  We establish the equivalence between a principle of almost absence of
arbitrage opportunities and nearly rational decision-making. The implications
of such principle are considered in the context of the aggregation of
probabilistic opinions and of stochastic choice functions. In the former a
bounded arbitrage principle and its equivalent form as an approximately Pareto
condition are shown to bound the difference between the collective
probabilistic assessment of a set of states and a linear aggregation rule on
the individual assessments. In the latter we show that our general principle of
limited arbitrage opportunities translates into a weakening of the
McFadden-Richter axiom of stochastic rationality, and gives an upper bound for
the minimum distance of a stochastic choice function to another in the class of
random utility maximization models.
