Entropy, Risk and Comparability

This chapter elaborates on some of the issues that arise in the theory and practice of distributional comparisons. These range from the nature and scope of probability judgements to the precise nature of the preference functions that may be involved. A recurring theme is that tail probabilities in themselves are not a sufficient guide to decision making; it is the length of the tail that matters. In this respect, tail entropy is an important complexity indicator. A standardisation is proposed that reduces the tail entropy for an arbitrary distribution to a locally equivalent logistic distribution, for which the regime entropies (tail versus the rest) are simply proportional to their respective probabilities. A further general theme concerns just what is meant when one says that outcome distribution A is preferred to B, and whether it is possible to ascribe a numerical value to the difference. This introduces the issue of whether any given underlying preference function is cardinal or ordinal in nature. Subjectivist probability in decision making is a further theme. Some concluding remarks concern possible applications to organisation theory.