Economic systems generate various distributions of opportunity sets for individuals to choose consumption bundles. This paper presents an axiomatic analysis on distributions of opportunity sets. We introduce several reasonable properties of distributions of opportunity sets, and characterize the...

Arrow's celebrated theorem shows that the aggregation of individuals' preferences into a social ordering cannot make the ranking of any pair of alternatives depend only on individuals' preferences over that pair, unless the fundamental Pareto and non-dictatorship principles are violated. In a...

Arrow's celebrated theorem of social choice shows that the aggregation of individual preferences into a social ordering cannot make the ranking of any pair of alternatives depend only on individual preferences over that pair, unless the fundamental weak Pareto and nondictatorship principles are...

In a standard framework of choice theory, we formulate two contrasting principles for social choice under the efficiency-equity trade-off. The equity-first principle states that we should select from equitable allocations if any, but if the equity criterion is not at all effective for selection...

In two-sided matching problems, we formulate (i) a concept of equity of matchings based on envy minimization, and (ii) a solidarity property of matching rules under "natural" and "simple" changes of preferences which represent enhancement of partnership of the pairs. We show that there exists no...

The Pareto efficiency criterion is often in conflict with the equity criteria as no-envy or as egalitarian-equivalence: An allocation x that is Pareto superior to another allocation y can be inferior to y in consideration of equity. This paper formalizes two differnet principles of social choice...

This paper considers two distinct procedures to lexicographically compose multiple criteria for social or individual decision making. The first procedure composes M binary relations into one, and then selects its maximal elements. The second procedure first selects the set of maximal elements of...

We propose the concept of a universal social ordering, defined on the set of pairs of an allocation and a preference profile of any finite population. It is meant to unify evaluations and comparisons of social states with populations of possibly different sizes with various characteristics. The...

This paper considers two distinct procedures to lexicographically compose two criteria for social or individual decision making. The first procedure composes two binary relations into one, and then selects its maximal elements. The second procedure first selects the set of maximal elements of...

When we construct social preferences, the Pareto principle is often in conflict with the equity criteria: there exist two allocations x and y such that x Pareto dominates y, but y is an equitable allocation whereas x is not. The efficiency-first principle requires to rank an allocation x higher...