Distributive justice

For a variety of reasons, the literature on decision theory has been interwined with the literature on social choice theory for a very long period, but the focus of the two literatures is rather different and I have certainly had more to say about decision theory than about the normative problems of social choice or distributive justice. To a large extent, this is an accident of where I have happened to have had some ideas to develop and not a matter of a priori choice. I have published two papers on distributive justice (19661, 1977a). The main results about justice in the first one, which were stated only for two persons, were nicely generalized by Amartya Sen (1970). The other paper, which was just recently published, looks for arguments to defend unequal distributions of income. I am as suspicious of simplistic arguments that lead to a uniform distribution of income as I am of the use of the principle of indifference in the theory of beliefs to justify a uniform prior distribution. The arguments are too simple and practices in the real world are too different. A classical economic argument to justify inequality of income is productivity, but in all societies and economic subgroups throughout the world differences in income cannot be justified purely by claims about productivity. Perhaps the most universal principle also at work is one of seniority. Given the ubiquitous character of the preferential status arising from seniority in the form of income and other rewards, it is surprising how little conceptual effort seems to have been addressed to the formulation of principles that justify such universal practices. I do not pretend to have the answer but I believe that a proper analysis will lead deeper into psychological principles of satisfaction than has been the case with most principles of justice that have been advanced. I take it as a psychological fact that privileges of seniority will continue even in the utopia of tomorrow and I conjecture that the general psychological basis of seniority considerations is the felt need for change. A wide range of investigations demonstrate the desirable nature of change itself as a feature of biological life (not just of humans) that has not been deeply enough recognized in standard theories of justice or of the good and the beautiful.

Foundations of probability

The ancient Greek view was that time is cyclic rather than linear in character. I hold the same view about my own pattern of research. One of my more recent articles (1974g) is concerned with approximations yielding upper and lower probabilities in the measurement of partial belief. The formal theory of such upper and lower probabilities in qualitative terms is very similar to the framework for extensive quantities developed in my first paper in 1951. In retrospect, it is hard to understand why I did not see the simple qualitative analysis given in the 1974 paper at the time I posed a rather similar problem in the 1951 paper. The intuitive idea is completely simple and straightforward: A set of ‘perfect’ standard scales is introduced, and then the measurement of any other event or object (event in the case of probability, object in the case of mass) is made using standard scales just as we do in the ordinary use of an equal-arm balance. This is not the only occasion in which I have either not seen an obvious and simple approach to a subject until years later, or have in fact missed it entirely until it was done by someone else.

On the other hand, what would appear to be the rather trivial problem of generalizing this same approach to expectations or expected utility immediately encounters difficulties. The source of the difficulty is that in the case of expectations we move from the relatively simple properties of subadditive and superadditive upper and lower measures to multiplicative problems as in the characteristic expression for expected utility in which utilities and probabilities are multiplied and then added. The multiplicative generalization does not work well. It is easy to give a simple counterexample to straightforward generalization of the results for upper and lower probabilities, and this is done in Suppes (l975a). I have continued to try to understand better the many puzzles generated by the theory of upper and lower probabilities, in joint research with Mario Zanotti (1977j).

Partly as a by-product of our extensive discussions of the qualitative theory of upper and lower probabilities, Zanotti and I (1976n) used results in the theory of extensive measurement to obtain what I think are rather elegant necessary and sufficient conditions for the existence of a probability measure that strictly agrees with a qualitative ordering of probability judgments. I shall not try to describe the exact results here but mention the device used that is of some general conceptual interest.