Given a squared Euclidean norm penalty, we examine some less well-known properties of shrinkage estimates. In particular, we highlight that it is possible for some components of the shrinkage estimator to be placed further away from the prior mean than the original estimate. An analysis of this effect is provided within three different modeling settings—encompassing linear, logistic, and ordinal regression models. Additional simulations show that the outlined effect is not a mathematical artefact, but likely to occur in practice. As a byproduct, they also highlight the possibilities of sign reversals (“overshoots”) for shrinkage estimates. We point out practical consequences and challenges, which might arise from the observed effects with special emphasis on psychometrics.

Bayesian statistics offers a normative description for how a person should combine their original beliefs (i.e., their priors) in light of new evidence (i.e., the likelihood). Previous research suggests that people tend to under-weight both their prior (base rate neglect) and the likelihood (conservatism), although this varies by individual and situation. Yet this work generally elicits people’s knowledge as single point estimates (e.g., x has a 5% probability of occurring) rather than as a full distribution. Here we demonstrate the utility of eliciting and fitting full distributions when studying these questions. Across three experiments, we found substantial variation in the extent to which people showed base rate neglect and conservatism, which our method allowed us to measure for the first time simultaneously at the level of the individual. While most people tended to disregard the base rate, they did so less when the prior was made explicit. Although many individuals were conservative, there was no apparent systematic relationship between base rate neglect and conservatism within each individual. We suggest that this method shows great potential for studying human probabilistic reasoning.

In this article, we discuss a recent dispute between two Canadian companies, Rogers and Aliant, which went before the Canadian Radio-television and Telecommunications Commission. This involved an apparently ambiguous provision in an agreement between these companies, the interpretation of which was widely seen to hinge on the placement of a single comma in this provision, although the dispute was ultimately resolved by reference to the unambiguous French version of this provision. We provide a syntactic and semantic analysis of the linguistic facts of the dispute, rejecting Aliant’s argument (and the CRTC’s original conclusion) that the placement of the comma provided robust evidence of the intended meaning of the disputed provision and showing how two temporal expressions in this provision, thereafter and prior, contribute to the meaning advanced by Rogers. We also demonstrate the essential equivalence of this meaning to that of the French version of the agreement.