Accumulating Advantages: A New Approach to Multialternative Forced Choice Tasks

Accumulator models have a relatively long history of application to choice and response time, especially for binary choice. When the number of response options is greater than two, these models usually posit one accumulator per response option. Here, we propose a theoretical framework in which there is one accumulator for every ordered pairwise difference between choices, each quantifying the evidence for one response over another (“advantages”). We instantiate and test this framework in the computationally tractable advantage linear ballistic accumulator model (ALBA), for which we derive explicit likelihoods that support efficient Bayesian estimation. In the first part of the paper, we present three model architectures that differ in terms of stopping rules: conditions on accumulator completions that have to be met for a response to be chosen. In the second part of the paper we present fits of each model architecture to a multiple-choice data set, and select the model architecture that provides the best account of Hick’s Law. In the third part of the paper, we discuss a recent claim by Teodorescu and Usher (2013) that accumulator models require response competition in order to account for the effect of strong distractors in their multialternative forced choice data. Counter to that assertion, we show that this effect naturally emerges from the independent accumulation of advantages, and that the data of Teodorescu and Usher (2013) are at least as well fit by the ALBA as by any of the response-competition models they considered.