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Comment by topynate | Hacker News Reader

A nice sentiment, but not really logical. An outcome in Pao's favour would have been taken as evidence for institutional bias; by conservation of probability, an outcome against must be taken as evidence against.

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That implies that the outcome has to be correct, which is - as always - debatable.

If you believe an unbiased society would have ruled in favor of Ellen Pao, you could actually take this outcome as evidence for a general bias against women.

If she had won would you have felt the same way?

Yes. I was not there, I have no idea what really happend and if it shows a systematic bias. What I know is that courts are not infallable, so I would stand by my opinion without looking at the actual outcome of the court process.

(P → Q) !=> (¬P → ¬Q)

I was speaking probabilistically.

Or, if you prefer: p(Q|P) > p(Q) => p(¬Q|¬P) > p(¬Q)

Then perhaps the 7th word in your comment should be probable and not logical.

No, probability theory itself is logical. topynate just showed you the (deductive) inference.

But it's correct to say that the criticized handling of probability is illogical.

Wait, I can phrase that better. OP said that this verdict is evidence of bias. Responder says conservation of probability means that, if the not-guilty verdict is evidence of bias, a guilty verdict must be evidence against, which is illogical. "Illogical" is a correct characterization of this use of probability.

Let's talk about a hypothetical case where we flip an unfair coin (more likely heads than tails). Every time it comes up heads we fire someone. Then some particular person says they were fired because we used an biased coin instead of a fair one. It's impossible to say that's why they were fired, but that isn't taken as evidence against bias.

Actually that's the opposite of logic. Absence of proof is not proof of absence.

The OP didn't use the word "proof". He or she is correct that absence of evidence is indeed evidence (but not proof) of absence.

Actually, no absence of evidence is not evidence of absence in the general case; absence of evidence for a position can coincide with absence of evidence against the position.

The conspicuous absence of evidence is evidence of absence.

I think the point is that people (mostly ones who don't really know the details of what actually happened) will just use the court outcome to advance their own pre-existing biases, regardless of what the court says.

Examples:

1) I am biased against Ms. Pao, and she wins: "This just goes to show that women can sue for anything these days, and win millions!"

2) I am biased against Ms. Pao and she loses: "See, women will sue you for discrimination even if you didn't do anything wrong!"

3) I am biased in favor of Ms. Pao and she wins: "See? This is clear proof that the bias against women goes all the way to the top of Silicon Valley!"

4) I am biased in favor of Ms. Pao and she loses: "See, this is proof that businesses can discriminate against women and not suffer any consequences."

Given that, in order for me to take someone's claim seriously, I would want them to pre-commit - before the result is announced - to a "court outcome interpretation." I don't care whether that interpretation is "regardless of what happens, the court outcome is irrelevant" or "I will accept the court ruling as 100% true and correct" - I just want consistency.

This interprets the situation as though everyone currently has a correct assessment of the probability of institutional bias, against which an outcome in Pao's favour would provide new evidence on which to condition to update the probability.

But that's not really the sense in which an outcome in Pao's favour would've been used dialectically.

Rather, people currently disagree in their assessment as to how probable it is that there is institutional bias. Those who are very confident that there is institutional bias feel that others, who are skeptical of the existence of institutional bias, are mis-assessing the existing evidence.

And so, yes, were an outcome in Pao's favour to come down, those who are currently confident that there is bias would use this to bolster their argument that the weight of evidence is on their side, such that others should revise their probabilities upwards to match. But even if an outcome in Pao's disfavour came down, they would still consider others to have mis-assessed the existing evidence, and would still feel the correct thing for bias-skeptics to do would be to revise their probabilities of institutional bias upwards, albeit perhaps not as much. And there would be nothing irrational or illogical in this.

[In the same way, if I were to argue with someone who claimed to have found an algorithm which could compress arbitrary data, and I challenged them to compress and restore a particular file, and they failed that challenge, I would say "See? You couldn't do it; that should convince you that your claim is erroneous". But if they happened to pass that one particular challenge? I wouldn't say "Ah, ok, you should feel even more confident in your claim to have found perfect compression". I would say "Ah, that challenge happened not to add to my evidence against your claim, but I still have good reason to disbelieve your claim, your claim is still false, and you should still sharply revise your credence in that claim downwards to match mine."]

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