Abstract
After the 2015 Spanish general election a row erupted over the allocation of physical seats in the Congress of Deputies, with certain parties left feeling they possessed an inferior selection of seats compared to other parties. Using this as motivation, this paper considers how mathematical optimization can be used to generate seating plans for political chambers, an application that has not been considered before. As well as being in some way ‘fair’ to all parties, the seating plan should ensure that each block of seats is well-defined and compact. Two optimization models are formulated and, due to their complexity, heuristic methods are developed to find ‘good’ solutions. Analysis shows that the heuristics are able to produce visually appealing seating plans for basic cases, but problems can occur when there are additional requirements to be satisfied.
Highlights
In recent years there have been arguments regarding the seating plans in the Spanish Congress of Deputies, with some parties believing they have been allocated inferior seats compared to other parties
Is to investigate how mathematical optimization can assist with decisions regarding how representatives should be seated in a congress chamber and, in particular, to propose methods for generating seating plans that all parties find acceptable
Since these models are both hard to solve for large instances, in Sect. 5 we develop a location-allocation heuristic (LAH) for the facility location model (FLM), and in Sect. 6 we develop a geometric cutting heuristic (GCH) for the minimum k-partitioning model (MPM) that uses straight lines to partition the seats into blocks of the correct sizes
Summary
In recent years there have been arguments regarding the seating plans in the Spanish Congress of Deputies, with some parties believing they have been allocated inferior seats compared to other parties. The seating plan following the 2015 general election, shown in the top left of Fig. 1, prompted Podemos spokesperson Íñigo Errejón to claim that, “They are sending the representatives of five million voters to the nosebleed section, separated from the rest.”. With this in mind, the aim of this paper is to investigate how mathematical optimization can assist with decisions regarding how representatives should be seated in a congress chamber and, in particular, to propose methods for generating seating plans that all parties find acceptable. The plan should abide by any pre-existing rules or traditions regarding where the different parties are seated
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