Abstract
The ultimate goal of proportional apportionment methods is the minimization of disproportionality, i.e., unequal distribution of political representation among voters, or citizens. The Gini index is a well known tool for measuring inequality. In this work we propose a quotient method that minimizes the Gini index of disproportionality. Our method reduces the rounding of quotas to an instance of quadratic knapsack, a widely studied combinatorial optimization problem. Preliminary computational results, including real cases from the EU Parliament and the US House of Representatives, show that the method is effective, since the instances to solve are rather easy.
Highlights
Proportional methods offer different recipes to mitigate the unavoidable distortion arising when votes are translated into seats
This approach is followed by Grilli di Cortona et al (1999), who describe proportional methods as procedures solving an underlying optimization problem, where the objective function corresponds to some inequality index
These Authors suggest that, beyond evaluation, new proportional methods may be defined based on the optimization approach: minimize a given index subject to constraints enforcing specific properties, such as the quota property
Summary
Proportional methods offer different recipes to mitigate the unavoidable distortion arising when votes are translated into seats. Inequality, have been proposed to measure this distortion; typically, it can be shown that a certain index (or class of indexes) is minimized by a corresponding (traditional or ad-hoc) apportionment method, see Grilli di Cortona et al (1999), Balinski and Young (2001) and Edelman (2006) for an overview of these results. This leads to and supports the practice of, quoting Edelman (2006): “. Grilli di Cortona et al (1999) suggest as a suitable choice (among others) the Gini index: we pursue this idea in the present work
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