Consensus on desirable properties of the social preference relation may lead to a “dead end,” when the expected resolution of the social choice problem is the axiomatization of the social preference relation. This is one of the lessons of Arrow's impossibility theorem presented in Chapter 4. Nevertheless, agreement on the desirable properties can result in axiomatization, that is, in a unique characterization of the social preference relation or of the social choice rule, as we have seen in the previous chapter. But there is a third possibility. Agreement on desirable properties may lead to the identification of many social preference relations or many social choice rules that satisfy the desirable properties. The meaning of such a situation is that the search for the appropriate social preference relation or social choice function has resulted in “excessive success,” which implies that the search has not ended. In other words, such success enables the selection of a desirable rule, but there is still an indeterminacy problem that raises the question: What is the most desirable rule, the rule that should be selected out of the rules satisfying the desirable properties? In this chapter we propose the metric approach of compromising with the unanimity criterion to resolve this problem.

THE UNANIMITY CRITERION

Naturally, identification of many social choice functions is expected when agreement on the desirable properties is limited, that is, when there are just a few agreed-upon desirable properties and, in particular, when the individuals agree on just one such property.