At least you're aware that there's a difference.

Context. The "assumed" probability" = the value you pick, be it 70% or 99.9%.

Yes. This was my argument as well.

You're not tracking with me (or I with you... I can't quite tell).

In conversation 1, there exists no causality by explicit assumption. There is no assumed future predictive power for the predictor. In this case, you just take the money.

In conversation 2, there exists causality between the decision to play the game and the result. However, the player decides that the track record is not sufficiently believable to take it as an assumption, and keeps the $1K.

In conversation 3, there exists the same causality between the decision to play the game and the result. This time, the player believes the track record is sufficiently convincing to accept the assumption and play the game.

Here's something else which you're probably going to want to reject by assumption, just like using a mixed strategy to tie the hands of the predictor.

Under the original scenario, it is entirely possible that NOBODY got the $1M. It could be that 999 people took the $1K and one person tried to be cute and refused it. The predictor could have always predicted that the the preson would take the money and therefore never put the $1M in the bank. This would make the historical EV record of taking/refusing the money:

EV(taking) = $1000
EV(refusing) = $0

This is why I was hinting at using two different variables for two different frequencies of right/wrong.

But you want to assume that he's just as good either way, so you don't see this as a possibility and why assumptions about the predictor makes a difference.

It's funny how ppl say that philosophers use outlandish thought experiments...but the ways that you're trying to twist the NP is getting increasingly outlandish.

It's also outlandish to...

* Assume a problem is well-posed when it isn't

* Think of taking/leaving the money as "betting" on the predictor AS THE PLAYER since it introduces causality that violates the assumption of non-casuality (the player is TRYING to influence the a past event).

* Argue that you should have changed who you were last week as if it's somehow a viable strategy (See posts #48/69)

* Restrict your choice of strategies in a way that hinders your ability to accomplish your desired goal

* Argue about causality and correlation but not answering a simple and narrow query about them:

I don't need to answer that question since it's irrelevant to the problem, I've said that before.

From what I've read, people divide fairly equally on their answer to this question. So I don't think it's unrealistic to specify a 50-50 divide amongst players of the game.

As far as tracking each other, I was quoting you here...

"I am arguing that "you should refuse" is correct if you assume the future probability of the predictor is going to be highly accurate (assumption 2). It will be true under this assumption at some value that is a finite distance from 1. So in the limit (ie, past that tipping point) under the ASSUMPTION that the predictor will continue to be correct (ie, there exists causality), you should reject the money."

Of course I could always be wrong, but I don't think your overall position would stand up well to peer review.

PairTheBoard

Past the "tipping point" you suddenly become unaware that this remains the controlling specification for you in the problem. Past the tipping point you forget which conversation you're in?


PairTheBoard

I no doubt missed it in the sea of posts. Please link to the one where you demonstrate the irrelevance of the claim that it doesn't matter whether there is a causal link or if it's merely correlative.

Okay, but you're continuing to add more assertions to the situation that are not logically founded upon the given information (while simultaneously, my assertions are being shut down -- you can assume me into a corner if you wish, but every new assumption you place on me weakens your ability to make your argument).

I'll explicitly compute the tipping point. Let x be the future probability that the predictor will be correct:

EV(taking) = 1000 + 1,000,000 * (1-x) = 1,001,000 - 1,000,000 x
EV(refusing) = 1,000,000 * x

The "tipping point" is the point at which EV(refusing) = EV(taking). Past this point is where the models disagree with each other. Apparently, it's 50.05%. I didn't really give that much thought because I don't really care where it is. (And it still matters that I'm following the assumption that the probability is the same in both the take case and the refuse case. As I explicitly demonstrated, if the probabilities of being right are dramatically different depending on the choices, you can reach other conclusions.)

If you believe this:

You take the money. What reason do you have to refuse the money? You refuse the money if you believe that your decision WILL INFLUENCE whether you think you will have $1M in the bank. In other words, you MUST ASSUME A CAUSAL LINK between your decision and the money in the bank. You are ATTEMPTING to control the outcome of the $1M by making a particular decision. I don't know if I can articulate the internal contradiction more explicitly than this.

It is stipulated that there is no causal link.

Whether the predictor is a cheater or not doesn't matter to the NP at all...because it's not part of it!

You're just all over the place. You asserted before that the "tipping point" was for epsilon "arbitrarily small" "IN THE LIMIT" going to zero and that for epsilon smaller than some tipping point it would infer causality in the assumption that the Predictor would continue predicting correctly with probability 1-epsilon thus negating the controlling premise in conversation #1 that "Nothing you do now will change his prediction and the money is either already in the bank or it is not".

Now you say the "tipping point" is 50.05% and based on an EV calculation of when it becomes worth risking the $1000 to win the $1M.

Simply incoherent and evasively incoherent to boot.

PairTheBoard

durkadurka,

I'd like to examine your Thesis. First, I was disappointed that you never faced Joyce's objection head on:

You never really "respond" to Joyce. You sidestep him and present your version of the Evidentialist Argument. I don't know if it's a novel one or not. If you're writing a paper based on it I presume you are representing it as a new approach. But as you criticized EnderIII in post #25 ...

... I think it's fair that you address the same issue.
How do you respond to the CDT where you're committed to holding those two propositions simultaneously?

When I confronted you with this issue in post #51 you responded with a wink in post #52:
Considering your criticism of EnderIII, I don't think a wink suffices for your response to the same issue.

I'm afraid your Thesis is inherently weak if somewhere within it you cannot meet Joyce's objection head on.


Now to begin an examination of your Thesis. You say,

I agree with your third party argument as you should be able to tell from my construction of the realistic experiment where an algorithm analyzing question/answer pschological profiles has a long track record of 70% accuracy. I think any reasonable person agrees you would demand odds that are fair based on the track record accuracy when betting with a bookie.

The same is true in the OP with 99.9% accuracy, although a stipulated track record of 999,000 out of 1,000,000 would provide better evidence that continued 99.9% accuracy is a figure we can have high confidence in.

When it's my turn to decide to Accept or Refuse I could place bets with the bookie. If I bet on the Predictor being wrong, I would need 999-1 odds to have a fair bet. If I bet $1000 on the Predictor being wrong I would want to get paid $999,000 if he indeed turns out wrong. I would consider it a 999-1 longshot for the Predictor to be wrong if I was to bet on it with a Bookie. If the Bookie only gave me 10-1 odds I certainly wouldn't make the bet. If the Bookie gave me 10,000-1 odds I would make the bet.

So I'm with you all the way with that discussion. For the purposes of making a Side Bet with a Bookie I would assume the Predictor will predict my decision correctly with 99.9% accuracy.

Here's where you start to lose me:

What does it mean to "try to MAKE the predictor be wrong"?

PairTheBoard

The truth is embarrassing sometimes. I had simply never asked the question "Where is the tipping point?" before I had computed it, and I really didn't care where it was located because it's not relevant to the assumptions in play. What's relevant is what you believe about the nature of your decision.

Intuitively, I knew that as the error gets small, under the assumption that your decision matters, you should eventually refuse. I also knew that for large errors very, you should take the money. And because the expected value is a continuous function of the assumed error, that there would exist a tipping point. And that's all I ever used in thinking about the question.

PTB, I'm having to do WAY too much work to respond to that post...I want to quote you and preserve the quoting YOU did, but it's too much work. I'll respond a bit at a time.

First, I respond by saying that CDT is simply the wrong way to think in this spot. I'm not actually 100% offering the EDT approach since I admit that on a higher level, I think CDT is more correct...but CDT gets stuff like NP wrong. What I'm doing is taking the "if you're so smart, why aren't you rich?" objection more seriously. Joyce explicitly discusses the objection, and it's in the 2nd half of his discussion where I think he screws up. I didn't want to get into what he says there, since it would confuse people more than they are, but the gist is that he thinks Rachel doesn't have the option of getting the $1M since she's so "rational". Only irrational Irene has any chance at the $1M. So, Joyce says, Rachel can wish that she had Irene's options while simultaneously NOT endorsing Irene's actual choice to refuse.

But, I think this is wrong: what he thinks Rachel can want is an impossibility. Rachel will never have the $1M in the bank (unless the predictor makes an error = unlikely). The only way for Rachel to have Irene's options is to NOT be Rachel (ie, what I call "Joyce Rational").

My argument has been to show that Irene IS rational here. The way that I do it is to use the help of the 3rd party bet.

There's no need to meet the "2 statement" objection head-on since I'm arguing that his approach isn't appropriate for the NP.

To "make" the predictor wrong is for the decider to hope that their decision is NOT the one that the predictor predicted. So, the only way to get both boxes is for the predictor to predict "refuse" and for the agent to choose "accept." That would be making the predictor wrong.

There's nothing controversial there.

If I refuse the $1000, then it's because supposedly there's no free will or my actions are 100% deterministic, in which case asking what I'd do is pointless.

Well, at least you understand the mathematics. It would be hard to get anywhere without at least that.

And CDT simply responds back that taking the "if you're so smart, why aren't you rich?" objection more seriously is the wrong way to think - or is WRONG HEADED if you like that treatment better - and that the right way to think is as follows:


PairTheBoard

No, I don't think their argument has any force if it globally underperforms another line of argument in NP/PD type games. The rational thing to do is to expect the predictor to be correct.

While I DO NOT support EDT as a global hypothesis, I do think that it gets these sorts of problems correct, while CDT gets it wrong.

The CDT arguments are very persuasive, but I take it as a reductio that it gets the NP wrong, therefore the arguments supporting it must be suspect.

The "two statements" argument is merely the dominance argument dressed up w/ a pretty bow.

What do you mean by this. You are asserting that CDT globally underperforms another line of argument in NP/PD type games.

What do you mean by "globally"?

What do you mean by "another line of argument"? Does EDT produce the same "line of argument" in every NP/PD type game?

What do you mean by "NP/PD type games"?




PairTheBoard

Ok. Let's take another look at the opening Assertion of your argument with the above clarification for what you mean by "trying to MAKE the predictor be wrong".

Assertion:
You say a Decider "trying to MAKE the predictor be wrong" means "to hope that their decision is NOT the one that the predictor predicted."

Let's replace that meaning in your Assertion.

Fixed1 Assertion:

First, it's not true that "to bet on the predictor being wrong is irrational". If I were given 10,000-1 odds it would be entirely rational for me to "bet on the predictor being wrong". And if I made such a bet with those odds it would be entirely rational for me to "hope my decision is NOT the one the predictor predicted."

What you mean to say rather than "to bet on the predictor being wrong is irrational" is more precisely, "to bet on the predictor being wrong at even money is irrational". For your Assertion to make sense it must be modified further. Let's see what it looks like with this modification.

Fixed2 Assertion:
The implication is not so clear now. It doesn't make sense to modify further with, "for a Decider to hope at even money that their decision is NOT the one that the predictor predicted is equally irrational."

What is the Decider really "hoping" when he takes the $1000? The $1M is either in the bank or it's not. At this point the Decider couldn't care less about the Predictor. The Decider is simply "hoping" that the $1M is in the bank. Whether he takes the $1000 or not he "hopes" the $1M is in the bank. He can either Refuse the $1,000 and "hope" the $1M is in the bank or he can Accept the $1,000 and "hope" the $1M is in the bank. Is his "Hope" a "More Rational Hope" if he refuses the $1,000? Why? Refusing the $1,000 has no effect on whether the $1M is in the bank. Refusing the $1,000 has no effect on whether the thing he hopes for is true or not. Or does it?

Let's see how your assertion looks with one more modification.

Fixed3 Assertion:
I don't think this inference is at all clear.


I like the 3rd party gamble approach. But I think you've got more work to do clarifying exactly what the relationship is between odds you would demand to make a side bet and your hope that the $1M is in the bank.

PairTheBoard

PTB, if I have to write a dissertation, I will pay you to critique it.

I'm thinking the Crux of Newcomb's Paradox is this.

You have a probability model in which the conditional probability that the $1M is in the Bank GIVEN the decider Refuses the $1,000 is 99.9%.

In a normal situation, that conditional probability would allow you to say that If the decider Refuses the $1,000 then the probability is 99.9% that the $1M is in the bank.

And a similiar conditional probability says that If the decider Accepts the $1,000 then the probability is 0.1% that the $1M is in the bank.

Yet it is causally true that the decider Refusing the $1,000 has no effect on whether the $1M is in the bank. That means, the decider Refusing the $1,000 does not make it more likely that the $1M is in the bank.

So we have a probability model that says Refusing the $1,000 implies a 99.9% probability the $1M is in the bank yet it is causally true that Refusing the $1,000 does not make it more likely that the $1M is in the bank.

Why does the probability model contradict what is causally true?

Exactly what is the probability model modelling? It's certainly a valid probability model for the bookie taking bets. And there is nothing inherently unrealistic about the setup as I showed with my 70% accurate algorithm making predictions based on a controlled question/answer psychological profile.


PairTheBoard

Yes, it does, in the sense of "likelihood" being a quality of your information rather than the objective reality which entirely is or isn't without mixed states.

To post 421:

First, look, you can guess what the spirit of that comment was. It's irrational to bet given even odds. Think of a deeper criticism...but thank you, that will go in a footnote.

Second, it IS relevant to the decider, once they take the $1000, now EDT works in full force and it is very good evidence for someone who just accepted the $1000 that the $1M is not in the bank. EDT and CDT are basically identical as soon as you've made your choice. So, it is very relevant, to both EDT and CDT.

And, why don't you think the final inference is clear? Even CDT grants that people who take the $1000 are probably not going to get the $1M. Their argument is merely that one can't rationalize refusing.