A Proposal for an Excessivist Social Welfare Ordering

Authors: V. De Sandi

Abstract:

In this paper, we characterize a class of rank-weighted social welfare orderings that we call ”Excessivist.” The Excessivist Social Welfare Ordering (eSWO) judges incomes above a fixed threshold θ as detrimental to society. To accomplish this, the identification of a richness or affluence line is necessary. We employ a fixed, exogenous line of excess. We define an eSWF in the form of a weighted sum of individual’s income. This requires introducing n+1 vectors of weights, one for all possible numbers of individuals below the threshold. To do this, the paper introduces a slight modification of the class of rank weighted class of social welfare function. Indeed, in our excessivist social welfare ordering, we allow the weights to be both positive (for individuals below the line) and negative (for individuals above). Then, we introduce ethical concerns through an axiomatic approach. The following axioms are required: continuity above and below the threshold (Ca, Cb), anonymity (A), absolute aversion to excessive richness (AER), pigou dalton positive weights preserving transfer (PDwpT), sign rank preserving full comparability (SwpFC) and strong pareto below the threshold (SPb). Ca, Cb requires that small changes in two income distributions above and below θ do not lead to changes in their ordering. AER suggests that if two distributions are identical in any respect but for one individual above the threshold, who is richer in the first, then the second should be preferred by society. This means that we do not care about the waste of resources above the threshold; the priority is the reduction of excessive income. According to PDwpT, a transfer from a better-off individual to a worse-off individual despite their relative position to the threshold, without reversing their ranks, leads to an improved distribution if the number of individuals below the threshold is the same after the transfer or the number of individuals below the threshold has increased. SPb holds only for individuals below the threshold. The weakening of strong pareto and our ethics need to be justified; we support them through the notion of comparative egalitarianism and income as a source of power. SwpFC is necessary to ensure that, following a positive affine transformation, an individual does not become excessively rich in only one distribution, thereby reversing the ordering of the distributions. Given the axioms above, we can characterize the class of the eSWO, getting the following result through a proof by contradiction and exhaustion: Theorem 1. A social welfare ordering satisfies the axioms of continuity above and below the threshold, anonymity, sign rank preserving full comparability, aversion to excessive richness, Pigou Dalton positive weight preserving transfer, and strong pareto below the threshold, if and only if it is an Excessivist-social welfare ordering. A discussion about the implementation of different threshold lines reviewing the primary contributions in this field follows. What the commonly implemented social welfare functions have been overlooking is the concern for extreme richness at the top. The characterization of Excessivist Social Welfare Ordering, given the axioms above, aims to fill this gap.

Keywords: comparative egalitarianism, excess income, inequality aversion, social welfare ordering