The Dorries paradox

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.

Comments

[Rob Spear]

The '70% fiction' remark might be one of her fictional statements of course.

Also, is fiction necessarily 100% false? My understanding is that it is meant to hint at deeper truths, so perhaps while the obvious meaning of a fictional statement might be false, logical consequences of that statement might have a higher chance of being true...

[Francis Sedgemore]

I’m afraid, Chris, that Rob Spear has exposed the fatal flaw in your reasoning. Bayes’ theorem is an occasionally useful tool for analysing real world as opposed to idealised scenarios, but therein lies the rub. For the results of a Bayesian analysis to make any quantitative sense, the input data cannot themselves be subject to a priori assumptions.

MPilf? Let it be known that I have absolutely no desire to fuck Nadine Dorries.

[Phil]

"our MPilf"

You speak for yourself, pal.

[TR]

Chris, 6he latent misogyny in so many of your posts is really quite tedious.

[Mr Eugenides]

I have to say that you lost me at the word "MPilf"...

[Stu]

"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"

To be fair Chris, that could be said to apply equally well to any other subject you care to name...