Figure 7.

Normative Model for D_2nd

(A) Schematic illustration of the impetus to change the strategy on a second decision, based on the confidence in the first. The expected reward after the D_1st decision increases monotonically with viewing duration (dashed lines). The expected reward is lower when D_1st confidence is low (compare black and green dashed lines). With a cost on time (dotted black line), the total reward (solid lines) has a maximum corresponding to the optimal decision time, which is longer following high-confidence D_1st decisions. Although this schematic provides an intuition for our results, we used dynamic programming to derive the optimal solution to maximize reward rate.

(B) Optimal time-dependent bounds from dynamic programming show that the bound height for D_2nd increases with D_1st confidence.

(C) Model simulation of accuracy and reaction time for second decisions using the optimal bounds in (B). For comparison to Figure 3, the three levels are comparable to a D_2^∗ decision (black: full confidence of 1.0), correct D_1st (blue: high confidence of 0.8), and an error on D_1st (red: low confidence of 0.6).