Imagine a society made up of two groups with different interests: the Elites and the Masses. The Elites are competent in determining which policies are likely to advance their interests, whereas the Masses often end up voting for policies that are contrary to their own interests, as they understand them. Luckily, there is a way for the Masses to compensate for this, and it requires only that they correctly identify those who share their interests and take a vote among them. As long as the Masses as a group are on average just a little better than random in voting for the right policy, a vote within the group will almost always yield the correct answer. By exercising such epistemic solidarity, the Masses can correctly determine the policies that advance their interests and overcome their epistemic disadvantage.

This is just one of the many ingenious and often counterintuitive findings that Robert Goodin and Kai Spiekermann offer in their excellent new book about the epistemic advantages of democracy. Most of their results are extensions and elaborations of the Condorcet Jury Theorem (CJT). In brief, the theorem states that, in a group of voters choosing between a correct answer and an incorrect one by majority vote, the probability that the majority chooses the correct answer approaches one as the number of voters approaches infinity. The result holds as long as three assumptions are met: each voter has competence that is better than random, votes are statistically independent, and voters vote sincerely. This theorem has fascinated theorists of democracy for the past few decades, appealing especially to those drawn to elegant technical results and those convinced that the ability to get things right is crucial for justifications of democracy. However, many others have questioned the relevance of the theorem on the grounds that its assumptions can rarely be met in real political situations.

Goodin and Spiekermann take this latter charge seriously and set out to show that it is wrong. Their main claim is that the theorem is, in fact, far more broadly applicable than assumed. They go about showing this in two main ways. The first is by focusing on the theorem’s assumptions and arguing that they have either been interpreted too narrowly or they could be relaxed or modified without losing the main result. The second is by demonstrating the theorem’s applicability to a wide range of political institutions and practices, ranging from the role of leadership and tradition to political parties, factions, and veto players, thus going far beyond the binary vote of Condorcet’s original. The technical results in the book build on a series of papers published over the years, including several by or with Christian List and Franz Dietrich, and readers are directed to these papers for the proofs. As a result, the book itself is very readable, engaging, and nontechnical.

It is worth clarifying that many of the epistemic benefits of voting emphasized in the book can be claimed by groups of about ten thousand people. This is true even when voters are assumed to be barely more competent than random. To be safe, a hundred thousand or even a million voters might be good. But additional voters beyond this number do nothing to improve the probability that the majority will be correct, which has effectively reached one by that point. This raises the question of whether the theory is rightly described as an epistemic theory of democracy. On the book’s purely epistemic argument, there is not much point to extending the franchise from one million to two million, let alone having universal suffrage. The authors point out that disenfranchising specific groups—women, foreigners—might create losses in diversity, which would be an epistemic bad, but they have no (epistemic) arguments against randomly disenfranchising 95% of the adult population of a large country. An “epistemic theory of rule by sufficiently large groups” does not have quite the same ring, but it may be a more apt title.

The success of the book’s main argument depends on how persuasive readers find the authors’ extensions of the assumptions. I found them to be both persuasive and interesting, and the authors are clear about the conditions under which the theorem would not apply. For instance, it is interesting to learn that the theorem still holds if a large number of people slavishly follow opinion leaders, just as long as these leaders have diametrically opposed views, the opposing groups of voters are roughly equal in size, and a sufficient number of voters remain independent of these influences. It is useful to know these conditions, but they are sometimes so elaborate that one begins to wonder whether we could ever tell when the conditions are fulfilled in real political situations. Are people following their opinion leaders slavishly or not? How many are, and how slavishly? This effort will not be easy. And if the epistemic challenge of determining whether the assumptions are met is itself too onerous, we will run the risk of wrongly assuming that the majority is right when in fact the assumptions have not been met, and vice versa. Because such mistakes have real consequences, it might begin to seem safer to ask a small number of competent people for the answer, despite well-known problems with doing so.

One of the most interesting insights of the book is that the result of the CJT is always conditional on the quality of the available evidence. The likelihood that the majority converges on the right answer can only be as high as the probability that the decision situation itself is truth conducive. The best that voters can do is to track the judgment of an ideal responder—someone who does the best possible with the available evidence. Once the authors point this out, it is of course eminently intuitive: if the evidence is misleading, even an ideal responder will not be able to give the correct answer.

However, this important result subtly undermines the broader enterprise. The worries are twofold. First, the available evidence on many questions of policy may not be very good. The evidence on policy issues usually comes from social science, which faces theoretical and practical challenges in establishing external validity and has questionable predictive success. The right kind of evidence may simply not be available to voters, which means that the best possible response to the available evidence may not have much truth value. The second and deeper worry is that this inescapable dependence on the quality of the evidence once again introduces science and expertise as the bottleneck in the epistemic success of democratic decision making. The advantages of large groups turn out to depend entirely on the quality of the evidence, which is usually produced and interpreted by experts. Once we realize this, it makes sense to think that the kind of competence most valuable for voters would be a meta-competence in assessing the quality of the decision situation and determining what to do in response to the limitations of expertise and the risks of error. But that moves us beyond the framework of the CJT.

It is further testament to the book’s success that it opens up many interesting questions that go beyond its own framework. This book is a valuable contribution to democratic theory and will be a touchstone for the rapidly expanding literature examining the relationship between democracy and truth. The authors not only succeed in establishing the reach and limits of the CJT, but also demonstrate how modeling tools can be used to clarify and illuminate real political questions without sacrificing either rigor or relevance.