Efficiency First or Equity First?: Two Principles and Rationality of Social Choice

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 under possible conflict of efficiency and equity. The efficiency-first principle requires that we should always select from efficient allocations, and when the efficiency criterion is not at all effective as a guide for selection, i.e., when all the available allocations are efficient or there is no efficient allocation, we should apply an equity criterion to choose desirable allocations. The equity-first principle reverses the lexicographic order of application of the two criteria. We examine rationality of the social choice rules satisfying these two principles. It is shown that the degree of rationality varies widely depending on which principle the social choice rules represent. Several impossibility and possibility results as well as a characterization theorem are obtained.

Partnership-Enhancement and Stability in Matching Problems

In two-sided matching problems, we consider “natural” changes in preferences of agents in which only the rankings of current partners are enhanced. We introduce two desirable properties of matching rules under such rankenhancements of partners. One property requires that an agent who becomes higher ranked by the original partner should not be punished. We show that this property cannot always be met if the matchings are required to be stable. However, if only one agent changes his preferences, the above requirement is compatible with stability, and moreover, envy-minimization in stable matchings can also be attained. The other property is a solidarity property, requiring that all of the “irrelevant” agents, whose preferences as well as whose original partners’ preferences are unchanged, should be affected in the same way; either all weakly better off or all worse off. We show that when matchings are required to be stable, this property does not always hold.two-sided matching problem, stable matching, partnership, solidarity

Egalitarian-Equivalence and the Pareto Principle for Social Preferences

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 than y if (i) x Pareto dominates y or (ii) x and y are Pareto-noncomparable and x is equitable whereas y is not. The equity-first principle reverses the order of application of the two criteria. Adopting egalitarian-equivalence as the notion of equity, we examine rationality of the social preference functions based on the efficiency-first or the equity-first principle. The degrees of rationality vary widely depending on which principle is adopted, and depending on the range of egalitarian-reference bundles. We show several impossibility and possibility results as well as a characterization of the social preference function introduced by Pazner and Schmeidler (1978). We also identify the sets of maximal allocations of the social preference relations in an Edgeworth box. The results are contrasted with those in the case where no-envy is the notion of equity.

Partnership-Enhancement and Stability in Matching Problems

In two-sided matching problems, we consider “natural” changes in preferences of agents in which only the rankings of current partners are enhanced. We introduce two desirable properties of matching rules under such rankenhancements of partners. One property requires that an agent who becomes higher ranked by the original partner should not be punished. We show that this property cannot always be met if the matchings are required to be stable. However, if only one agent changes his preferences, the above requirement is compatible with stability, and moreover, envy-minimization in stable matchings can also be attained. The other property is a solidarity property, requiring that all of the “irrelevant” agents, whose preferences as well as whose original partners’ preferences are unchanged, should be affected in the same way; either all weakly better off or all worse off. We show that when matchings are required to be stable, this property does not always hold.two-sided matching problem, stable matching, partnership, solidarity

International Negotiations for Reducing Greenhouse Gases with Emission Permits Trading

We build a three-stage game model of international negotiations on regulation of global emissions of greenhouse gases, and examine the Pareto optimality of an equilibrium allocation. First, we derive the condition for Pareto optimal allocations, which is an extension of the celebrated Samuelson condition. Next, we show that although production efficiency of a final allocation is always met at an equilibrium of the game, overall Pareto optimality may not be satisfied. This is because in negotiations on the level of global emissions in the first stage of the game, countries make expectations on the effect of the total supply of emission permits on the revenue from or the expenditure for emission permits in a later stage.

Egalitarian-Equivalence and the Pareto Principle for Social Preferences

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 than y if (i) x Pareto dominates y or (ii) x and y are Pareto-noncomparable and x is equitable whereas y is not. The equity-first principle reverses the order of application of the two criteria. Adopting egalitarian-equivalence as the notion of equity, we examine rationality of the social preference functions based on the efficiency-first or the equity-first principle. The degrees of rationality vary widely depending on which principle is adopted, and depending on the range of egalitarian-reference bundles. We show several impossibility and possibility results as well as a characterization of the social preference function introduced by Pazner and Schmeidler (1978). We also identify the sets of maximal allocations of the social preference relations in an Edgeworth box. The results are contrasted with those in the case where no-envy is the notion of equity.

Partnership-Enhancement and Stability in Matching Problems

In two-sided matching problems, we consider "natural" changes in prefer- ences of agents in which only the rankings of current partners are enhanced. We introduce two desirable properties of matching rules under such rank- enhancements of partners. One property requires that an agent who be- comes higher ranked by the original partner should not be punished. We show that this property cannot always be met if the matchings are required to be stable. However, if only one agent changes his preferences, the above requirement is compatible with stability, and moreover, envy-minimization in stable matchings can also be attained. The other property is a solidarity property, requiring that all of the "irrelevant" agents, whose preferences as well as whose original partners' preferences are unchanged, should be affected in the same way; either all weakly better off or all worse off. We show that when matchings are required to be stable, this property does not always hold.two-sided matching problem, stable matching, partnership, solidarity

Possibility and Optimality of Agreements in International Negotiations on Climate Change

We build a three-stage model of international negotiations on regulation of the level of total emissions of greenhouse gases, and examine the possibility of a cooperative agreement and the Pareto optimality of the outcome. First, we derive the condition for Pareto optimal allocations, which is an extension of the celebrated Lindahl-Bowen-Samuelson condition and Chichilnisky et al.'s (2000) result. Next, we show that if the distribution rule of initial emission permits is the proportional rule to the Nash equilibrium emissions in the noncooperative game, then some cooperative agreement can be reached in the negotiations. However, for many other (equitable) distribution rules, no cooperative agreement is possible. Even if a cooperative agreement is attained, the outcome is rarely Pareto optimal.

Choice-Consistent Resolutions of the Efficiency-Equity Trade-Off

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 either because all the available allocations are equitable or because no allocation is equitable, we should select from Pareto efficient allocations. The efficiency-first principle switches the roles of the equity criterion and the efficiency criterion above. We examine the choice-consistency properties, known as Path Independence (Arrow, 1963) and Contraction Consistency (Chernoff, 1954), of the social choice correspondences satisfying the equity-first or the efficiency-first principle. Several possibility and impossibility theorems are obtained, which indicate that possibility of consistent social decisions depends crucially on which principle we take as well as what is the precise notion of equity.equity, efficiency, lexicographic composition, choice-consistency, path-independence

The Fundamental Theorems of Welfare Economics in a Non-Welfaristic Approach

This paper investigates extensions of the two fundamental theorems of welfare economics to the framework in which each agent is endowed with three types of preference relations: an allocation preference relation, an opportunity preference relation, and an overall preference relation. It is shown that, under certain conditions, the two theorems can be extended. It is also pointed out that the conditions underlying the positive results are restrictive.