Probabilistic choice: A simple invariance

When subjects must choose repeatedly between two or more alternatives, each of which dispenses reward on a probabilistic basis (two-armed bandit ), their behavior is guided by the two possible outcomes, reward and nonreward. The simplest stochastic choice rule is that the probability of choosing an alternative increases following a reward and decreases following a nonreward (reward following ). We show experimentally and theoretically that animal subjects behave as if the absolute magnitudes of the changes in choice probability caused by reward and nonreward do not depend on the response which produced the reward or nonreward (source independence ), and that the effects of reward and nonreward are in constant ratio under fixed conditions (effect-ratio invariance )--properties that fit the definition of satisficing . Our experimental results are either not predicted by, or are inconsistent with, other theories of free-operant choice such as Bush-Mosteller, molar maximization, momentary maximizing, and melioration (matching).