Decision confidence is a forecast about the probability that a decision will be correct.
From a statistical perspective, decision confidence can be defined as the Bayesian
posterior probability that the chosen option is correct based on the evidence contributing
to it. Here, we used this formal definition as a starting point to develop a normative
statistical framework for decision confidence. Our goal was to make general predictions
that do not depend on the structure of the noise or a specific algorithm for estimating
confidence. We analytically proved several interrelations between statistical decision
confidence and observable decision measures, such as evidence discriminability, choice,
and accuracy. These interrelationships specify necessary signatures of decision confidence
in terms of externally quantifiable variables that can be empirically tested. Our
results lay the foundations for a mathematically rigorous treatment of decision confidence
that can lead to a common framework for understanding confidence across different
research domains, from human and animal behavior to neural representations.
