The Power Index Curse Strikes Again: Over-representation of Major Cities in French Inter-communal Structures
Résumé
In 2020, the issue of improving local collaboration between French municipalities reached a milestone. From January of this year, every municipality would, for the first time, belong to one of 1,254 French Inter-municipality structures. This achievement was accompanied by precise rules describing the distribution of seats among the different cities of the inter-municipal councils that govern each structure. However, the fairness of seat allocations proposed by French law, based on principles of proportionality can be questioned. Indeed, since the pioneering contributions of Penrose (1946) and Banzhaf (1965), the theory of power indices has warned us that representing cities in proportion to their population would give too much power to major cities. We assess whether this phenomenon can also be observed in France since 2020, using a new database that accurately reports the number of seats per city. Though we encounter a large variety of situations across the country, our results show that the provisions in the seat allocation rules often lead to the over-representation of major cities. Alternative allocation rules are presented to reduce these inequalities in representation.
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