Tyrrell_McAllister comments on Talking Snakes: A Cautionary Tale - Less Wrong

107 Post author: Yvain 13 March 2009 01:41AM

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Comment author: SilasBarta 16 November 2009 07:20:19PM *  0 points [-]

Sorry, probability and inference don't work like that. I didn't "misread him as saying she was culturally traditional". I correctly read exactly what the post said. It's just that I made the inference based on the strong cues in the story that she was devout. That's not the same as misreading a word or two.

I admit -- I certainly could have made the basis for that belief more clear, but you also should have applied the principle of charity and thought about the possibility that it wasn't just a misreading, and that there are reasons to infer someone is a "devout Muslim" other than "oh, someone told me with those exact words."

In addition to what I mentioned in my response to Zack_M_Davis, there's the fact that the Muslim woman has actually thought through the implications of her faith enough to actually want to persuade others, and has ranked the different reasons for disagreement for their plausibility. This is the same kind of person who would watch that they're going above and beyond to adhere to their faith's requirements.

Furthermore, I need not have "made the baseless inference that all creationist Muslims are culturally traditional." The world isn't black and white. If the evidence justifies believing with 95% probability that she's a devout Muslim, I can tentatively hold that belief with high confidence without believing that all (your term) creationist Muslims are culturally traditional. There were more cues in the passage.

Come on, this is basic Bayesian probability theory here. You should have dropped the rhetoric of "you think X implies a 100% probability of Y" a long time ago.

Comment author: Tyrrell_McAllister 16 November 2009 09:30:08PM *  3 points [-]

[T]he Muslim woman has actually thought through the implications of her faith enough to actually want to persuade others, and has ranked the different reasons for disagreement for their plausibility. This is the same kind of person who would watch that they're going above and beyond to adhere to their faith's requirements.

On my reading, this implies that, if you think that the woman is devout, you should think it less likely that Yvain lied when he reported his conversation with her.

Here's why:

Let ARGUES be the proposition that an arbitrary Muslim woman in Cairo is willing to argue for creationism with a stranger.

Let DEVOUT be the probability that an arbitrary Muslim woman in Cairo is devout---that is, that she "would watch that [she's] going above and beyond to adhere to [her] faith's requirements."

You consider p(ARGUES | DEVOUT) to be low enough to justify calling Yvain a liar. Thus, DEVOUT must refer to a devotion strong enough to make p(ARGUES | DEVOUT) this small. But, I claim, you should consider p(ARGUES) to be even smaller.

On my reading, you assert above that, if the woman argues for creationism, she is very likely to be devout. That is,

(1) p(DEVOUT | ARGUES) > 1 - epsilon,

where epsilon is small enough to justify your omission of any phrase like "very likely to be". On my reading, this makes epsilon small enough so that, in a cosmopolitan city like Cairo,

(2) p(DEVOUT) < 1 - epsilon,

where, again, DEVOUT refers to a devotion strong enough to make p(ARGUES | DEVOUT) small enough to justify calling Yvain a liar.

Putting (1) and (2) together gives

(3) p(DEVOUT | ARGUES) > p(DEVOUT).

Therefore,

p(ARGUES)
= p(ARGUES) * p(DEVOUT | ARGUES) / p(DEVOUT | ARGUES) [multiplying by 1]
< p(ARGUES) * p(DEVOUT | ARGUES) / p(DEVOUT) [by (3)]
= p(ARGUES | DEVOUT) [Bayes's formula],

so that p(ARGUES) < p(ARGUES | DEVOUT), as claimed.

ETA: Edited to correct typo in derivation.

ETA2: Sorry, more corrections to the argument . . .

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