or ) surpasses a decision threshold, illustrated with a dashed line, the corresponding alternative is selected by the decision-maker. Flow lines indicate sample noise-free trajectories over time, demonstrating fast convergence to a slow, invariant manifold. A singular perturbation analysis (Text S1) proves this separation of timescales, and gives the expression Eq. 2 for the slow manifold (magenta line), which is independent of (thus, the slow manifold is the same in the right and left plots). The dynamics on the slow manifold depend on parameters of the decision problem and and of the cross-inhibition rate ; stable attractors (filled circles) can co-exist with unstable saddle-nodes (hollow circles) on the slow manifold. Thus, decision-making can be reduced to a single decision-variable; this is the form of several classic models of decision-making, including those implementing provably optimal statistical tests.