Probability Matching

Another phenomenon that is formally related (Herrnstein & Loveland, 1975) to the matching law is probability matching, which concerns choices made by agents faced with competing alternatives.  Under probability matching, the likelihood that an agent makes a choice amongst alternatives mirrors the probability associated with the outcome or reward of that choice (Vulkan, 2000).  Probability matching has been demonstrated in a variety of organism including insects (Fischer, Couvillon, & Bitterman, 1993; Keasar, Rashkovich, Cohen, & Shmida, 2002; Longo, 1964; Niv, Joel, Meilijson, & Ruppin, 2002), fish (Behrend & Bitterman, 1961), turtles (Kirk & Bitterman, 1965), pigeons (Graf, Bullock, & Bitterman, 1964) and humans (Estes & Straughan, 1954).

References:

1. Behrend, E. R., & Bitterman, M. E. (1961). Probability-matching in the fish. American Journal of Psychology, 74(4), 542-551.
2. Estes, W. K., & Straughan, J. H. (1954). Analysis of a verbal conditioning situation in terms of statistical learning theory. Journal of Experimental Psychology, 47(4), 225-234.
3. Fischer, M. E., Couvillon, P. A., & Bitterman, M. E. (1993). Choice in Honeybees as a function of the probability of reward. Animal Learning & Behavior, 21(3), 187-195.
4. Graf, V., Bullock, D. H., & Bitterman, M. E. (1964). Further experiments on probability-matching in the pigeon. Journal of the Experimental Analysis of Behavior, 7(2), 151-157.
5. Herrnstein, R. J., & Loveland, D. H. (1975). Maximizing and matching on concurrent ratio schedules. Journal of the Experimental Analysis of Behavior, 24(1), 107-116.
6. Keasar, T., Rashkovich, E., Cohen, D., & Shmida, A. (2002). Bees in two-armed bandit situations: foraging choices and possible decision mechanisms. Behavioral Ecology, 13(6), 757-765.
7. Kirk, K. L., & Bitterman, M. E. (1965). Probability-learning by the turtle. Science, 148(3676), 1484-1485.
8. Longo, N. (1964). Probability-learning and habit-reversal in the cockroach. American Journal of Psychology, 77(1), 29-41.
9. Niv, Y., Joel, D., Meilijson, I., & Ruppin, E. (2002). Evolution of reinforcement learning in uncertain environments: A simple explanation for complex foraging behaviors. Adaptive Behavior, 10(1), 5-24.
10. Peterson, C. R., & Beach, L. R. (1967). Man as an intuitive statistician. Psychological Bulletin, 68(1), 29-46.
11. Vulkan, N. (2000). An economist's perspective on probability matching. Journal of Economic Surveys, 14(1), 101-118.

(Added October 2010)