Mathematical Programming Formulations for Practical Political Districting

Political districting is a very well-known technical problem related to electoral systems in which the transformation of votes into seats depends on the subdivision of the national electoral body into a given number of smaller territorial bodies. After a proper discretization of the territory, the problem consists of partitioning the territory into a prefixed number of regions which satisfy a set of geographic and demographic criteria. The problem structure falls back into one of the more general territory design problems, which arises also in other types of applications, such as school and hospital districting, sales districting, etc. In the application to political elections, the aim is to prevent districts’ manipulation which may favor the electoral outcome of some specific party (Gerrymandering). Many political districting models and procedures have been proposed in the literature since the 1960s following different optimization strategies. Among them, many exploit mathematical programming which is one of the most used tools to solve problems in practice. The attractive feature of mathematical programming is that the model is easy-to-read, its resolution can be automated, and good compromise solutions can be computed in reasonable computational time for small and medium size problems.