Conspiracy Believers Really Do Hold Contradictory Ideas at Once

Suppose you think Princess Diana was murdered by the secret services. Suppose you also think she faked her own death and slipped away. Both cannot be true. Hold each as a near-certainty, though, and you have done something a probability textbook forbids, and a new analysis says that this small act of logical trespass is one of the clearest fingerprints of conspiratorial thinking there is. The strongest believers turn out to be incoherent in this precise sense far more often than the weakest, and after a decade of the claim being fought over, the numbers behind it now look hard to dodge.

The idea sounds almost too neat to trust, which is roughly what a lot of researchers concluded. If someone will swallow one theory, the thinking went, they will swallow its opposite too, because the machine that manufactures suspicion does not much care about consistency. Belief in one conspiracy does reliably track belief in others, even unrelated or fictitious ones. Tidy. Also, until recently, on shakier ground than it looked.

Where the Old Method Went Wrong

The trouble was in the measuring. The original studies leaned on a correlation: if agreement that Diana was murdered rises alongside agreement that she faked her death across a group of people, that positive correlation was read as evidence of incoherence. But a correlation like that can appear even when nobody endorses either claim. People who firmly reject the first tend to firmly reject the second, and their answers march in step just the same. In 2023, a team led by Jan-Willem van Prooijen pressed on exactly this point and reported that, on average, fewer than 3 per cent of participants actually endorsed a pair of incompatible theories at once. Researchers, they suggested, had overestimated the whole phenomenon.

So the literature ended up arguing with itself. One camp said incoherence was a hallmark of conspiracism; another said it was mostly a statistical mirage. What was missing was a way to pin the thing down inside a single person rather than smeared across a sample.

Alessandro Miani at the University of Bristol, with Nicole Cruz and Stephan Lewandowsky, went back to first principles, and the principle they picked was Bayesian. Treat each agreement rating not as a yes or no but as a degree of belief, a probability. Two claims that cannot both be true are allowed to share the probability you have to spend: you might put 50 per cent on each, or 80 and 20, whatever you like, as long as the total does not climb past 100. Put 90 per cent on both and you have overspent. That overspend, the distance past the boundary, is a number, and the team called it an incoherence score.

It is, in a way, a pizza problem. You can slice the pie however you please, but you cannot serve more pizza than the one pie holds, and a person who is 90 per cent sure of two mutually exclusive stories is trying to.

Two Studies, One Boundary

With that yardstick they did two things. First they reanalysed data from eight earlier studies, more than 8,500 people in all, and asked how the incoherence score tracked with conspiracist thinking. It tracked hard. Running from the weakest conspiracy believers to the strongest, the model’s predicted probability of holding incoherent beliefs climbed from roughly 3 per cent to about 91 per cent. Among people high in conspiracism, 58 per cent were incoherent on at least one pair of claims; among those low in it, only 11 per cent were. A simulation ruled out the dull explanation that this was just careless clicking: the real incoherence sat well above what random responding would produce. So the same dataset van Prooijen read as deflationary, read through a Bayesian lens, says the opposite. The link is real, and it’s large.

Then the harder question. Is this specifically about conspiracies, or are these people just loose with logic across the board?

For the second study the team built 469 US participants a set of 16 fictional scenarios, deliberately set in Europe so nobody would have heard of them. In one, an eight-year-old girl, daughter of a member of the European Parliament, vanishes for three days. Participants rated how likely each of two explanations was, on a zero-to-100 scale. Sometimes both explanations were conspiratorial and mutually exclusive: she was secretly held by her father to misuse public funds, or she had escaped a ring that forced her into child labour. Sometimes they were mundane and mutually exclusive: she fell from a cliff, or she was caught in an avalanche. And sometimes one statement was simply the flat negation of the other, true versus false, where the probabilities are forced to sum to exactly 100.

The pattern that fell out was not one thing but two. When both explanations were conspiratorial, higher conspiracism predicted more incoherence, people inflating two incompatible plots at once. When the explanations were mundane accidents, that link vanished; a taste for conspiracy did not make people bungle the cliff-versus-avalanche sums. But when the pair was a strict true-or-false negation, conspiracism predicted incoherence again, whatever the content, conspiratorial or not.

Reduced Monitoring, and a Worldview That Pulls

The authors read this as two mechanisms wearing one coat. The strict-negation result points to something general: a slackness in logical monitoring, a reduced habit of noticing that two numbers are being asked to sum to more than they can. The conspiracy-versus-conspiracy result points to something specific: a worldview that rewards any story counter to the official one, so two rival plots get talked up together because both flatter the same underlying suspicion that the authorities are lying. One is a failure to check the arithmetic. The other is a reason not to want to.

None of this proves that conspiratorial thinking causes the muddle; conspiracism here is measured, not manipulated, so the arrow could run either way, or both could feed a common source. There are other caveats worth keeping in view. The experiment stacked several helpful design features at once (a numeric scale, explicit true-false labels, both claims shown side by side) and cannot say which did the work, and its participants were an online US panel judging invented European dramas, which is a narrow window on the world.

Still, the reframing has teeth. Interventions that simply point out the contradiction to people have mostly failed, because believers reconcile the clash rather than dropping a belief, and if two different things are going on, one arithmetical and one motivational, then a single fix was never going to catch both. The next move, the team suggests, is to pull those threads apart one at a time, and perhaps to see whether the worldview itself can be coaxed to notice its own sums.

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