On bias, signal detection, and sequential sampling
We aim to address two issues. First, empirical work on how payoff asymmetries can bias decisions has used the total number of false positives compared to the total number of false negatives as a criterion. We explain why and when this criterion dissociates from bias c such that one criterion can indicate a liberal bias while the other indicates a conservative bias. Second, what is the optimal decision criterion in a sequential sampling problem, in which noise can be reduced by increased sampling, but at a cost? We derive a function for the cost of sampling, and use that to find the optimal sampling effort for a range of parameters. We will examine both using the case of male sexual overperception, the tendency of men to either believe or to act as if women are more interested in sex than is actually the case. The argument generalises to other examples of decisions under asymmetric payoffs.