Logit function in stochastic categorizations

Abstract

Binary categorizations refer to the behaviour for which a decision maker puts the alternatives from a menu into binary categories (authorization category and rejection category). For example, a judge approves/denies parole for inmates, a doctor administers/withholds treatment to patients, and a teacher passes/fails essays. Categorizations are observed to exhibit randomness in various contexts, but the stochasticity in categorizations has received little attention in economic studies. We consider stochastic categorizations using a logit categorization function, which expresses the probability of authorizing an alternative from a menu in a ‘logit-like’ form. We characterize the model from a simple condition on authorization frequencies. Furthermore, we derive an empirical version of our model, which not only provides insight into applications of the model, but also gives an intuitive interpretation of the stochasticity in categorizations. We use simple examples to show that our model can bring new insights and research possibilities in the economic studies.