Choice procedure consistent with similarity relations

Abstract

We deal with the approach, initiated by Rubinstein, which assumes that people, when evaluating pairs of lotteries, use similarity relations. We interpret these relations as a way of modelling the imperfect powers of discrimination of the human mind and study the relationship between preferences and similarities. The class of both preferences and similarities that we deal with is larger than that considered by Rubinstein. The extension is made because we do not want to restrict ourselves to lottery spaces. Thus, under the above interpretation of a similarity, we find that some of the axioms imposed by Rubinstein are not justified if we want to consider other fields of choice theory. We show that any preference consistent with a pair of similarities is monotone on a subset of the choice space. We establish the implication upon the similarities of the requirement of making indifferent alternatives with a component which is zero. Furthermore, we show that Rubinstein's general results can also be obtained in this larger class of both preferences and similarity relations.