Inequity aversion, welfare measurement and the Gini index

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The measurement of economic welfare has also received substantial attention in the current political debate. An example is the “beyond GDP initiative” of the European Commission, the European Parliament, the Club of Rome, OECD and WWF which has promoted the development of welfare indicators which are as clear and appealing as the traditionally used GDP, but more inclusive of environmental and social aspects of progress (see https://​ec.​europa.​eu/​jrc/​en/​event/​beyond-gdp-measuring-progress-true-wealth-and-well-being-nations-7763).

See Rohde (2010) for an axiomatic foundation of the Fehr and Schmidt model.

For example, the lowest income is weighted by \(\frac{1}{n}+\frac{\alpha +\beta }{n}>\frac{1}{n}\), the highest income by \(\frac{1}{n}-\frac{\alpha +\beta }{n}<\frac{1}{n}\) whereas the median income receives precisely the weight 1 / n.

For this specific example, the trade-off between average income and equality is determined by the sum of \(\alpha \) and \(\beta \), i.e. the sum of parameters of aversion to disadvantageous and advantageous inequity. This is arguably an artefact of the simplifications made in the choice of individual utility functions (for \(\alpha + \beta =1\), we obtain the special case of \(W=\mu (1-G)\); cf. Sen 1974). In general, we would indeed expect the relative weighing to be more complex. The purpose of this paper, however, was not to determine the best possible social welfare function but only to demonstrate that once we acknowledge monetary and distributional preferences on an individual level this translates rather simply—by aggregation—into a combination of well known social measures of aggregate wealth and distributional aspects.

Ben Porath and Gilboa define various axioms for a social preference relation, including inequity aversion regarding the distribution of income in society. As a result, they obtain a social welfare function, similar to the one derived here, combining aggregate income and the Gini index. Different from the present approach, they do not consider individual preferences, though. By contrast, the present approach shows that if individual preference relations display inequity aversion such that they can be represented by Fehr-Schmidt utility, the Gini coefficient arises naturally as welfare measure.

See Footnote 4.