Rowman and Littlefield International

Seats, Votes, and the Spatial Organisation of Elections

By Peter Taylor and Graham Gudgin

Its re-publication makes this classic piece of spatial (political) science available to contemporary audiences, for whom it is as relevant as when the book first appeared in 1979.

Paperback ISBN: 9781907301353 Release date: Sep 2012
£36.00 €49.00 $58.00

Pages: 314

ECPR Press

In many elections – especially those using single-member constituency systems – the allocation of seats is incommensurate with each party's share of the votes cast. Seats, Votes and the Spatial Organisation of Elections provides a convincing, rigorous analysis of this disproportionality which has not been improved on since its publication over 30 years ago. Its formal analysis, illustrated by empirical examples from a range of countries, stresses the importance of three geographies as key influences on how votes are translated into seats: the geography of partisan support (where people with different political persuasions cluster); the homogeneity of those clusters; and their relative size. Its re-publication makes this classic piece of spatial (political) science available to contemporary audiences, for whom it is as relevant as when the book first appeared in 1979; Ron Johnston's introductory essay sets the work in context and identifies its importance as the foundation for three decades of subsequent work into this key feature of electoral system operation.

contents

New Introduction: Seats, Votes and the Spatial Organisation of

Elections Revisited by Ron Johnston ix

Preface xli

1 Translating votes into seats

1.1 Seats and votes 1

1.1.1 Electoral reform 2

1.2 The spatial organisation of plurality elections 4

1.2.1 The distribution of party voters 5

1.2.2 Drawing constituency boundaries 8

1.2.3 The interaction of voters and boundaries 11

2 A modelling framework for the seats-votes relationship

2.1 The frequency-distribution approach 13

2.1.1 The constituency proportion distribution 14

2.1.2 Basic types of seats-votes relationships 17

2.2 The normal distribution and the cube law 20

2.2.1 Normal predictions of seat proportions 22

2.2.2 The cube law as a normal model 26

3 Explaining the cube law

3.1 The binomial method 32

3.1.1 Variants on the binomial distribution 33

3.1.2 The distribution of constituency proportions and spatial clustering 35

3.2 The Markov method 39

3.2.1 A model of individual voters 40

3.2.2 A model of clusters of voters 42

3.3 An empirical investigation of the Markov explanation 47

3.3.1 The sample survey 48

3.3.2 The political mosaic of Newcastle upon Tyne 49

3.4 The normal distribution as an electoral norm 52

4 Malapportionment, nonuniform swing, and nonnormality

4.1 Malapportionment 55

4.1.1 The effective party vote proportion 56

4.2 Nonuniform swings 59

4.2.1 Variations in patterns of swing 59

4.2.2 Simple random or linear swing-votes relationships 61

4.2.3 Other swing-votes relationships 64

4.3 Nonnormality in constituency proportion distributions 65

4.3.1 Nonnormality 1: skewness 68

4.3.2 Nonnormality 2: kurtosis and bimodality 71

4.3.3 Empirical studies of constituency proportion distributions 73

4.4 The components of electoral bias 86

vi seats, votes, and the spatial organisation of elections

5 Three-party elections

5.1 The three-party seats-votes relationship and the election triangle 93

5.1.1 Election triangles 94

5.2 The case of nationally uniform third-party vote 96

5.2.1 Equal attraction rates 97

5.2.2 Unequal attraction rates 99

5.3 Nonuniform levels of third-party support 102

5.3.1 Independent variable support for the third party 102

5.3.2 Third-party support related to major-party strength 106

5.3.3 Regional variation in third-party support 107

5.4 Empirical applications 109

5.4.1 Three-party elections in Britain 109

5.4.2 A permanent minority: Social Credit in New Zealand 116

5.5 Conclusion: three-party elections, the Achilles heel of the 119

plurality system

6 Decisionmaking in electoral districting

6.1 Types of districting agencies 122

6.1.1 Partisan decisionmaking 122

6.1.2 Nonpartisan decisionmaking 125

6.1.3 Bipartisan districting 127

6.1.4 Beyond the USA 131

6.1.5 The question of South African elections 133

6.2 A statistical framework 140

6.2.1 Constituencies as combinatorial structures 140

6.2.2 Algorithms for finding feasible solutions 143

6.3 The two-constituency case 146

6.3.1 Alternative solutions 146

6.3.2 Constituencies for Sunderland 149

6.3.3 Districting decisions of alternative agencies 151

6.3.4 A formal derivation of majority-party bias 152

6.4 Extensions to more than two constituencies 154

6.4.1 Variance and party fortunes 155

6.4.2 Constituencies for Newcastle upon Tyne 156

6.4.3 Congressional districts for Iowa 158

6.5 Is there a satisfactory districting procedure? 160

7 Beyond pluralities

7.1 Systems of voting 162

7.2 Majority systems of voting 165

7.2.1 The alternative vote in Australia 165

7.2.2 The double ballot in France 169

7.2.3 A majority-vote system for Britain 172

preface vii

7.3 The single-transferable-vote system 176

7.3.1 STV in Ireland 176

7.3.2 STV for British elections 179

7.4 A mixture of pluralities and PR 188

7.4.1 The ‘mixed system’ in the Federal Republic of Germany 190

7.4.2 Additional members for the British parliament 192

7.5 Conclusions: electoral engineering 195

8 Concluding comments and summary 200

Appendix 1

Alternative approaches to explaining the cube law 205

March’s behavioural rationalisation 205

Taagepera’s communication theory 208

A game-theoretic approach 211

Appendix 2

Functional relationships between seats and votes in multiparty

elections 213

Qualter’s multiparty equation 213

A general seats-votes equation 215

Casstevens and Morris’s decomposed system 218

Spafford’s regression approach 219

Appendix 3

Derivation of the seats-votes relationship: uniform support 222

and even attraction

Appendix 4

Derivation of the seats-votes relationship: uneven attraction 223

from major parties

Appendix 5

Construction of figure 5.10 225

Appendix 6

Derivation of equations for linear relations between third-party 226

support and the strength of other parties

Appendix 7

Alternative explanations of bimodal CPDs 228

References 231

Index 237

Graham Gudgin is Senior Research Fellow at the University of Cambridge's Centre for Business Research and Senior Economic Advisor with Oxford Economics, having previously worked as Director of the Northern Ireland Economic Research Centre and as Special Advisor to the First Minister. He started his lecturing career at Newcastle University.


Peter Taylor is a professor in the Department of Geography and Environment at the University of Northumbria, having previously worked at Newcastle and Loughborough Universities. He is a Fellow of the British Academy.

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