Majority voting and Gini-based social welfare: testing the hypothesis of symmetry

Abstract

Majority voting accords with the class of social evaluation functions consistent with the Gini coefficient when income distributions are symmetric under a rank-dependent transformation (Rodríguez and Salas, 2014). Under this assumption, median income and the equally distributed equivalent income are the same, and the Gini coefficient is an affine function of the median–mean ratio. Despite the importance of these findings, the empirical plausibility of the symmetry hypothesis has not been tested yet. In this article, we contrast the symmetry assumption with an empirical exercise based on the Survey on Income and Living Conditions data set for the European Union in the period 2005–2007. We find that the symmetric condition is generally fulfilled.

Keywords:

• symmetric distribution
• social evaluation function
• the Gini coefficient
• majority voting

JEL Classification:

• D31
• D63
• P16

Acknowledgements

We are grateful to Juan Prieto Rodríguez for his assistance with the database. We also acknowledge the helpful comments and suggestions offered by P. Lambert and R. Aaberge. The usual disclaimers apply.

Notes

¹ Previously, Salas and Rodríguez (2013) found that majority voting and the AKS class of utilitarian social evaluation functions are consistent for any set of income distributions symmetric under a strictly increasing transformation.

² The EDE income is the level of income that if distributed equally to all individuals would generate the same social welfare as the existing income distribution.

³ Many of the existing tests of symmetry examine high order moments (see, for example, Premaratne and Bera, 2005). Bai and Ng (2005) report the difficulties with estimating higher-order moments, such as kurtosis, as well as the greater power of test which are based simultaneously on several odd-order moments.

Additional information

Funding

This research has benefited from Spanish Ministry of Finance and Competiveness Project ECO2013-46516-C4-4-R.