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Democracy and the Common Good FINAL Democracy and the Common Good A Study of the Weighted Majority Rule Katharina Berndt Rasmussen ©Katharina Berndt Rasmussen, Stockholm 2013 ISBN 978-91-7447-738-2 Printed in Sweden by US-AB, Stockholm 2013 Distributor: Department of Philosophy, Stockholm University To Nika Contents 1 Introduction ............................................................................................... 11 1.1 Majority conundrums .............................................................................................. 11 1.2 The ubiquity of the unequal vote ............................................................................ 15 1.3 The value of democracy ......................................................................................... 17 1.4 Main thesis and disposition .................................................................................... 19 2 The basics ................................................................................................. 23 2.1 Introduction ............................................................................................................. 23 2.2 The weighted majority rule ..................................................................................... 23 2.2.1 The weighted majority rule and democratic theory ........................................ 25 2.3 Individual well-being and the common good .......................................................... 31 2.3.1 Individual well-being ....................................................................................... 31 2.3.2 The common good ......................................................................................... 34 2.3.3 Terminology ................................................................................................... 40 2.4 Democracy and the promotion of the common good .............................................. 40 2.4.1 Arrow's theorem and related problems .......................................................... 41 2.4.2 Returning to the weighted majority rule .......................................................... 43 2.5 Notes on methodology and philosophical framework ............................................. 45 2.5.1 The moral-philosophical framework ............................................................... 45 2.5.2 Formal models ............................................................................................... 46 3 A case for the weighted majority rule ........................................................ 51 3.1 Introduction ............................................................................................................. 51 3.2 The original argument from collective optimality .................................................... 51 3.2.1 Alternative versions of the argument .............................................................. 56 3.3 The generic argument from collective optimality .................................................... 61 3.4 Further clarifications ............................................................................................... 63 3.5 Conclusions ............................................................................................................ 70 4 Self- and common-interested voting ......................................................... 71 4.1 Introduction ............................................................................................................. 71 4.2 The extended argument from collective optimality ................................................. 71 4.2.1 Rebutting the ‘mixed motivation’ problem ...................................................... 74 4.3 Erratic voting behaviour .......................................................................................... 76 4.3.1 Why a voter may vote erratically .................................................................... 77 4.4 Conclusions ............................................................................................................ 80 5 Less than fully competent voters .............................................................. 83 5.1 Introduction ............................................................................................................. 83 5.2 The argument from weak collective optimality ........................................................ 85 5.2.1 Introducing the Condorcet jury theorem ......................................................... 85 5.2.2 Equal-stakes cases with common-interested voters ...................................... 90 5.2.3 Equal-stakes cases with self-interested voters .............................................. 92 5.2.4 Equal-stakes mixed-motivation cases ............................................................ 99 5.2.5 ‘Mixed’ cases with heterogeneously end-competent voters ......................... 101 5.2.6 Unequal-stakes cases and the independence assumption .......................... 104 5.2.7 Unequal-stakes cases and direct causal dependence ................................. 108 5.2.8 Unequal-stakes cases and common cause dependence ............................. 117 5.3 Conclusions .......................................................................................................... 122 6 Two more arguments and one alleged paradox ..................................... 125 6.1 Introduction ........................................................................................................... 125 6.2 The behavioural argument from weak collective optimality .................................. 125 6.3 The better-than-the-average-voter argument ....................................................... 128 6.4 Some remarks on the discursive paradox ............................................................ 131 6.5 Conclusions .......................................................................................................... 136 7 Multi-option decisions ............................................................................. 139 7.1 Introduction ........................................................................................................... 139 7.2 The further-extended argument from collective optimality .................................... 142 7.3 Logrolling for self-interested voters ...................................................................... 146 7.3.1 Is logrolling eventually against the logrollers' self-interest? ......................... 150 7.3.2 Can logrolling be avoided by devising compound decisions? ...................... 154 7.3.3 Why logrollers at best can achieve cycles or ties ......................................... 156 7.3.4 Why logrolling in compound decisions is worse for logrollers and better for all (than in separate binary decisions) ....................................................................... 162 7.3.5 Why logrollers in compound four-option decisions do not face the logrollers' dilemma ................................................................................................................. 164 7.3.6 Results so far ............................................................................................... 167 7.4 Individual strategies for self-interested voters ...................................................... 168 7.4.1 Why any individual at best can achieve a cycle ........................................... 170 7.4.2 Results so far ............................................................................................... 172 7.5 Alternative versions of the weighted majority rule ................................................ 172 7.6 Common-interested voters and strategic voting ................................................... 174 7.7 Less than fully competent voters .......................................................................... 177 7.8 Conclusions .......................................................................................................... 179 8 Summary and discussion ........................................................................ 183 8.1 Introduction ........................................................................................................... 183 8.2 The original argument can be adapted to other criteria of the common good ...... 184 8.2.1 The original argument from collective optimality .......................................... 184 8.2.2 The generic argument from collective optimality .......................................... 185 8.3 The assumption of self-interested voting can be logically weakened ................... 187 8.3.1 The extended argument from collective optimality ....................................... 187 8.3.2 Arguments from weak collective optimality .................................................. 189 8.3.3 The better-than-the-average-voter argument ............................................... 194 8.3.4 The behavioural argument from weak collective optimality .......................... 194 8.4 The scope of the argument can be extended to multi-option decisions ............... 195 8.4.1 The further-extended argument from collective optimality ........................... 196 8.5 Conclusion ............................................................................................................ 199 Appendix .................................................................................................... 202 A.1 Introduction .......................................................................................................... 202 A.2 Rae’s
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