A Note on Characterising the Median

Consider the situation where one has to choose one among three differently priced birthday cakes, to give to a friends. It is very likely, that in the absence of strong personal reasons, one would select the cake whose price lies between the two extremes. A similar emphasis on the middle path is found in the teachings of Buddha as also in Confucian philosophy. That the choice of an alternative from a finite set of alternatives, need not conform to some optimising behaviour, is a possibility that has been discussed in Baigent and Gaertner (1996). In a sense this is a position on human behaviour which is contrary to the received view of a decision maker as an optimizer of some objective function that is favored for instance by Sen (1993). That the median does not satisfy the requirements of underlying optimising behaviour has been noted by Kolm (1994) and Gaertner and Xu (1999). However, the median is a reasonable compromise, in practical decision making.