Normative Uncertainty, Normalization, and the Normal Distribution

Abstract

Maximizing expected choiceworthiness under normative uncertainty requires intertheoretic comparisons, which are frequently operationalized via statistical normalization methods such as variance normalization. However, normalizing choiceworthiness claims to have equal variance generally conflicts with Bayesian updating. Within a framework where an agent observes candidate theories’ evaluations only up to positive affine transformations, updating on the observed internal structure yields posterior expectations with equal variances across theories if the prior distribution over evaluations is normally distributed (or more broadly, rotationally symmetric about the identity line). When evaluations are drawn from non-normal distributions, such as a uniform distribution, Bayesian updating produces posterior distributions whose variances systematically differ depending on the observed cardinal structure of the choices. Because departures from Bayesian updating introduce decision-theoretic pathologies analogous to departures from expected utility maximization, an acute tension exists between maximizing expected choiceworthiness and relying on prior-free statistical normalizations. These findings apply symmetrically to interpersonal comparisons of utility based solely on cardinal rankings. – AI-generated abstract.