economies Article A New Quota Approach to Electoral Disproportionality Miguel Martínez-Panero 1,* , Verónica Arredondo 2, Teresa Peña 1 and Victoriano Ramírez 3 1 PRESAD Research Group, BORDA Research Unit, IMUVa, Departamento de Economía Aplicada, Universidad de Valladolid, 47011 Valladolid, Spain;
[email protected] 2 PRESAD Research Group, Unidad Académica de Matemáticas, Universidad Autónoma de Zacatecas, Zacatecas 98000, Mexico;
[email protected] 3 Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain;
[email protected] * Correspondence:
[email protected]; Tel.: +34-983-186591 Received: 10 January 2019; Accepted: 26 February 2019; Published: 5 March 2019 Abstract: In this paper electoral disproportionality is split into two types: (1) Forced or unavoidable, due to the very nature of the apportionment problem; and (2) non-forced. While disproportionality indexes proposed in the literature do not distinguish between such components, we design an index, called “quota index”, just measuring avoidable disproportionality. Unlike the previous indexes, the new one can be zero in real situations. Furthermore, this index presents an interesting interpretation concerning transfers of seats. Properties of the quota index and relationships with some usual disproportionality indexes are analyzed. Finally, an empirical approach is undertaken for different countries and elections. Keywords: electoral systems; proportionality; electoral quota; disproportionality indexes; measurement; Spain; Sweden; Germany 1. Introduction Electoral systems are mechanisms by which votes become seats in a parliament. In order to reflect the overall distribution of voters’ preferences, some of these systems advocate for proportional representation, so that political parties will receive percentages of seats corresponding to their respective percentages of votes.