On the Qualitative Comparison of Decisions Having Positive and Negative Features

Making a decision is often a matter of listing and comparing positive and negative arguments. In such cases, the evaluation scale for decisions should be considered bipolar, that is, negative and positive values should be explicitly distinguished. That is what is done, for example, in Cumulative Prospect Theory. However, contrary to the latter framework that presupposes genuine numerical assessments, human agents often decide on the basis of an ordinal ranking of the pros and the cons, and by focusing on the most salient arguments. In other terms, the decision process is qualitative as well as bipolar. In this article, based on a bipolar extension of possibility theory, we define and axiomatically characterize several decision rules tailored for the joint handling of positive and negative arguments in an ordinal setting. The simplest rules can be viewed as extensions of the maximin and maximax criteria to the bipolar case, and consequently suffer from poor decisive power. More decisive rules that refine the former are also proposed. These refinements agree both with principles of efficiency and with the spirit of order-of-magnitude reasoning, that prevails in qualitative decision theory. The most refined decision rule uses leximin rankings of the pros and the cons, and the ideas of counting arguments of equal strength and cancelling pros by cons. It is shown to come down to a special case of Cumulative Prospect Theory, and to subsume the “Take the Best” heuristic studied by cognitive psychologists.

When opportunity matters: Comparing the risk taking attitudes of prisoners and recently released ex-prisoners

Risk-taking tendencies and environmental opportunities to commit crime are two key features in understanding criminal behavior. Upon release from prison, ex-prisoners have a much greater opportunity to engage in risky activity and to commit criminal acts. We hypothesized that ex-prisoners would exhibit greater risk-taking tendencies compared to prisoners who have fewer opportunities to engage in risky activity and who are monitored constantly by prison authorities. Using cumulative prospect theory to compare the risky choices of prisoners and ex-prisoners our study revealed that ex-prisoners who were within 16 weeks of their prison release made riskier choices than prisoners. Our data indicate that previous studies comparing prisoners behind bars with nonoffenders may have underestimated the risk-taking tendencies of offenders. The present findings emphasize the central role played by risk-taking attitudes in criminal offending and highlight a need to examine offenders after release from prison.