## The auction values of uncertain outcomes in win and loss type situations

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http://hdl.handle.net/2144/7886##### Abstract

The three studies that are reported in this dissertation compare human behavior with the normative behavior called for by the following expected value model:
EV = pR + (1-p)L, where
EV = expected value, p = probability of winning, R = amount of reward, (1-p) = probability of loss, and L = amount of loss.
The deviations from the model, when rationalized, give information about decision making in risky situations. The studies grew out of an experiment by Preston and Baratta (American Journal of Psychology, 1948) which indicated that individuals overestimate the likelihood of the occurrence of an event when its probability of occurrence is 0.01 and 0.05 and underestimate the likelihood of an event with probabilities ranging from 0.25 to 0.99.
The concept of psychological or subjective probability was used to make the behavior studied more meaningful. Psychological probabilities are those subjective values, derived from observations of behavior, corresponding to the objective probability values which range from 0 to 1.
The first study done consisted of a replication of the Preston and Baratta work, using normal and schizophrenic subjects. This study gave information about behavior in a win type situation. The second study gave information about behavior in a risky situation in which the subject was given another person's probability of winning. To conform to the expected value model the subjects had to complete a (1-p) estimation process. The third study yielded information about behavior in a loss type situation.
Data from the three studies gave information about the question, of the summation of psychological probabilities whose corresponding objective probabilities sum to 1 .
A total of 80 subjects, 40 normals and 40 schizophrenics participated in the studies. The schizophrenics were hospitalized veterans and the normals were psychiatric aides employed at a Veterans Administration Hospital. The subjects played three experimental dice games, using play money, for prizes consisting of cigarettes and candy. Measures of intellectual and arithmetic ability were administered to the subjects.
The results of the three studies indicated that both normals and schizophrenics are capable of making numerous and somewhat complex expected value estimations. In general the behavior of subjects follows the expected value model, however, certain systematic deviations from the rational model occurred in each study.
In the first study, the previous underestimation, overestimation findings were confirmed: both schizophrenics and normals overbid at probability values 0.01 and 0.05 and underbid at objective probability values ranging from 0.25 to 0.99.
In the second study similar effects were found. Where the subjects' likelihood of winning was 0.01 and 0.05, overestimation occurred: where their likelihood of winning ranged from 0.25 to 0.99 underestimation occurred.
In the third study, the loss type situation, underestimation occurred for probabilities of loss of 0.25, 0.50, 0.95 and 0.99. The data appear to indicate that subjects tend to overestimate the likelihood of loss very slightly at p = 0.75.
Comparison of the behavior in win and loss type situations, both for normals and schizophrenics, indicates that behavior conforms more closely to the expected value model in a loss type situation than a win situation.
When psychological probabilities were summed underestimation of the rational model was the general finding. In general, the deviations from the rational model were greater for schizophrenics than for normals.

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Thesis (Ph.D.)--Boston University