Extended social ordering functions for rationalizing fair allocation rules as game forms in the sense of Rawls and Sen

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We examine the possibility of constructing social ordering functions, each of which associates a social ordering over the feasible pairs of allocations and allocation rules with each simple production economy. Three axioms on the admissible class of social ordering functions are introduced, which embody the values of procedural fairness, non-welfaristic egalitarianism, and welfaristic consequentialism, respectively. The logical compatibility of these axioms and their lexicographic combinations subject to constraints are examined. Two social ordering functions that give priority to procedural values rather than to consequential values are identified. These two can uniformly rationalize a nice allocation rule in terms of the values of procedural fairness, non-welfaristic egalitarianism, and Pareto efficiency.