INTRODUCTION

This chapter seeks to clarify some features of social ordering functions that may appear intriguing to the specialist of social choice theory or of fair allocation theory. The reader who is more interested in the applications of the approach may skip this chapter. Three issues are examined, which all have to do with the informational basis of SOFs.

The first issue is connected to the fact that we define SOFs as functions R(RN,Ω) instead of functions R(RN). It may appear strange that the ranking of allocations should vary as a function of the available resources, as if an ethical objective could depend on feasibility constraints. Section 4.2 explains why this dependence is important for obtaining some results, although it is not essential to the notion of the SOF in general.

Section 4.3 examines how our theory relates to the theory of social choice in economic environments. We already mentioned in Chapter 3 that our SOFs satisfy a weaker axiom of independence – namely, unchanged-contour independence – than Arrow's famous independence of irrelevant alternatives. Relaxing Arrow's independence axiom is the key ingredient that enables us to obtain possibility results. In Section 4.3 we examine how the possibility results are affected when one varies the quantity of information that is used, through various axioms of independence.

Finally, Section 4.4 compares the theory of SOFs to the theory of fair allocation, in which allocation rules, instead of SOFs, are the subject.