A fun little probability puzzle for you.

[Flannel Jesus]

No, I understood the answer.

This is 100% a scenario where you're taking a word in an entirely different direction than literally everybody else in the conversation. What bobmax means by 'overestimating / underestimating' is definitely, definitely not the same thing you're talking about. Your taking it in a direction that nobody else is taking it, and nobody else wants to take it, and you can't even tell that you're doing it.

This is a perfect example of the problems with communication that I think you have.

[bobmax]

It seems to me that there is a tendency to overestimate the probability that the chosen box is the one that contains 100 and 1.

Why does this overestimate?

In my opinion, because the $ 100 bill is thought to say more than it actually does.
That is, we think as if that extracted bill is uniquely identified.

While it is not.

If there is another 100 bill in the box it was taken from, these two bills are indistinguishable, one is worth the other.

You're saying the mistake is treating the two $100s as different is the mistake, but wouldn't that cause someone to overestimate the probability that the chosen box is the one that contains 2x 100, and not the one that contains 100 and 1?

In fact, I think it's the reverse of what you're saying - the problem is that people AREN'T treating the two 100s as different, when they are.

Yes, they are different.

But when I find the 100 bill in my hand, that's it.

And I find it hard to think that as a probability there is no difference between this and that in the box.
That is, I overestimate the collapse of possibilities because I do not consider that the bill in my hand is equivalent in all respects with the other.

[Flannel Jesus]

It seems to me that there is a tendency to overestimate the probability that the chosen box is the one that contains 100 and 1.

Why does this overestimate?

In my opinion, because the $ 100 bill is thought to say more than it actually does.
That is, we think as if that extracted bill is uniquely identified.

While it is not.

If there is another 100 bill in the box it was taken from, these two bills are indistinguishable, one is worth the other.

You're saying the mistake is treating the two $100s as different is the mistake, but wouldn't that cause someone to overestimate the probability that the chosen box is the one that contains 2x 100, and not the one that contains 100 and 1?

In fact, I think it's the reverse of what you're saying - the problem is that people AREN'T treating the two 100s as different, when they are.

Yes, they are different.

But when I find the 100 bill in my hand, that's it.

And I find it hard to think that as a probability there is no difference between this and that in the box.
That is, I overestimate the collapse of possibilities because I do not consider that the bill in my hand is equivalent in all respects with the other.

I think you missed the bulk of my reply:

You're saying the mistake is treating the two $100s as different is the mistake, but wouldn't that cause someone to overestimate the probability that the chosen box is the one that contains 2x 100, and not the one that contains 100 and 1?

[Skepdick]

No, I understood the answer.

This is 100% a scenario where you're taking a word in an entirely different direction than literally everybody else in the conversation. What bobmax means by 'overestimating / underestimating' is definitely, definitely not the same thing you're talking about. Your taking it in a direction that nobody else is taking it, and nobody else wants to take it, and you can't even tell that you're doing it.

This is a perfect example of the problems with communication that I think you have.

And why should I care what bobmax means? He means what he means and I mean what I mean.

I am giving you my perspective and I am using the words that I am using in the way that I am using them.
Either you understand how I am using them; or you don't.

If you understand then I have communicated perfectly. Why you think that is some sort of "communication problem" - I don't really know.

Is it a problem for you that I may not want to go where you want to take the conversation?

[Flannel Jesus]

No, I understood the answer.

This is 100% a scenario where you're taking a word in an entirely different direction than literally everybody else in the conversation. What bobmax means by 'overestimating / underestimating' is definitely, definitely not the same thing you're talking about. Your taking it in a direction that nobody else is taking it, and nobody else wants to take it, and you can't even tell that you're doing it.

This is a perfect example of the problems with communication that I think you have.

And why should I care what bobmax thinks? He can speak for himself. I can speak for myself.

I am giving you my perspective and I am using the words that I am using in the way that I am using them.
Either you understand it; or you don't understand it.

If you understand it then I have communicated perfectly.

Why that is a "problem" for you - I don't really know.

Because you're not even answering the question he has actually asked, you're having your own conversation and introducing confusion to the conversation because you've decided to use your own meanings for words that nobody else is using or wants to use. I don't want the confusion to be introduced, so I'm pointing it out.

[Skepdick]

Because you're not even answering the question he has actually asked

Why are you speaking on his behalf?

you're having your own conversation and introducing confusion to the conversation because you've decided to use your own meanings for words that nobody else is using or wants to use. I don't want the confusion to be introduced, so I'm pointing it out.

Surely I answered exactly the question you asked?

In what sense is it an overestimation? You ran the experiments yourself. You know there really is a 66% chance, once you've pulled the first 100, that we're in the box with 2 100s. You've done the experiment. By what metric have you decided that it's an overestimation, if it matches your experimental results?

By the existence of two possible futures.

Future 1: I draw a 1 next. Which would re-calibrate my over-estimated 0.666... into a 0.
Future 1: I draw a 100 next. Which would re-calibrate my under-estimated 0.666... into a 1.

If you didn't understand - say so.
if you understood my answer - what "problem with communication" are you pointing to?

[Flannel Jesus]

Is it a problem for you that I may not want to go where you want to take the conversation?

The problem isn't WHERE you want to take the conversation. The problem is how you get there - you get there by twisting words into confusions and nonsense.

[bobmax]

The mistake is not to treat the bills as different.
But in not considering the perfect equivalence of the two 100 bills.

This does not happen with regard to the box of 100 and 1 because the question of equivalence does not arise.
Which instead is present in the box of 100 and 100.

[Skepdick]

The problem isn't WHERE you want to take the conversation. The problem is how you get there - you get there by twisting words into confusions and nonsense.

Which part of my explanation confused you; or you think was "nonsense"?

As an idea-driven person (read: goal/action driven) my objective is to determine the true value (TV) of some variable. The TV is either 0 or 1.

If TV == 0, then 0.666... is an over-estimation.
If TV == 1 then 0.666... is an under-estimation.

[Flannel Jesus]

The problem isn't WHERE you want to take the conversation. The problem is how you get there - you get there by twisting words into confusions and nonsense.

Which part of my explanation confused you; or you think was "nonsense"?

The true value (TV) of the variable you are measuring is either 0 or 1.

If TV == 0, then 0.666... is an over-estimation.
If TV == 1 then 0.666... is an under-estimation.

The nonsense is that you think "overestimation" and "underestimation" are compared to some individual specific reality, where there's one particular answer about whether the box contains anotehr $100 or the $1.

That's not what "overestimation" or "underestimation" means to anybody else. That's not what we're comparing "over" / "under" to.

[Flannel Jesus]

The mistake is not to treat the bills as different.
But in not considering the perfect equivalence of the two 100 bills.

This does not happen with regard to the box of 100 and 1 because the question of equivalence does not arise.
Which instead is present in the box of 100 and 100.

Bob, you still haven't addressed the main inconsistency of your post -- you said people are overestimating that the box is 100+1, but if peoples mistake is because they're treating the two 100s as different (or treating them as not perfectly equivalent), then wouldn't that cause them to overestimating the 100+100 box, and not the 100+1 box?

This is what I'm not getting.

[Skepdick]

The nonsense is that you think "overestimation" and "underestimation" are compared to some individual specific reality, where there's one particular answer about whether the box contains anotehr $100 or the $1.

That's not what "overestimation" or "underestimation" means to anybody else. That's not what we're comparing "over" / "under" to.

Why aren't you comparing over/under to the true value ?!?

If you are action/idea-driven is it not your objective to determine the true value of the variable?

Maybe that's your problem? You have failed to state your goals explicitly.

[Flannel Jesus]

The nonsense is that you think "overestimation" and "underestimation" are compared to some individual specific reality, where there's one particular answer about whether the box contains anotehr $100 or the $1.

That's not what "overestimation" or "underestimation" means to anybody else. That's not what we're comparing "over" / "under" to.

Why aren't you comparing over/under to the true value ?!?

If you are action/idea-driven is it not your objective to determine the true value of the variable?

Maybe that's your problem? You have failed to state your goals explicitly.

No, the objective here has never been to discover 1 single answer to whether or not any single individual bill is 100 or 1.

The objective here is about determining probabilities. There is no real individual single answer to discuss, because we haven't really ran the scenario. There's only probabilities.

So the important question isn't "is the other bill $100" or "is it $1?" It's "what's the probability?"

[Skepdick]

No, the objective here has never been to discover 1 single answer to whether or not any single individual bill is 100 or 1.

Who's trying to answer that? Not me!

The objective here is about determining probabilities.

And what is it that you think I am doing?!?

There is no real individual single answer to discuss, because we haven't really ran the scenario. There's only probabilities.

So the important question isn't "is the other bill $100" or "is it $1?" It's "what's the probability?"

FFS. It's impossible to communicate with people who have no ideas!

The objective is to discover which box I have chosen.

Either I have chosen the 100/100 box with 1 probability
Or I have chosen the 100/1 box with 1 probability.

The objective is to determine which hypothesis has probability 1.

[Flannel Jesus]

Sounds like you're actually not into ideas that much, given your reply here. You're uncomfortable with talking about probabilities as ideas, and you keep trying to force the conversation into 1 particular concrete reality. That's not ideas. That's the opposite of ideas.

There's no "probability 1" here. If you were into the idea of all this, you'd be comfortable with the fact that we do not know which box we've chosen, so we don't have a "probability 1" for anything.