Is George Osborne doing a great job? From one perspective, it is logically impossible that he is.
What I mean is that Nadine Dorries says he’s doing a great job. But she also says her blog is “70% fiction.” Which raises the question: what is the probability that Osborne is doing a great job, conditional upon our MPilf saying he is?
Enter Bayes’ theorem.
Let P(A) = the probability that Osborne is doing a great job. Let P(B) = Dorries saying he is doing a great job. So P(A¦B) is the probability of him doing a great job, conditional upon Dorries saying so, and P(B¦A) is the probability of Dorries saying he’s doing a great job, conditional on him doing so.
Let’s suppose you are well disposed to Osborne, so the value of P(A) is high, at 0.8. We know from her “70% fiction, 30% fact” remark that P(B¦A) is 0.3. And let’s call P(B) 0.9; you might think it should be one, given that you’d expect Tories to support Osborne, but Dorries might have remained silent instead.
It follows that P(A¦B) is: (0.3 x 0.8)/0.9 = 0.266.
In other words, even if your prior belief was that Osborne was doing a great job, the fact that Dorries says he is means that you must attach only a low probability to him doing so.
The simple maths tells us Osborne is probably not great.
How can we avoid this conclusion?
One possibility is that Dorries’ mis-spoke; she claims that she intended to say “30% fiction”: women and numbers, eh? If P(B¦A) is 0.7, then P(A¦B) rises to 0.62.
However, this does not greatly help the Tory cause. If you’re undecided about Osborne’s competence - P(A) = 0.5 - then P(A¦B) is only 0.39. A floating voter reading Dorries’ amended statement would therefore infer that Osborne was probably not great.
Another possibility is that Dorries does not intend her “70% fiction” remark to apply to this statement. She might say: “My statement ‘Osborne is doing a great job’ is true.” However, this statement must itself be subject to her “70% fiction” statement. We have, then, a variant of Epimenides’ paradox. This cannot overturn my reasoning.
Another possibility is simply that her “70% fiction” remark was wrong. We can rule out the possibility that it was a lie; an “honourable member” would not lie to a parliamentary commissioner. So we’re left with the possibility that it simply has no truth-value at all.
Here, though, we must draw a sharp distinction between statements that might have truth-value, and ones that are pure nonsense. The principle of insufficient reason suggests that when Dorries says “Osborne did a great job“, we should attach a 50% probability to him doing so. But if P(B¦A) is 0.5, then P(A¦B) is only 0.44. Again, we must infer that - even from a high prior support for Osborne - that he is doing a bad job.
We can only avoid this conclusion by reading “Osborne did a great job” as “whshfn ghe n dkp henlg” - mere meaningless nonsense.
My conclusion here is simple. If you want to support Osborne you must regard Dorries as a nonsensical figure, who’s utterances have as much meaning as the barking of a mad dog.