Equity theory

The theory of fairness or equity theory, including fair allocations theory and even appli­cations to public economics, borrowed the axiomatic methods from social choice theory and the theory of bargaining to study the implications of equity criteria in the framework of the Arrow-Debreu general equilibrium model.

Different fairness criteria can be contemplated for division rules. The idea of “no envy” was independently introduced by Jan Tinbergen (1953), Duncan Foley (1967) and developed by Serge-Christophe Kolm (1971), Allan Feldman and Alan Kirman (1974). An allocation is “envy free” if no individual would like better anybody else’s basket. A fundamental result of equity theory is such that the competitive equilibrium with equal endowments, that is, equal budgets, satisfies both the criteria of “no envy” and Pareto. Refinements of such analyses were first conducted in the context of distribution of a consumption economy without production, then to study equal opportunities, incentives and optimal taxation, division of a single divisible good with single-peaked or monot­onic preferences, the allocation of several commodities, the properties of a production economy, and so on.

The no-envy criterion, however, may conflict with the criterion of efficiency. This was proved by Elisha Pazner and David Schmeidler in 1974: no allocation respects Pareto efficiency and fairness (as no envy) in the context of production with unequal skills - that is, with production handicaps. This impossibility result can be interpreted as the incom­patibility between a principle of reward and a principle of compensation. The no-envy test indeed requires that the allocation of individuals with identical preferences is on the same indifference curve. According to the principle of reward, individuals with similar talents should not envy each other, since there should not be any different treatment for different preferences. Also, according to the principle of compensation, individuals who have identical preferences should have the same benefit, eliminating the inequalities due to talents.

The same authors proposed in 1978 another test of fairness based on egalitarian equivalent allocations. An allocation is egalitarian-equivalent when each one is indif­ferent between the basket of goods in the allocation and the basket she would have in an egalitarian economy. In this perspective, Marc Fleurbaey and Franςois Maniquet (2005) - among other similar contributions - considered the introduction of skills het­erogeneity, and studied the consistency between compensation of skills inequalities and the condition of equal access to resources for all preferences. For a deeper understand­ing of the subject of responsibility and unequal handicaps, see Fleurbaey (2008) and, for a comprehensive presentation of the economic theory of fairness, see Fleurbaey and Maniquet (2011).

The theory of equity took up the different challenges welfare economics was facing. First, it is worth noticing it eventually overcame the Arrovian impossibility. Second, it did reject interpersonal comparisons of utility. Unlike standard economics which relies on the model of subjective revealed preferences, welfare is here described as an index of resources; and unlike the comparative approach, they still keep some account of individual ordinal preferences, which avoids the risk of paternalism. Third, the theory of fairness accepts the challenge of value judgements transparency in making clear the criteria of justice.