Generality of likelihood ratio decisions

Abstract

A basic assumption of Signal Detection Theory - a special case of Bayesian Decision Theory - is that decisions are based on likelihood ratios (the likelihood ratio hypothesis). In a preceding paper, Glanzer et al. (2009) tested this assumption in recognition memory tasks. The tests consisted of formal proofs and computational demonstrations that decisions based on likelihood ratios produce three regularities (1. the Mirror Effect, 2. the Variance Effect, and 3. the z-ROC Length Effect). Glanzer et al. found that the three implied regularities do indeed hold for a wide range of item recognition memory studies taken from the literature. We now claim that the likelihood ratio regularities hold for decisions generally: decisions about sensory events, reasoning, weather forecasting, etc. An examination of past decision studies supports the generalization. We also report new experimental studies of decisions in two additional areas, semantic memory and mental rotation, further supporting the generalization. The results highlight the optimal characteristics of decision making in contrast to the current emphasis on its inefficiencies.

Keywords: Bayesian Decision Theory; Decision theory; Decision-making; Likelihood ratio; Mirror effect; Recognition memory; Signal Detection Theory.