[0,
).
Arrow’s Theorem concerns Social Welfare Function Generating Mechanisms (SWF-GMs) like the c above. Thus, a constitution can be seen as a mechanism that uses the population as input and generates a SWF that orders all elements in the commodity space. This can be compared to a Social Decision Function (SDF) that selects only one element, namely the best of a budget set. This can be weakened further by considering preference orderings instead of functions. Constitutions generally associate better with SDF-GMs since parliaments generally don’t care ordering all proposals. However, these concepts can be translated into each other via varying the budget set. Since the SWF is the conventional concept in economics, the word “constitution” can remain associated with a SWF-GM.
It suffices to restrict S to preference orderings. These orderings satisfy reflexivity, transitivity and completeness. It is important to add that there is no cheating. Let R denote normal preference, P strict preference, and I indifference. When there is no confusion, we can also use the symbols
, < and =. A suffix denotes an individual preference, otherwise it is the aggregate. An element in Sn is called a profile, and R = c(R1, ...Rn).
There are the following Arrowian axioms:
AWP the weak Pareto principle
AU universal domain (wide ranging preferences)