The multiple threshold race

The aim of this thesis is to develop a mathematical method to expand simple binary choice models to account for confidence judgements, with an applied focus on recognition memory experiments. More broadly I aim to set out a mathematical method that allows simple evidence accumulator models to explain more complex decisions where responses can be ordered along a single dimension. As an example: binary decisions can be described as a race between two possible responses but they can also be conceptualised as choosing between either end of a continuum of possible responses. This is most stark in noisy perceptual tasks, e.g. a task to detect if the dots are mostly moving left or moving right. This binary judgement could be extended to include responses like \all the dots are moving left\" \"more dots are moving left than right\" or \"as many dots are moving left as right\". Some judgements do not as naturally translate to a continuum of responses but rather the strength or confidence in the decision. This is a particularly important response in tasks with a strong applied setting such as eye-witness identification."