Optimizing Districting and Seat Allocation for Enhanced Representativeness in Chile’s Chamber of Deputies

Abstract

This paper presents a mathematical programming model to simultaneously create districts and allocate seats in Chile’s Chamber of Deputies, improving representativeness. In addition, it explicitly incorporates constraints that ensure the contiguity of the communes that form the districts while respecting natural and administrative boundaries. Implementing specific strategies and methods has resulted in significant enhancements in particular metrics used to assess the degree of representativeness. These improvements have effectively addressed certain shortcomings and resulted in more accurate and reliable representation measurements in the given context. This study proposes a novel mathematical programming model that simultaneously tackles district creation and seat allocation for Chile’s Chamber of Deputies. This integrated approach aims to achieve a more representative body. The results demonstrate a substantial decrease in malapportionment, from 11.07 in the 2015 reform to 6.55 under the proposed model. Furthermore, the sum of deviations has diminished, and the number of overrepresented districts has decreased from 17 to 13 out of 28 districts. Consequently, the malapportionment has been significantly reduced and falls within the permissible range of deviations, as outlined by the European Commission for Democracy through Law.