Do we really need a ‘contingency model’ for concept formation? A reply to Richardson & Bhavnani (1984)

In a recent paper, Richardson & Bhavnani (1984) proposed a new model of concept formation christened ‘the contingency model’ which would supersede the so‐called ‘prototype model’. To support their model, they ran an experiment in which the contingency model apparently surpassed a prototype model. It is argued here that their conclusions are doubtful for several reasons. Firstly, some miscomputations have slipped into the data analysis. Secondly, the prototype model used is not appropriate. Precisely, Richardson & Bhavnani have computed their ‘Contingency Values' (CV) assuming that the features composing the exemplars are nominal variables, but have computed one ‘distance to prototype’ assuming the features are ordinal variables. The alleged superiority of the contingency model vanishes when a correct analysis is performed, or when it is evaluated against what we call a ‘mimimal prototype model’ in which the features are nominal variables. The ‘minimal prototype model’ can be interpreted as a particular and simple case of most of the current ‘prototype models’ (recalling that there is not one but several models). Consequently, it provides an overall test between the CV model and most of the current prototype models. The minimal model is shown to be a particular case of the ‘distance to prototype’ models, and the ‘family resemblance to exemplars models’; (including Tversky's contrast model), and the ‘distributed memory models’. Finally, we note that the contingency model (as tested by Richardson & Bhavnani) is a variant of a ‘distance to prototype model’, in which the distance from the prototype to an exemplar is given by an entropic measure. Thus the opposition proposed by Richardson & Bhavnani between the CV model and the prototype models is meaningless.