A new investigation is launched into the problem of decision-making in the face of 'complete ignorance', and linked to the problem of social choice. In the first section the author introduces a set of properties which might characterize a criterion for decision-making under complete ignorance. Two of these properties are novel: 'independence of non-discriminating states', and 'weak pessimism'. The second section provides a new characterization of the so-called principle of insufficient reason. In the third part, lexicographic maximin and maximax criteria are characterized. Finally, the author's results are linked to the problem of social choice.
Several authors, [2], [3],
[7], and [9] have dealt with the problem of an individual who must choose from a set of alternatives when he cannot associate a probability distribution with the possible outcomes of each alternative. The problem has been called that of decision-making under complete ignorance; presumably 'complete ignorance' captures the notion that the axioms of subjective probability cannot be fulfilled. This paper is a further investigation in that tradition. In the first section we suggest a set of properties which might characterize a criterion for decision-making under ignorance. Most of these properties are familiar, but, in particular, 'independence of non-discriminating states' and 'weak pessimism' are new in this context. The second section recapitulates some of the important decision criteria in the literature and suggests a new characterization of the so-called principle of insufficient reason. In the third part, we drop the assumption invariably made by previous authors that preferences for consequences satisfy the von Neumann-Morgenstern axioms, and characterize the so-called lexicographic maximin and maximax criteria. We also provide a new axiomatization of the ordinary maximin principle. Finally, we show that several of our results translate quite easily into the theory of social choice.
THE PROPERTIES
Let C be a consequence or 'outcome' space. C contains a subset C* of 'sure' or 'certain' outcome as well as all finite lotteries 1 with outcomes in C*, We Theory and Decision 11 (1979) 319-337. 0040-5833/79/0113-0319~01.90.