It’s all relative

Do you believe in psychic powers? If not, how much evidence would you need to change your mind? Let’s say that your level of belief is so low that you think the odds that such powers exist are utterly miniscule (though crucially not zero). How much evidence would constitute proof for you? And how would that required weight of evidence differ for someone who was more amenable to the idea?

For example, let’s say that someone has performed a card-guessing experiment and found that out of 20,000 guesses the subject got the correct answer 9,410 times when, in the absence of psychic powers, the expected mean result would only be 7,420. That variance is 25 standard deviations from the mean, so you would not have expected to see such a variance by chance unless the experiment had been repeated every second since the Big Bang.

Convinced? I thought not. And yet your open-minded friend is now looking at you gobsmacked. They have seen the same evidence as you and it has confirmed everything they had expected: psychic powers are real and – congratulations, by the way – you have now become a psychic powers denier.

The example I have just provided is not hypothetical. A British mathematician and parapsychologist called Samuel Soal did indeed get those results in the 1940s when performing an experiment into psychic phenomena. So being a good Bayesian, you should have taken your prior belief in the reality of psychic phenomena and applied Bayes Rule in order to calculate a posterior level of belief that is now very high. After all, that’s only what your open-minded friend did. Admittedly, your friend started from a higher prior but, when the evidence is so strong, the level of the prior becomes somewhat immaterial. That’s Bayes for you. Ultra-strong evidence means that you don’t have to worry so much about how you chose your priors. You should be a convert and be apologising for ever having doubted your friend. So, what’s wrong with you?

Actually, the reason why you and your open-minded friend have responded so differently to the evidence is not just because of your relative prior beliefs in psychic powers, but also the relative trust you have placed in the scientific community. Either psychic powers may exist and the evidence proves it, or they don’t exist and the outcome of the experiment was due to pure chance. So, you might think there is only one pair of prior beliefs to consider here. But what about the idea that psychic powers still don’t exist and the result wasn’t pure chance but an artifact of something fishy going on? Even though fraudulent behaviour is unlikely in the general case, it is still much more likely than the existence of genuine psychic powers – at least that is how the sceptic will see it. To you as a sceptic, the results are surprising but they don’t prove the existence of psychic powers at all; they simply prove that the experimenter must be a fraud. What you would need to see, in addition to the experimental results, is proof that the figures were not fiddled. Unfortunately, no such evidence would be forthcoming in this instance because Soal had indeed been fiddling away merrily.

The climate change question

Now let’s move on. Do you believe that anthropogenic global warming poses such a threat to mankind that achieving net zero by 2050 is essential? If not, how much evidence would you need to change your mind? I presume that you are not so against the idea that you would need 25 standard deviations to overcome your scepticism. After all, the hypothesis of catastrophic anthropogenic global warming (CAGW) is not nearly as kooky as the existence of psychic powers. But the same principle exists: how you update your prior belief in the light of evidence depends crucially upon how you perceive the ratio between the likelihood of the hypothesis and the likelihood of the evidence being other than what it seems to be. You don’t have to believe in hoaxes, fiddled data or conspiracies; you just have to understand that the scientific community is not as infallible as the average Guardian or BBC journalist would have you believe. And yet, to someone who starts out with the idea of CAGW being perfectly plausible, and for someone that has developed a high degree of trust in the climate science community, the evidence that you would question will seem to them so compelling that anyone who does not fall in line with their way of thinking will be perceived as a denier rather than a sceptic.

The logic I have outlined above is very much the logic taken by hydrologist David Huard in a presentation titled ‘A Bayesian Perspective on Climate Denialism’. He appreciates that evidence offered for a Bayesian update doesn’t necessarily result in a strengthened belief, and that is because a sceptic is prepared to question the reliability of the evidence in the context of the likelihood of the hypothesis. To that extent, he and I are on the same page. However, he uses this principle to draw a distinction between true scepticism and the denier. He accuses those who dispute AGW of engaging in an ‘inferential switch’ which enables them to bolster their position irrespective of the evidence. When the evidence is against AGW, it is accepted by the sceptic and a Bayesian update lowers their strength of belief. However, when the evidence supports AGW, the sceptic suddenly invokes the hypothesis that the climate science community is ‘motivated’ and uses a low prior level of belief in the AGW hypothesis as an excuse to discredit the evidence. He refers to this as the ‘Skeptic Hijack’, and, yes, we really are deemed to be that shallow and transparent!

Like all arguments used against the sceptic, it can just as easily be used against those who support the orthodox view – and yet it never is. For example, I could argue that the same inferential switch is being made when the alarmist takes on board any and all evidence that supports the idea of catastrophic global warming, but then rejects counter-evidence because it is deemed to be offered by sceptics who are engaging in motivated reasoning. Huard calls the inferential switch a ‘hijack’ when a sceptic does it, but evidently it is perfectly okay to do this when defending the orthodoxy. As far as I can see, the only difference seems to be that the sceptical accusation that climate scientists can be motivated is deemed to be unfounded and unreasonable, and yet the sceptics’ own motivated reasoning is held to be well-evidenced and self-evidently problematic.  

Well, they say it is well-evidenced, but it is evidenced by the likes of Naomi Oreskes, who, unfortunately, is also someone who doesn’t seem to understand the true definition of statistical significance. And frankly, it is the fact that the strongest critics of the climate sceptic can also be so ignorant of basic statistical theory that encourages me to question the evidence they themselves present. Oreskes would have you believe that I am in the thrall of Big Oil propogandists who have conned me into doubting the science, but – to be honest – I was initially quite susceptible to accepting the science uncritically until the likes of Oreskes came along and drove me into the arms of the sceptical orc army. And now I’m here, my willingness to return to the fold is hardly helped by individuals such as Huard who would selectively weaponize Bayesian logic to attack the climate sceptic’s reasoning.

Motivated reasoning or just poor reasoning?

So, what would it take to impress me? Well, first and foremost, I would prefer that the IPCC (an organisation dedicated to the idea of science by consensus) recognised that the probability of seeing something happen under a given hypothesis is not the same as the probability of a given hypothesis being true just because you see something happen. That was Oreskes’ mistake, but she’s just a historian out of her depth. The IPCC, on the other hand, is supposed to represent the finest minds on the job. And yet there is a statement in one of their technical reports to the effect that if you assumed that there was little man-made impact then there was less than a 5% chance of observing the warming that has been measured, which is then transposed in the summary for policy makers into the statement that there is at least a 95% chance that more than half the warming was man-made. This is the IPCC committing the prosecutor’s fallacy and, as such, it is a significant blow to its credibility. Which is ironic if you think about it, because here I am, a sceptic being put off by seeing supposed experts committing a classic Bayesian error, and yet Huard thinks he can use Bayesianism to demonstrate that I am pulling some sort of trick by pointing the error out.

When we are presented with new evidence we all evaluate it critically. We use evidence to update our prior beliefs, but the likelihood that we change our minds depends upon how likely we believe the evidence to be reliable, compared to how likely it is that the hypothesis being proposed is correct. When dealing with psychic powers, most of us find such a comparison easy to make. But when it comes to CAGW and the evidence proposed for it, the calculation becomes a great deal more problematic. Keep in mind that we are not just dealing with the question of whether or not mankind is contributing towards global warming; we are dealing with much more difficult questions relating to how much a contribution is being made, exactly what the impact might be, and whether the risks involved are above a threshold that can justify the damage caused by the proposed transition to net zero. In the final analysis, it’s not that needing such a transition to avoid CAGW is such a wacky idea; it’s more a case of it being too easy to believe that the evidence offered for the idea is unsound. Moreover, the more I look into how climate scientists and their advocates misapply the principles of risk management and uncertainty analysis (at least as I had come to understand them) the more difficult I find it to retain my uncritical acceptance of the warnings of doom and the resulting demands for net zero by 2050.

And whilst I am on my soap box, I might as well point out that Huard finishes his presentation by invoking the Dunning-Kruger effect, and we all know about that, don’t we boys and girls?