"Expected Utility" Analysis without the Independence Axiom

Subjective and estimated objective winning probabilities are obtained from 20,247 harness horse races. It is shown that subjectively a horse with a low winning probability is exaggerated and one with a high probability of winning is depressed. Various hypotheses characterizing the bettors' behavior to explain the observed subjective-objective probability relation are explored. Under some simplified assumptions, a utility of wealth function of a decision maker is derived, and a quantitative summary measure of his risk attitude is defined. Attitude toward risk of a representative bettor is examined. It is found that he is a risk lover and tends to take more risk as his capital dwindles.

https://www.jstor.org/stable/pdfplus/1828704.pdf

Probability and Utility Estimates for Racetrack Bettors

Animals process sensory information according to specific computational rules and, subsequently, form representations of their environments that form the basis for decisions and choices. The specific computational rules used by organisms will often be evolutionarily adaptive by generating higher probabilities of survival, reproduction, and resource acquisition. Experiments with enclosed colonies of bumblebees constrained to foraging on artificial flowers suggest that the bumblebee's cognitive architecture is designed to efficiently exploit floral resources from spatially structured environments given limits on memory and the neuronal processing of information. A non-linear relationship between the biomechanics of nectar extraction and rates of net energetic gain by individual bees may account for sensitivities to both the arithmetic mean and variance in reward distributions in flowers. Heuristic rules that lead to efficient resource exploitation may also lead to subjective misperception of likelihoods. Subjective probability formation may then be viewed as a problem in pattern recognition subject to specific sampling schemes and memory constraints.

https://science.sciencemag.org/content/sci/253/5023/980.full.pdf

Animal choice behavior and the evolution of cognitive architecture.

Racetrack betting and informed behavior

This paper examines the efficiency of the Association Football betting market in the United Kingdom. The notable features of this market are that the odds are fixed some time before matches occur and differ between bookmaking firms. While there is some evidence of ex post inefficiency, there does not appear to be profitable betting strategies that could have been implemented ex ante during the sample period. Copyright 1989 by The London School of Economics and Political Science.

Information, prices and efficiency in a fixed-odds betting market

The five experiments described in this paper are the modest final product of an initially ambitious attempt to verify a theory of choice under uncertainty. Yaari [5] in 1965 reported the results of some experiments he had performed in which he attempted to show that the acceptance of unfair gambles is better explained by the assumption that gamblers are optimistic about the occurrence of low probability events, than by the assumption of increasing marginal utility of wealth as postulated by Friedman and Savage [1] and as demonstrated experimentally by Mosteller and Nogee [2]. The hypotheses I attempted to test in these five experiments all rest on the assumption that a subject faced with a choice under uncertainty will calculate the expected utility of each alternative, in the sense of von Neumann and Morgenstern [3], and will choose that alternative for which the expectation is greatest. In the first and second experiments I was testing a theory having to do with the formation, by the subject, of his beliefs as to the proper probabilities to use in the calculation. In the third I was interested in verifying Yaari's experimental findings, and in the fourth and fifth experiments I was trying merely to obtain very weak evidence to support the hypothesis that decisions are made under uncertainty so as to maximize expected utility.

R. N. Rosett

Papers

Weak Experimental Verification of the Expected Utility Hypothesis