Characterizing Inequality Equivalence Criteria

We introduce an axiomatic framework to analyze the perception of inequality across distributions with different total income. The main result is the characterization of a new two parameters generalized version of the inequality equivalence criterion (IEC), the Flexible IEC (FIE). This criterion is able to encompass all the most used criteria of inequality equivalence and is sufficiently flexible to provide a perception consistent with recent evidence from questionnaire investigations, namely that the inequality perception goes from the relative view (focussing on income shares) to the absolute view (focussing on absolute income differentials) as incomes increase. One parameter of the FIE is associated with the Bossert and Pfingsten (Math. Soc. Sc. 1990) Intermediate IEC (IIE) while the other is shown to lead to an alternative single parameter version of the IEC, the Proportional IEC which is dual to the previous. We provide independent characterizations both of PIE and IIE. Also alternative IECs existing in the literature are characterized within the axiomatic framework suggested. These results are consistent with those obtained in the surplus sharing literature by Moulin (Int. J. Game Theory 1987), Young (Math. Op. Res. 1987, J. Econ. Theory 1988) and Pfingsten (Math. Soc. Sc. 1991), and with recent results in inequality measurement by Ebert (Math. Soc. Sc. 2004) and Zheng (Soc. Ch. Wel. 2007). We complete the analysis investigating the implications of extending the domain of the income distributions including negative incomes. The basic consistency properties suggested in order to characterize the IECs are sufficient to select the absolute IEC when unbounded negative incomes are included in the domain.