One Man, One Vote Part 2: Measurement of Malapportionment and Disproportionality and the Lorenz Curve

Abstract

The main objective of this paper is to explore and estimate the departure from the “One Man, One Vote” principle in the context of political representation and its consequences for distributive politics. To proceed to the measurement of the inequalities in the representation of territories (geographical under/over representation) or opinions/parties (ideological under/over representation), we import (with some important qualifications and adjustments) the Lorenz curve which is an important tool in the economics of income distribution. We consider subsequently some malapportionment and disproportionality indices. It is applied to the 2010 Electoral College and the French parliamentary and local elections with a special attention to the electoral reform of 2015. In these applications, the Lorenz curve ordering is almost conclusive and consequently the Gini and DK indices are aligned and complement the almost complete ranking derived from Lorenz.

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Reference

Olivier de Mouzon, Thibault Laurent, and Michel Le Breton, “One Man, One Vote Part 2: Measurement of Malapportionment and Disproportionality and the Lorenz Curve”, TSE Working Paper, n. 20-1089, April 2020, revised April 2022.