Overview

Nash [1950] proposed to generalize SWOs to more complex choice rules that we call social choice functions (SCFs). The idea is to take into account the whole feasible set of utility vectors to guide the choice of the most equitable one. Accordingly, any two utility vectors may no longer be compared independently of the context (namely, the actual set of feasible vectors), as was the case with SWOs. To understand how this widens the range of conceivable choice methods, think of relative egalitarianism as opposed to plain egalitarianism. Say that two agents must divide some commodity bundle. The egalitarian program simply chooses the highest feasible equal utility allocation (assuming away the equality-efficiency dilemma) independently of the feasible unequal utility vectors. Relative egalitarianism, on the other hand, computes first the utility w, that each agent would derive from consuming alone the whole bundle; then it chooses this efficient utility vector where the ratio of the actual utility to the highest conceivable utility w, is the same for each agent. In other words, relative egalitarianism equalizes individual ratios of satisfaction (or of frustration) by defining full satisfaction (i.e., zero frustration) in a context-dependent manner. We give a numerical example (Example 1.1), stressing the difference between egalitarianism and relative egalitarianism.