MBS 93-31
An Ergodic Theory for the Emergence and the Evolution of Preference
Relations
Jean-Claude Falmagne
This paper presents a theory describing the emergence and the evolution
of preference relations over (real) time. the subject or consumer is regarded
as immersed in a random environment of the Poisson type. Events arise at
random times which consist of tokens of information about the alternatives.
Some of these tokens have the potential of creating or modifying some edges
of the graph of the preference relation. General axioms are given which
lead to a stochastic process of Markovian character. In a special case
of these axioms, a random utility model is obtained as an asymptotic result.
Specifically, it is shown that the Markov process converges to a random
walk on a unique ergodic set composed of all the rankings of the set of
objects. Precise asymptotic results are derived and the explicit expression
for the probability distribution on the set of rankings is obtained. In
another special case, the asymptotic random walk on on the set of all weak
orders. It is also shown how the theory can account for the resemblance
between preference relations obtained, from the same subject, at time t
and t + k.