Not that long ago, I reflected upon the supposed wisdom of a group of academics who had put their heads together to form what they considered to be an ‘all-star team’. Regrettably, the constellation failed to brighten up the night sky. To readers of Climate Scepticism, however, this would not have come as much of a surprise. After all, on this ‘all-star team’ we had an academic who thought that risk was a purely mental construct, and hence failed to see the all-important difference between risk in reality and risk in its perception. We had another that lectured the world on the implications of statistical significance, but does not seem to have heard of transposed conditionals, thereby completely misunderstanding what statistical significance actually meant! Then we had research into scientific consensus that was so poorly conducted that the results were basically meaningless. Or how about an academic who thinks that epistemic uncertainty can be fully captured by a probability distribution curve and so goes on to incorrectly conclude that greater uncertainty inevitably leads to greater risk? And this is before I get back on my hobbyhorse regarding the farcical proposal of a backfire effect, or the tendentious taxonomies of failed critical thinking from which only a climate ‘denier’ is supposed to suffer. I could go on, but the point already made is this: As individuals, they have been responsible for such a catalogue of basic gaffes and muddled thinking that it would be unreasonable to think that a collaboration could result in anything better. And it didn’t.

So it is with a heavy heart that I have to report to you that I have discovered yet another paper from the same team, and once again, despite being written by a collection of supposed intellectual behemoths, a very basic error lies at its heart.

Not for the first time, our team of all-stars whines that misinformation is the greatest threat to democracy. Apparently, it’s all about ‘epistemic integrity’ — a quality that, ironically, they fail to demonstrate just as soon as they try to explain how democracy works:

Dating back to the 18th century, Condorcet’s Jury Theorem has provided mathematical justification for majority-rule voting by showing that collectively, members of a group who have imperfect but above-chance information about competing alternatives are more likely to choose the “correct” alternative than any one member of the group. Proponents of epistemic democracy can point to much empirical support for the “wisdom of crowds”, which in many (but not all) circumstances can deliver superior decisions.

Very interesting, but under exactly what circumstances does the wisdom of crowds fail to deliver superior decisions? The paper provides what you are expected to accept as the obvious answer:

One concern is that the idealized conditions under which democracy can yield “correct” decisions are undermined when the citizenry is pervasively misinformed.

Unsurprisingly, the remainder of the paper is dedicated to much talk of misinformation, bad actors and playbooks, predictably illustrated with references to climate change ‘denial’ and Covid-19 conspiracies.

And yet did they not just say ‘one concern’ regarding ‘idealised conditions’? Does that mean there are more?  Are there other idealised conditions necessary for Condorcet’s jury theorem to work – conditions that are either not known to our illustrious team or not thought worthy of mention? Well, since they are not going to tell you, I will have to.

The problem is this: Condorcet’s jury theorem does indeed provide a theoretical basis for democracy, but it is notorious for requiring that votes are cast independently in order for its maths to work. Only then will the probability of arriving at the correct decision increase as the number of above-average competent voters increases. As soon as there is correlation between voting, the mathematics breaks down. This is not an obscure detail. It is a well-known limitation of the theorem that was apparent from the very outset. As this paper puts it:

Does majority-rule voting steer an imperfectly informed assembly of people towards the full-information outcome? Condorcet’s jury theorem provides an affirmative answer under certain conditions. A key condition is that the votes be statistically independent; however, it is unrealistic, and hence, unacceptable.

It is possible to generalise the theorem in order to introduce statistical correlation between voting, but this inevitably results in a degradation of mass wisdom:

This paper generalizes the jury theorem to certain general models of correlated voting, viz., normal, hypergeometric and Polya distributions. The paper proves that the effectiveness of majority-rule voting decreases as the correlation between votes increases.

That, my friends, is the real problem with Condorcet’s jury theorem. It is a problem that has nothing to do with the impact that misinformation has on epistemic integrity, and everything to do with the social interactions that inevitably accompany a democratic society. The real threat to democracy does not lie with misinformation, it lies with the failure to understand that consensus does not equate to epistemic integrity. Our all-star team either does not understand this or chooses to misdirect its audience by failing to mention this massive limitation of Condorcet’s theorem.

This gaffe is typical of what I have come to expect from the likes of Lewandowsky, Oreskes, Cook and van der Linden. Time and again they wax technical in order to give their ideas some semblance of mathematical rigour, and time and again they end up being well out of their depth. By invoking Condorcet, they had hoped to ‘prove’ their point but instead ended up demonstrating why their thesis is unsound. Or at least they would have done if they had been more candid regarding the limitations of the mathematics they had proudly cited.

None of this is to say that voters don’t need to be well-informed in order to cast their votes wisely. Of course they do. But part of that quality of information entails a proper evaluation of what they are being told. One has to understand that authoritative narratives gained their authority by a number of means, one of which is often by benefitting from a strong correlation of views — a correlation that can just as easily propagate misapprehensions as it can propagate truths. Far from ruling such a problem out, Condorcet’s jury theorem demonstrates its virtual inevitability. Without independence of thought, there can be no wisdom of the crowds.