Probabilistic choice: A simple invariance.

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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).






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Horner, JM, and JE Staddon (1987). Probabilistic choice: A simple invariance. Behav Processes, 15(1). pp. 59–92. 10.1016/0376-6357(87)90034-9 Retrieved from

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John E. R. Staddon

James B. Duke Distinguished Professor Emeritus of Psychology and Neuroscience

Until my retirement in 2007, my laboratory did experimental research on learning and adaptive behavior, mostly with animals: pigeons, rats, fish, parakeets.  We were particularly interested in timing and memory, feeding regulation, habituation and the ways in which pigeons and rats adapt to reward schedules. The aim  is to arrive at simple models for learning that can help to identify the underlying neural mechanisms. I continue to do theoretical and historical work on the power law in psychophysics, operant learning, timing and memory, habituation and feeding regulation.  I have applied some of these ideas to economics and financial markets and social issues such as traffic control (Distracting Miss Daisy, The Atlantic, 2008; Death by Stop Sign) and smoking (Unlucky Strike, Private Health and the Science, Law and Politics of Smoking, with David Hockney, UBP, 2013).  A second edition of Adaptive Behavior and Learning (Cambridge UP) was published in 2016. Most recently I have published Scientific Method: How Science Works, Fails to Work, and Pretends to Work. published by Routledge in December, 2017, Unlucky Strike Second Edition, and Science in an age of unreason (Regnery, 2022). 

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