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      On individual neutrality and collective decision making

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          Abstract

          We derive a simple mathematical "theory" to show that two decision-making entities can work better together only if at least one of them is occasionally willing to stay neutral. This provides a mathematical "justification" for an age-old cliche among marriage counselors.

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          The meaning and use of the area under a receiver operating characteristic (ROC) curve.

          A representation and interpretation of the area under a receiver operating characteristic (ROC) curve obtained by the "rating" method, or by mathematical predictions based on patient characteristics, is presented. It is shown that in such a setting the area represents the probability that a randomly chosen diseased subject is (correctly) rated or ranked with greater suspicion than a randomly chosen non-diseased subject. Moreover, this probability of a correct ranking is the same quantity that is estimated by the already well-studied nonparametric Wilcoxon statistic. These two relationships are exploited to (a) provide rapid closed-form expressions for the approximate magnitude of the sampling variability, i.e., standard error that one uses to accompany the area under a smoothed ROC curve, (b) guide in determining the size of the sample required to provide a sufficiently reliable estimate of this area, and (c) determine how large sample sizes should be to ensure that one can statistically detect differences in the accuracy of diagnostic techniques.
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            An Essay towards Solving a Problem in the Doctrine of Chances. By the Late Rev. Mr. Bayes, F. R. S. Communicated by Mr. Price, in a Letter to John Canton, A. M. F. R. S.

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              Author and article information

              Journal
              2012-04-24
              Article
              1204.5334
              ebb58724-1dff-4fcd-8e09-53d929d7ec7d

              http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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              The Mathematical Scientist, December 2012, Vol. 37, No. 2, Pages 141 - 146
              The Mathematical Scientist, Vol. 37, No. 2, accepted and to appear in December 2012
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