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.
Climate Scepticism 
You could look at the All Stars’ paper alternatively as a covert explanation for why state-sponsored propaganda is ‘good’ and populism is bad, very bad.
The ‘social interactions that inevitably accompany a democratic society’ could be defined as ‘populism,’ which means that, in essence, Condorcet’s theorem fails whenever populist sentiments take hold in society because: “A key condition is that the votes be statistically independent; however, it is unrealistic, and hence, unacceptable.“
The antidote to populism is state sponsored propaganda (misinformation, disinformation and malinformation) to try to ensure that the voting public choose the ‘correct’ option rather than the incorrect populist one. Alas, it didn’t work with Brexit. Either way though, Condorcet’s Theorem, describing an idealised population comprised of a large group of statistically independent individuals, is fine in theory but not applicable in reality.
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Jaime,
Yes, the conditions required for Condorcet’s theory to apply are completely unrealistic and so if there is any such thing as the wisdom of the crowds then it can’t have anything to do with ‘epistemic democracy’. And yet the All-Stars say that “Proponents of epistemic democracy can point to much empirical support for the “wisdom of crowds”. I haven’t the faintest idea what that empirical support is supposed to be. As far as I can see, democracy is all about socially-driven decision-making in which opinions are anything but independently arrived at. I can see plenty of evidence for the madness of the crowds but not much regarding mass wisdom. Mass formation psychosis anyone?
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John,
Perhaps they were referring to the recent stunning empirical successes of the Behavioural Insights Team?
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Jaime,
Ah yes, that paragon of non-interference — the surreptitious nudger. Democracy is indeed safe in their hands.
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Just to remind you that this is what protecting democracy looks like to the All-Stars:
https://wherearethenumbers.substack.com/p/youtube-still-censoring-content-questioning
Is that really what epistemic integrity is supposed to do for us? Is automatically censoring work because it challenges the wisdom of the masses supposed to be a good thing?
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Thank you John, I have now read it: and it is a piece of work. It never seems to occur to them that their side is as vulnerable to believing wrong things as their political opponents. It is, as usual, an excuse to attack the other side. But to whom are they talking? In general, only “their” side reads their diatribes. And it’s quite obvious that they are seriously lacking in objectivity, and are simply trying to find a cudgel to beat the other side. Who aren’t reading it anyway. Until we did.
On seeing the title of this blog, I was immediately transported back in time to a moment when I discovered that crowds aren’t wise after all. Not that it benefited me at all. I suppose my example fails the test, because the crowd were uninformed. [Dull anecdote follows.]
I had arrived unexpectedly in a pub in Yorkshire, and had been press-ganged into joining a pub quiz team. Alas, the unexpected nature of my arrival meant that I had no cash, and this was before they let you wave your debit card at them. Not to worry: my host bought me a mild.
However, the mild didn’t last, and the jars on our table of four were looking empty. Alas, I could neither buy a round, nor ask someone else to buy one (not being that kind of guy).
Then, a bonus round question was asked: what is the melting point of iron? The other three at the table wanted 500 to 600 degrees C. “No,” said I, “It’s more like 2000.”
“Are you sure?”
“No.”
Debate ensued. I prevailed, although my confidence was gradually evaporating. We put in for 2000 – nearest wins a tenner.
Well, all the other tables were 500-600 as well, so we won by a country mile. (True answer nearer to 1500. Maybe 1550. I won’t cheat just now.)
Over strode the landlord with our well-earned £10 note.
Alas! One of our team seized it before I could, and put it straight in the collection box. (It was a charity quiz.)
My thirst went unquenched, and I could not replenish my comrades’ beers either.
As to the overall, we did not feature in the top 3. I think the sports round did for us.
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Jit,
Yes, it’s all very well slagging your political opponents but you can’t do so whilst committing basic errors. When attempting to validate your own position, you at least should acknowledge what the rest of academia has already understood.
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Another thought has just occurred. How did this paper pass peer review without someone noticing the Condorcet gaffe?
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John – well read the “paper – Current Opinion in Psychology Volume 54, December 2023, 101711″
I would call it a rant & how anybody thinks it worthy is beyond me.
“The results suggest that the U.S. public broadly endorses moderation policies that remove harmful content, and in extreme cases, de-platform individuals who repeatedly post misinformation.”
“At the time of this writing, it is difficult to avoid the realization that one side of politics—mainly in the U.S. but also elsewhere—appears more threatened by research into misinformation than by the risks to democracy arising from misinformation itself.”
ps – notice it had this – “This review comes from a themed issue on The Psychology of Misinformation (2024); Edited by Gordon Pennycook and Lisa K. Fazio“
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Dfhunter,
Yes, it is indeed a rant. It looks like a group of notoriously left-wing academics attempting to use a basic theorem of political science to argue that the right-wing are the enemies of democracy. To do this, they invoke a theorem that only works under special conditions, and then they claim (without any supporting argument) that one of those special conditions has to be that the voters are not being subjected to misinformation. That may be an issue, but it does not bear upon the applicability of Condorcet’s theorem. What does, however, is the need for the voters to be voting independently – a condition that is seriously unrealistic. They don’t mention that problem for two reasons. Firstly, it doesn’t support their case. Secondly, it draws attention to the fact that the censorship they feel is necessary to combat misinformation will have the effect of further denying the independence of thought that Condorcet’s theorem relies upon.
Incidentally, there is an argument that they could have made, but didn’t. As they pointed out, Condorcet’s theorem demonstrates the wisdom of crowds when the voters statistically possess ‘imperfect but above-chance information about competing alternatives’. If they possess below-chance information then the same theorem shows the effect will act in reverse, i.e. adding voters makes the situation worse. They should have argued that this is what will happen under conditions of misinformation. I would then counter-argue that censorship, as a means of keeping the information ‘above-chance’, can be counterproductive because it destroys the special condition for Condorcet’s theorem to work.
But none of this matters when the academics concerned can say, “Contrarian efforts have also focused on quote-mining scientists’ emails to construct conspiratorial narratives about alleged malfeasance, for example during the scandal arising from the release of stolen emails between climate scientists in 2009.” This demonstrates that they wouldn’t recognise ‘above-chance’ information if it hit them on the head.
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Looks like my vote like button/option has been disabled again, so good comment/info/reply John.
ps – is it just me or have the site got a new “log in to comment” policy?
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dfhunter,
I can’t speak for WordPress, but we here at Cliscep haven’t changed anything. Hope it works for you again soon.
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Been a while since I’ve looked on on Cliscep. This is such a good review. You really have a first rate mind, John.
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That’s very kind of you to say, Ian. I’m pleased you enjoyed the read.
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