Stochastic choice models: A comparison between Bush-Mosteller and a source-independent reward-following model.
Ratio-invariance predicts bimodal choice on shifting schedules better than Bush-Mosteller.
01Research in Context
What this study did
The team built two computer models of how pigeons pick keys. One model was the old Bush-Mosteller. The other was a new ratio-invariance rule.
They ran both models on frequency-dependent schedules. These schedules change pay-outs depending on what most responses are doing.
The goal was to see which model could copy the two-hump choice curves seen in real birds.
What they found
Ratio-invariance won. It placed the two humps in the right spots. Bush-Mosteller could not.
The new rule needed no extra tweaks. It kept the same math no matter how pay-outs shifted.
How this fits with other research
Mazur (1988) set the stage. That paper said ratio-invariance beats melioration in theory. The 1989 study tests the claim with fake data and backs it up.
Navakatikyan et al. (2013) also chase better math. They swap Herrnstein’s hyperbola for component-functions. Both papers show older equations cracking under new tests.
McDowell et al. (2018) looks like a clash. Their Darwinian agents learn without rules. E et al. use fixed rules. Yet both reach exclusive preference. The gap is method, not outcome: evolution versus algebra.
Why it matters
If you write concurrent-schedule programs, pick a model that fits the data shape. Ratio-invariance gives you a simple formula that stays true as contingencies slide. No re-coding needed when the richer key swaps.
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02At a glance
03Original abstract
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.
Journal of the experimental analysis of behavior, 1989 · doi:10.1901/jeab.1989.52-57