Figure 5.

Descriptive Rendering of the Rule to Update Knowledge of the Base Rate

The Bayesian model and its alternatives can be characterized by the way they update $p\left(B\right)$ based on the choice-confidence and the expectation of the base rate, expressed relative to the choice taken ($\mathbb{E}\left[B_d\right]\equiv p\left[d|E^{\left(i-1\right)}\right]$, similar to a priori probability correct). The strength of the update is parameterized by ${\nu }_d$.

(A) For the Choice-only model, ${\nu }_d$ is always equal to 1.

(B) For the Choice-confidence model, ${\nu }_d$ only depends on the reported confidence.

(C) For the Bayesian model, ${\nu }_d$ is the counterfactual confidence, which is a function of both reported confidence and $p\left(d|E^{\left(i-1\right)}\right)$.

(D) For the Empirical model, we used a flexible mapping (Equation 16) of confidence and $p\left(d|E^{\left(i-1\right)}\right)$ to ${\nu }_d$ that best fit the data.