[aspenmayer]

Presupposing that the same coin is used for every flip (which is implicit in the example), it would be fair to question whether the coin could possibly be a fair coin after 500 heads in a row, even (and especially) if the flipping process were ideally fair.

I’m not a whiz with the math involved, but I am of the opinion that 500 consecutive same-side flips is a large enough sample size to calculate that the coin in question is biased, so it would be unreasonable to assume that the next flip is 50/50.

https://en.wikipedia.org/wiki/Checking_whether_a_coin_is_fai...

[sfn42]

I already said the coin is known to be fair.

[aspenmayer]

> I already said the coin is known to be fair.

The coin can be assumed to be fair before the flips, but after the flips we have no mathematical reason to believe that the coin is fair, as our results heavily suggest that it quite simply isn’t fair.

However, for the purposes of discussion, assuming an ideal coin, the probability of 500 same flips in a row is so statistically unlikely that fairness of the flipping process and/or flipper must then be called into question.

Even if the coin, flipping process, and flipper are all ideal (which wasn’t stated, but we will also assume for the sake of argument that we have ideal immovable goalposts), the likelihood of the 500-in-row event is so improbable as to be unreasonable to use as an example or even a metaphor, because it doesn’t have much predictive power in a conversation, as ideal coins don’t exist any more than ideal coin flippers.

Even a coin designed to be fair would be fairly deemed defective after so many same-side flips, and any reasonable gambler would demand that the coin be replaced with another; at that point an argument could reasonably be made to also change the coin flipper and/or the venue.

[sfn42]

Bro just assume there's been a billion flips right before my example indicating it's close to perfectly fair, the only point of my comment was to illustrate that previous flips don't influence future flips. Pretend I said 5 instead of 500 if it makes you feel better.

[aspenmayer]

> Bro just assume there's been a billion flips right before my example indicating it's close to perfectly fair, the only point of my comment was to illustrate that previous flips don't influence future flips.

I agree: the events are independent in probability, which was never under debate, and is a separate matter to whether or not the coin is fair.

As for your edit:

> Pretend I said 5 instead of 500 if it makes you feel better.

At this point, wouldn’t you say that’s a bridge too far? It’s uncharitable to ask of your interlocutor as that changes the entire context and implications of what you originally said upthread.

Asking me to just pretend that you made a different argument than you originally made, when the mathematical implications of your original argument are the context under question, is literally moving the goalposts.

If you had said it was 5 flips in a row instead of 500 flips, then I wouldn’t have said what I said, because there’s a difference so wide between the two statements in their degree of probability as to be different arguments entirely. You didn’t say that though, and so I don’t know what you’re trying to say now.

[sfn42]

I'm saying the thing you just declared "never under debate". The only one having a debate here is you. The only point I was making was never under debate. You reading too deeply into it and getting hung up on irrelevant details of what I said is entirely tangential, I'm neither agreeing nor disagreeing, honestly I haven't even really bothered reading your comments because you're just off on your own little tirade and I have no interest in it. I intentionally chose a really high number to make my point, it's not meant to be realistic it's meant to make a point.

[aspenmayer]

> I'm saying the thing you just declared "never under debate". The only one having a debate here is you.

The thing that isn’t under debate (that the flips are independent) is the thing which we both agree upon, and I believed no declaration was previously necessary because it is beside the point and obvious, and it also has no bearing on anything else you claimed. It doesn’t support your argument that the coin, the flipping mechanism, and output of the process as a whole can be assumed to be fair after 500 same flips.

The context of the original discussion is the question of bias in hiring, and whether AI introduces unknown or unpredictable bias. If we used a coin flip instead of AI in hiring decisions, and that coin had the property of resulting in 500 heads in a row, it would be fair to re-examine our test setup as well as the coin in the context of using it to make hiring decisions, because that result is not consistent with our prior belief that the coin is fair.

Due to disparate impact, the result of using such a coin in hiring decisions, even if said coin itself in isolation were measured to be fair, would still result in an unfair result as part of a larger decision-making process, which was the point I was getting at.

The purpose of a system is what it does. If a coin flipping system, or an AI, used for hiring or any other decision-making results in such an astronomically improbable result as 500 heads in a row would imply, it is not fit for purpose.

> I intentionally chose a really high number to make my point, it's not meant to be realistic it's meant to make a point.

Choosing a high number undercuts your argument or is tangential to the flip events being probabilistically independent, so that’s why I commented in the first place, in order to draw out your point, because what was meant by what you stated originally was unclear to me.

> I'm neither agreeing nor disagreeing, honestly I haven't even really bothered reading your comments because you're just off on your own little tirade and I have no interest in it.

Framing our discussion in such terms is strange to me. I thought your coin flip example was interesting as a metaphor in the context of a potentially unfair AI used for hiring decisions, and I genuinely thought you were earnestly discussing the topic, and I still do, though it’s hard to read your admission of not reading my comments as anything but an explicit admission of not arguing in good faith.