Network models and biproportional rounding for fair seat allocations in the UK elections

Research output: Contribution to journalArticle

Abstract

Systems for allocating seats in an election offer a number of socially and mathematically interesting problems. We discuss how to model the allocation process as a network flow problem, and propose a wide choice of objective functions and allocation schemes. Biproportional rounding, which is an instance of the network flow problem, is used in some European countries with multi-seat constituencies. We discuss its application to single seat constituencies and the inevitable consequence that seats are allocated to candidates with little local support. However, we show that variants can be selected, such as regional apportionment, to mitigate this problem. In particular, we introduce a parameter based family of methods, which we call Balanced Majority Voting, that can be tuned to meet the public's demand for local and global ``fairness''. Using data from the 2010 and 2015 UK General Elections, we study a variety of network models and implementations of biproportional rounding, and address conditions of existence and uniqueness.
LanguageEnglish
Pages1-19
Number of pages19
JournalAnnals of Operations Research
Volume253
Issue number1
Early online date22 Sep 2016
DOIs
Publication statusPublished - 30 Jun 2017

Fingerprint

Network Flow Problem
Rounding
Elections
Seats
Network Model
Majority Voting
Fairness
Existence and Uniqueness
Objective function
Network model
Seat
Model
Family
Demand
Network flow

Keywords

  • fair seat allocation
  • integer programming
  • biproportional matrices
  • networks and graphs

Cite this

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title = "Network models and biproportional rounding for fair seat allocations in the UK elections",
abstract = "Systems for allocating seats in an election offer a number of socially and mathematically interesting problems. We discuss how to model the allocation process as a network flow problem, and propose a wide choice of objective functions and allocation schemes. Biproportional rounding, which is an instance of the network flow problem, is used in some European countries with multi-seat constituencies. We discuss its application to single seat constituencies and the inevitable consequence that seats are allocated to candidates with little local support. However, we show that variants can be selected, such as regional apportionment, to mitigate this problem. In particular, we introduce a parameter based family of methods, which we call Balanced Majority Voting, that can be tuned to meet the public's demand for local and global ``fairness''. Using data from the 2010 and 2015 UK General Elections, we study a variety of network models and implementations of biproportional rounding, and address conditions of existence and uniqueness.",
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