Congress Seat Allocation Using Mathematical Optimization

Roland Hales, Sergio Garcia Quiles

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)426-455
Number of pages30
Issue number3
Early online date29 Apr 2019
Publication statusPublished - 31 Oct 2019

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