MBS 94-25
Stochastic Evolution of Rationality
Jean-Claude Falmagne, Jean-Paul Doignon
Following up on previous results by Falmagne (1993), this paper investigates
possible mechanisms explaining how preference relations are created and
evolve over time. We postulate a preference relation which is initially
empty and becomes increasingly intricate under the influence of a random
environment delivering discrete tokens of information concerning the alternatives.
The framework is that of a class of real time stochastic processes having
interlinked Markov and Poisson components. Specifically, the occurrence
of the tokens is governed by a Poisson process while the succession of
preference relations is a Markov process. In an exemplary case, the preference
relations are the various possible semiorders on the set of alternatives.
Asymptotic results are obtained in the form of the limit probabilities
of any semiorder. The arguments extend to much a more general situation
including interval orders, biorders and partial orders. The results provide
(up to a small number of parameters) complete quantitative predictions
for panel data of a standard type, in which the same sample of subjects
has been asked to compare the alternatives a number of times.