  We define the information threshold as the point of maximum curvature in the
prior vs. posterior Bayesian curve, both of which are described as a function
of the true positive and negative rates of the classification system in
question. The nature of the threshold is such that for sufficiently adequate
binary classification systems, retrieving excess information beyond the
threshold does not significantly alter the reliability of our classification
assessment. We hereby introduce the "marital status thought experiment" to
illustrate this idea and report a previously undefined mathematical
relationship between the Bayesian prior and posterior, which may have
significant philosophical and epistemological implications in decision theory.
Where the prior probability is a scalar between 0 and 1 given by $\phi$ and the
posterior is a scalar between 0 and 1 given by $\rho$, then at the information
threshold, $\phi_e$:
  $\phi_e + \rho_e = 1$
  Otherwise stated, given some degree of prior belief, we may assert its
persuasiveness when sufficient quality evidence yields a posterior so that
their combined sum equals 1. Retrieving further evidence beyond this point does
not significantly improve the posterior probability, and may serve as a
benchmark for confidence in decision-making.
