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Preface
This is a book in democratic theory, not applied mathematics. Much valuable technical work has been done on the Condorcet Jury Theorem and related results. We have benefited enormously from that work in writing our own book. But this book itself is not a contribution to any highly technical literature. Although we hope that some of its insights (particularly the more conceptual ones in Part I of the book) might be of interest to more technically minded readers, the principal intended audience for this book is the non-technical reader who is interested in what the practical political upshot of the Condorcet Jury Theorem might be for the theory and practice of democracy.
In this book, we offer some conjectures but no proofs. A few of the results reported are analytically derived. But the vast majority are computationally generated, utilizing a Monte Carlo simulation procedure, described in Appendix A2.
Through those, we strive to get a sense of ‘how these functions behave’ across a range of scenarios likely to mirror those commonly found in the real political world. Establishing what would occur across a realistically likely range of cases is much more important, for the practical political purposes of this book, than establishing what is necessarily the case across the entire range of possible cases. For the same sort of reasons, we typically present our results as diagrams rather than tables. For our purposes, it is more important to convey a general sense of what is going on across the relevant range rather than to fixate on any particular point on the curve.
For the purposes of our computational exercises, we typically need to plug in numbers for some of the crucial variables to enable us to estimate the values of others. The numbers we plug in are, to some extent, plucked out of thin air. We offer no grounds for thinking that they are empirically the true values, necessarily. Nonetheless, we hope readers will share our sense that they are plausible enough values for results based on them to be of genuine political interest.
Books resting on mathematics, however lightly, might naturally be expected to be somewhat plodding. No doubt some non-technical readers will find our discussion in some places rather hard going, and alas unavoidably so. But overall the spirit of the book is meant instead to be ‘playful’. Or, perhaps more precisely, it is ‘exploratory’. Our aim, more than anything, is simply to ‘see what happens’ when you vary the many interrelated conditions that might affect the overall epistemic performance of modern democratic government.
The bulk of this book was drafted well before the unsettling political events of 2016. Brexit and Trump are indeed worrying results from the point of view of epistemic democrats. But as our epilogue shows, there are perfectly good
ways of making sense of those results in terms of the Condorcet Jury Theorem, because there are good reasons to think some of its key assumptions were violated in those cases. If its assumptions fail to obtain, that does not mean the Condorcet Jury Theorem and analyses based on it are false. It merely means that those analyses do not (always) track the real world, and it is important to see why. The mathematics are as they are, nonetheless, and it is well worth seeing what they imply for more ordinary democratic politics, even if those politics will be wracked from time to time by such extraordinary cataclysms as Brexit and Trump.
Acknowledgements
We have been working on these themes off and on, jointly and separately, for a dozen years or more. Naturally, we have incurred a great many debts over that time.
The first is to Christian List. Bob Goodin coauthored a first paper on these topics with him while Christian was a doctoral student visiting ANU as our first Harsanyi Fellow. Christian went on to supervise Kai Spiekermann’s own doctoral dissertation, and to coauthor several related papers with him in turn. Our thinking on these topics has been sharpened by conversations with him over many years. Kai Spiekermann’s has been sharpened in similar fashion by conversations and collaborations with Franz Dietrich, their sometime colleague at LSE.
We should record, more generally, our gratitude to colleagues at the institutions at which we worked during the gestation of this book. For Bob Goodin that includes: the School of Philosophy at ANU; the Bioethics Department at the National Institutes of Health, Bethesda, Maryland; and the Government Department at the University of Essex. For Kai Spiekermann that includes: the Philosophy Department at the University of Warwick; the Department of Government at LSE; and the School of Philosophy at ANU.
Earlier versions of these materials were presented at conferences, workshops and seminars at: Australian National University, University of Copenhagen, Wissenschaftskolleg Greifswald, Harvard Law School, London School of Economics, Trinity College Dublin, University of Maryland, Università degli Studi Milan, New York University, Princeton University, l’Université ParisSorbonne, University of Turku, the Swedish Collegium for Advanced Study in Uppsala, Washington University St. Louis, and the APSA meetings in Washington, DC. We are grateful to those audiences for their helpful comments and suggestions. We are particularly grateful for advice from Martin Marchman Andersen, Antoella Besussi, Giulia Bistagnino, Geoff Brennan, Randy Calvert, Stef Collins, Garrett Cullity, Franz Dietrich, John Dryzek, Lina Eriksson, Dave Estlund, Greta Favara, Barbara Fried, Archon Fung, Jerry Gaus, David Gauthier, Charles Girard, Alvin Goldman, Bernie Grofman, Russell Hardin, Clarissa Hayward, Jeff Howard, Adam Kern, Tony King, Saul Levmore, Skip Lupia, Klemens Kappel, Dimitri Landa, Jenny Mansbridge, Iain McLean, David Miller, Nick Miller, Mick Moran, Dennis Mueller, Cara Nine, Bertell Ollman, Joe Oppenheimer, Fabienne Peter, Philip Pettit, Ryan Pevnick, John Quiggin, Andrew Rehfeld, Mathias Risse, Don Saari, Theresa Scavenius, Norman Schofield, Katri Seiberg, Piotr Swistak, Ana Tanasoca, Larry Temkin, Mariam Thalos, Jeremy Waldron, and Jurgen De Wispelaere.
Acknowledgements
At Oxford University Press, we are grateful to Dominic Byatt, first for arranging a pair of insightful referees for the book and subsequently for so efficiently seeing the book into print. It is always a pleasure to work with him.
This book borrows in places on previously published articles. We are grateful to their publishers for permission to reuse some of that material, typically in somewhat different ways, in this book.
Robert E. Goodin and Kai Spiekermann, ‘Epistemic aspects of representative government’, European Political Science Review, 4 (no. 3) (Nov. 2012), 303–25.
Robert E. Goodin and Kai Spiekermann, ‘Epistemic solidarity as a political strategy’, Epistème, 12 (no. 4) (Dec. 2015), 439–57.
Kai Spiekermann and Robert E. Goodin, ‘Courts of many minds’, British Journal of Political Science, 42 (no. 3) (July 2012), 555–72.
5.3
5.4
4.3.1
6.
5.5
4.6.1
4.6.2
6.2
6.3
5.2.3
PART II. EPISTEMIC ENHANCEMENT
7.2.3
8.
7.3
8.2.4
PART III. POLITICAL PRACTICES
12.
12.4
PART IV. STRUCTURES OF GOVERNMENT
15. Epistocracy or Democracy
15.1 Beating the Smartest Guy in
15.1.2
15.2
15.2.1
15.2.2
15.2.3
15.4 Competence-Weighted
15.5 Epistemic Considerations
15.5.1
15.5.2
15.5.3
15.6
16.1.1
19.
PART V. CONCLUSIONS
20.1.2 All’s Well So Long As There Are Sufficient, Numerous, Competent, Independent Influences at Work Somewhere
20.1.3 There Are Ways of Coping with Incompetent Voters
20.1.4 The Case for Large Groups
20.1.5 Smaller Groups to Deliberate and Winnow the Options
20.1.6 The Decision Situation Is Crucial
20.2 Central Implications for Political Practice
20.2.1 Avoid Epistemic Deference
20.2.2 Pluralism Is Good
20.2.3 More High-Quality Evidence Is Good
20.2.4 Small-Scale Deliberative Conclaves to Advise the Electorate Are
20.3 Getting It
List of Figures
2.1
3.1 Probability that the majority of voters, each pc = 0.51 competent (and voting with equiprobability for all incorrect alternatives), will vote for the correct alternative, with 2, 3, 4, and 5 alternatives.
3.2 Probability that the plurality of voters, each pc = (1/k) + 0.01 competent and equiprobable to vote for false alternatives, will vote for the correct alternative. 31
3.3 Comparing group competence for three alternatives, voters with pc = 0.34 and equiprobable votes for the other two alternatives, with decision taken by Borda Count, Condorcet Pairwise Criterion, and Plurality Vote.
4.1 Probability that the majority of voters is correct, if voters are individually pc=0.45 likely to be correct, for electorates of varying sizes.
4.2 Probability that the majority of 200 voters is correct, depending on whether voters vote independently (cases I and II) or are certain to follow an opinion leader (cases III and IV) who is 0.40 likely to be correct or who is 0.60 likely to be correct, for electorates of varying levels of homogeneous individual competence.
5.1 Independence conditional on the State of the world.
5.2 Direct violation of independence conditional on the State of the world.
5.3 Indirect violation of independence conditional on the State of the world.
5.4 Independence conditional on the available Evidence about the State of the world.
5.5 Independence conditional on the Opinion Leader.
5.6 Violation of Independence due to multiple common causes.
5.7 Voters are influenced by both Evidence and a common cause.
5.8 Convergence of probability of the majority among n voters being correct, for various values of the probability that the decision situation is truth-conducive (ω), shown with homogeneous pBR =0.55 .
5.9 Experts versus laymen facing different decision situations.
6.1 Different distributions of individual competence and the resulting group competences.
7.1 One common cause and many common causes.
7.2 Several common causes and direct access to Evidence.
8.1 Rugged policy landscape. 113
8.2 Search on 1,000 patches, probability of finding correct patch depending on numbers of search parties.
116
8.3 Rugged policy landscape and inertia-induced equilibria. 118
8.4 Population and specialist votes in comparison. 130
10.1 Differing points at which deference might set in. 152
10.2 Probability of correct majority decision from a court with nine members, each pc*= 0.55 likely to be individually correct, with weight w = 1. 156
10.3 Probability of correct majority decision from a court with nine members, each pc*= 0.55 likely to be individually correct. 158
10.4 Discerning traditionalists. 160
10.5 Probability of correct majority decision from a heterogeneous nine-member court (each judge pc*= 0.55 likely to be individually correct), where four judges vote on the basis of their private signal and the rest decide by weighting on the basis of their own private signal w = 1 and only take into account informative votes. 161
11.1 Multiple votes influenced by the same Opinion Leader, either without (a) or with (b) direct influence of Evidence on Votes. 166
11.2 Probability of correct majority decision among voters with individual competence pc* = 0.55, given a single opinion leader of competence pOL = 0.55 followed with probability π 167
11.3 Probability of correct majority decision among voters with individual competence pc* = 0.55, given a single opinion leader of competence pOL = 0.4 followed with probability π. 168
11.4 Perfectly positively correlated Opinion Leaders and some independent Votes. 170
11.5 Negatively correlated Opinion Leaders and independent Votes. 171
11.6 Many multiply mediated Opinion Leaders, direct links between Evidence and LOLs and Evidence and Votes are omitted. 176
12.1 One Cue as the only access to the Evidence for all voters. 186
12.2 Several Cues as well as direct access to the Evidence. 187
12.3 Probability of majority voting for correct alternative, with varying levels of individual competence pc* and probability of being guided by any given cue π, for 990 voters, nine cues, and probability of any given cue being correct of pK = 0.70.
192
13.1 Baseline scenario with two groups of equal size and all pcV = 0.55. 198
13.2 60% of voters with value V1, 40% with V2 and with all pcV = 0.55. 199
13.3 Two groups of equal size, but voters with V1 have pcV1 = 0.8 while voters with V2 have pcV2 = 0.55. 200
13.4 60% of voters subscribing to value V1 with pcV1 = 0.8 and 40% of voters subscribing to value V2 with pcV2 = 0.55. 201
13.5 60% of voters subscribing to value V1 with pcV1 = 0.55 and 40% of voters subscribing to value V2 with pcV2 = 0.8. 202
13.6 Five equally large groups, but two groups support X1. 203
13.7 Five equally large groups, four of which systematically err in the same direction. 204
14.1 Probability of victory for the majority faction from majority voting, as population size increases. 210
14.2 Approximate expected vote distribution, E = 200,000, M = 1,000,000; pcE = 0.7, pcM = 0.51. 215
14.3 Probability of Mass majorities as a function of group selection competence. 218
14.4 Probability of Mass majorities as a function of the Elite group selection competence, Mass group selection competence fixed. 219
15.1 Isocompetence curve showing points at which a group with nREST and pcREST has the same epistemic performance as a group with nSMART = 100 and pcSMART = 0.7. 228
15.2 Group competence as a function of n, given that the first fifty voters have pc= 0.6, while all others have pc = 0.52. 232
15.3 Group competence as a function of n, given that the first fifty voters have pc = 0.6, while all others have pc = 0.52., shown with unweighted (equal) votes and with Grofman and Shapley’s weighted voting rule. 235
15.4 Learning by experience among twenty voters with an initial pcEXPERT = 0.6 and 1,000 voters with an initial pcLAY = 0.501, with the competence of each increasing by 1% in each round. 241
15.5 Learning by experience with twenty voters with an initial pcEXPERT = 0.6 and 1,000 voters with an initial pcLAY = 0.49, with the competence of each increasing by 1% in each round. 243
16.1 The epistemic competence of an assembly mixing delegates and trustees, with the number of delegates among ninety-nine representatives on the x-axis and group competence on the y-axis. 258
List of Tables
4.1 Interaction of the Competence and Independence Assumptions. 56
6.1 US presidential election outcomes if all voters voted the same way as informed voters of the same demographic. 90
7.1 Independent and negatively correlated votes. 102
7.2 Voters with partial information. 106
8.1 Group competence as a function of declining individual competence with many alternatives. 122
8.2 Voting on multiple alternatives, either with three experts selecting their top two options and 303 voters voting in the run-off, or a direct plurality vote among population with voter competence as in Table 8.1.
8.3 Alternatives and voting competence. 129
11.1 Probability of correct majority decision among 1,000 voters with individual competence pc* = 0.55 split evenly among multiple opinion leaders (pOL = 0.50), each voter following his respective opinion leader with probability π. 173
11.2 Probability of correct majority decision among 1,000 voters with individual competence pc* = 0.55 split evenly among multiple opinion leaders (pOL = 0.55), each voter following his respective opinion leader with probability π. 174
11.3 Probability that a majority of voters will be correct if they follow, to varying degrees, three opinion leaders each with competence pOL = 0.55, uninfluenced voters being competent with pc* = 0.55. 175
11.4 Probability of correct majority decision among 990 voters with individual competence pc* = 0.55 split evenly among multiple opinion leaders (pOL = 0.55 when not following another opinion leader), each voter following his respective Local Opinion Leader (and each Local Opinion Leader his respective Big Opinion Leader) with probability π. 177
14.1 Competence threshold Mass voters have to exceed to make true Mass interest more likely to win than Elite interest, for various values of pcE and E/M 212
16.1 Estimated necessary individual competence of representatives to make their collective decision epistemically equal to that of the electorate or no more than 1 percentage point worse (assuming voters are individually pc = 0.51 competent). 252
17.1 The collective competence of assemblies divided into similarly sized parties with party leaders dictating party policy (where the probability of the party leader being correct is pOL = 0.550).
17.2 Probability of correct majority decision among 1,000 MPs with individual competence pc* = 0.55 split evenly among multiple party leaders (pOL = 0.55), each voter following his respective party leader with probability π = 0.5.
17.3 Probability of a majority vote for the correct outcome in committees and whole legislatures, of varying sizes (pc = 0.55).
17.4 The probability of a correct decision from Congress (assuming each legislator is pc = 0.55 competent).
17.5 The collective competence of assemblies divided into strictly whipped parties with party policy chosen by majority vote of that party’s MPs (for a 603-member legislature, each MP having individual competence of pc = 0.55).
17.6 The collective competence of assemblies divided into strictly whipped parties with party policy chosen by majority vote of that party’s MPs, with a pivotal small party (for a 603-member legislature, each MP having individual competence of pc = 0.55).
21.1 Fact-checking Trump’s lies.
A2.1 Sources of numerical data in tables and figures.
263
264
266
269
275
276
328
371
In general, a law which has not been voted unanimously involves subjecting men to an opinion which is not their own, or to a decision they believe contrary to their interest. It follows that a very great probability of the truth of this decision is the only reasonable and just grounds according to which one can demand such submission. —Condorcet
