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.