Stochastic choice models: A comparison between Bush-Mosteller and a source-independent reward-following model

Horner and Staddon (1987) argued that a class of reward-following processes defined by a property they termed ratio invariance is a better model for the probabilistic choice performance of pigeons than competing molecular accounts such as momentary maximizing, melioration, and the Bush-Mosteller model. The critical data were provided by choice distributions-distributions of a variable S, the proportion of Right choices, defined on a moving window typically 32 choices long-obtained under a frequency-dependent schedule. The schedule prescribed equal payoff probabilities, p(S), for both choices. p(S) was a maximum when S = 0.5 and declined linearly for S values above and below 0.5. Pigeons showed generally bimodal choice distributions with the modes at equal p(S) values. These data do not follow easily from melioration or momentary maximizing and are inconsistent with molar maximizing, but they may be consistent with Bush-Mosteller. We present here the results of computer simulations showing that the ratio-invariance model studied yields, as expected, choice modes at equal p(S) values, but that Bush-Mosteller, although capable of generating bimodal choice distributions, does not have choice modes at equal p(S) values.