Can the wrong horse win: The ability of race models to predict fast or slow errors

Abstract

This report continues our probe of the fundamental properties of elementary psychological processes. In the present instance, we first distinguish between descriptive and state–space based parallel race models. Then we show, engaging previous results on stochastic dominance in Theorem 1, that descriptive race models can be designed that predict either faster ‘right’ channels or faster ‘wrong’ channels. Moving to state–space based models and in particular, to inhomogeneous Poisson counter models, we use Theorem 1 to prove Theorem 2 which offers sufficient conditions for such models to elicit faster ‘rights’ than ‘wrongs’. Then, constraining ourselves to models possessing proportional processing rates, we revisit an important finding by Smith and Van Zandt (2000) to the effect that in such models, mean processing times conditional on ‘right’ decisions are faster than those conditional on ‘wrong’ decisions. Theorem 3 expands that property to the much stronger level of ordered conditional distribution functions. The penultimate section constructs an example of an inhomogeneous Poisson race model that predicts faster ‘wrongs’ for fast processing times but faster ‘rights’ for slower processing times. We leave as an open problem the question of whether there exist inhomogeneous Poisson race models where ‘wrongs’ are stochastically faster than ‘rights’ for all durations of processing.