It’s not mere correlation. Our reward is determined by the choice we make (and the choice our clone makes). I win $1,000,000 because I chose the red box (and because my clone chose the red box), and you win $1,000 because you chose the blue box (and because your clone chose the blue box). It’s literally premises (6) - (9).
There is $1,000,000 in the box because your clone chose the red box so you win at least $1,000,000 ONLY because your clone chose the red box. You win $1,000,000 instead of $1,001,000 because you chose the red box. That’s why you should choose the blue one.
You seem to be arguing that the amount we are rewarded is determined independently of our choice (and our clone’s choice), but it’s not.
I never said it’s independent of your clone’s choice, in fact the whole reason why it’s independent of your choice is precisely because it is only dependent on your clone’s choice.
There is no money in any box. The boxes are empty. Replace them with coloured badges that we pin to our chest if this is difficult for you to understand. Also note that we make our choice before our clone does.
As per premises (6) - (9), my reward is determined by both my choice and the clone’s choice. That’s why there are four possible rewards and not just two.
There is no money in any box. The boxes are empty. Replace them with coloured badges that we pin to our chest if this is difficult for you to understand.
I guess I phrased it poorly. Here’s the clean version:
You win at least $1,000,000 ONLY because your clone chose the red box. You win $1,000,000 instead of $1,001,000 because you chose the red box. That’s why you should choose the blue one.
As per premises (6) - (9), my reward is determined by both my choice and the clone’s choice. That’s why there are four possible rewards and not just two.
Indeed and the fact that you can win at least $1,000,000 is independent of your choice.
If this is not the case then your game isn’t equivalent to the Newcomb problem and yes one box if you want.
I win $1,001,000 because I chose the blue box (and because…)
I win $1,001,000 because my clone chose the red box (and because…)
I win $1,000,000 because I chose the red box (and because…)
I win $1,000,000 because my clone chose the red box (and because…)
I win $1,000 because I chose the blue box (and because…)
I win $1,000 because my clone chose the blue box (and because…)
I win $0 because I chose the red box (and because…)
I win $0 because my clone chose the blue box (and because…)
You are trying to ignore all the odd numbers, which is dishonest.
So, once again, if there are 200 participants, and if 100 of them are committed red-boxers, and if 100 of them are committed blue-boxers, and if the clones agree with their original 99% of the time, then we could expect on average:
99 red-boxers will leave with $1,000,000
99 blue-boxers will leave with $1,000
1 red-boxer will leave with $0
1 blue-boxer will leave with $1,001,000
This is not mere correlation. Their rewards are determined by the choices they (and their clones) make. And I am much more likely to be in (1) than you are in (4) (or me in (3)). This is the fact that any rational game theorist ought use to justify their decision, and the fact that your reasoning almost certainly puts you in (2) demonstrates that it is the wrong reasoning to use in this game.
It’s exactly the same. Game 3 is equivalent to Game 2 which is equivalent to Game 1. You are simply being deceived into the wrong reasoning when considering Game 1. It’s not a bizarre coincidence that most one-boxers will become millionaires and most two-boxers won’t.
I actually looked at them now. I am sorry to have assumed that they were equivalent to the Newcomb problem by adding assumptions from the Newcomb problem. So Game 1 is equivalent to the Newcomb problem but Game 1 isn’t equivalent to Game 2 or Game 3. Game 2 and Game 3 are equivalent and one should OB in Game 2/3 and TB in Game 1.
The assumption being what I wrote earlier:
the fact that you can win at least $1,000,000 is (causally) independent of your choice.
Game 1 and the Newcomb problem satisfy this, Game 2 and Game 3 don’t.
They aren’t and I told you why. The process (the prediction in the newcomb problem) that determines whether the million is in the box or whether you can win at least a million must not depend on your choice. Game 2 doesn’t satisfy this while Game 1 does.
Suppose I am a fallible predictor and you are the player. If we agree to repeatedly play the game until I correctly guess your action, then I am, by construction, an infallible predictor in the final round of our game. And yet I didn’t force you to choose whichever course of action you took in the final round. Hence (1) and (2) obtain in the final round.
This simulation of quantum non-locality gives the general idea, even if it requires further explanation to account for the possibility of divergent strategies.
You may have missed my reply to you. I said this about your repeated case.
Indeed, even in the non-repeated case, it is possible the predictor guessed correctly, but we cannot deduce that the predictor was infallible, as there was a chance he would have failed. Same here: sure, there might be a point where the predictor finally succeeds, but we can’t deduce that the meta-predictor is infallible, as there is a chance the game continues.
Yes, that is classically true; we are after all, simulating or illustrating, but not necessarily emulating (1) + (2) in our iterated game.
But why does that matter, given that humans are quantum systems that exist in super-positions?
How do you know that the state of an unopened box has already been reduced, via quantum decoherence, into a definite state?
How can you even know that a regular game of rock-paper-scissors in the school-yard that is iterated until there is a winner isn’t the quantum version that is guaranteed to have a final round?
In practice, we make classical assumptions to get classical answers, but our classical assumptions are grounded in untestable counterfactual assumptions. Hence there is nothing inherently implausible or untrue about interpreting Newcomb’s paradox in the limit in which (1) and (2) are true at the expense of (3). All one can say, is that this set of assumptions isn’t a classical set of assumptions.
But why does that matter, given that humans are quantum systems that exist in super-positions?
Well if you want to show that (1) and (2) are compatible, you need to show there exists a world where (1) and (2) are true at the same time. You haven’t.
Hence there is nothing inherently implausible or untrue about interpreting Newcomb’s paradox in the limit in which (1) and (2) are true at the expense of (3)
Well, I am telling you there is something inconsistent. (1) contradicts (2).
You said yourself (1), (2) and (3) are incompatible. What’s implausible or untrue about having the three assumptions?
They’re the same. I’ll introduce Game 1.5 to show this:
Game 1
$1,000 is placed in a blue box
You are cloned and the clone is asked to choose between either a) the red box or b) the red and the blue box
The clone is destroyed
If the clone chose (a) then $1,000,000 is placed in a red box
You are asked to choose between either a) the red box or b) the red and the blue box
You win the contents of the box(es) you chose
Game 1.5
There is an empty red box and an empty blue box
You are cloned
You are asked to choose between either a) the red box or b) the red and the blue box
The clone is asked to choose between either a) the red box or b) the red and the blue box
The clone is destroyed
$1,000 is placed in the blue box
If the clone chose (a) then $1,000,000 is placed in the red box
You win the contents of the box(es) you chose
Game 2
There is an empty red box and an empty blue box
You are cloned
You are asked to choose between either a) the red box or b) the red and the blue box
The clone is asked to choose between either a) the red box or b) the red and the blue box
The clone is destroyed
If you both chose (a) then you win $1,000,000
If you both chose (b) then you win $1,000
If you chose (a) and your clone chose (b) then you win $0
If you chose (b) and your clone chose (a) then you win $1,001,000
Game 1 is equivalent to Game 1.5 which is equivalent to Game 2. It doesn’t matter if the money is placed in the boxes before or after your choice, or how your reward is given to you.
Again, we can even assume that you don’t know which of these three games you are playing (because both boxes are closed). It is rational to one-box.
Introducing 200 variations won’t save you from having to acknowledge the difference between Game 1 and Game 2. I gave you the difference.
So, you either tell me that I am wrong and Game 1 actually doesn’t satisfy the assumption or Game 2 does actually satisfy the assumption. Whatever you do, my point is that the original problem does satisfy the assumption and if a game satisfies the assumption then you should TB. So really the best is to take a game that satisfy the assumption and tell me why you think you should OB in such a game without referencing games that don’t satisfy the assumption.
Your claimed difference is bad reasoning. They’re not different. Games 1, 1.5, 2, and 3 are equivalent, and the rational choice in Game 3 is (a). And it is not a coincidence or mere correlation that in all four games almost all those who follow my reasoning leave with $1,000,000 and almost all those who follow your reasoning leave with $1,000. This outcome is a direct consequence of their commitments to make the choice they do.
Your continued insistence that the poorer group are more rational than the richer group is the greatest irrationally of all.
Fine. That is too much dodging even for me. If you were serious in the discussion, you would stop claiming stuff (e.g. “there are equivalent”) without making any argument or counter-argument.
I know you understand the situation and I hope you can make peace with the fact that one should TB.
This all depends on what is known, what is explained to whoever is making the choice. This has not been spelled out in game 3. In game 1, the clones are a method used by the predictor, one that doesn’t work if they know about it. In game3, if all your text is what is explained, then the contestant(s) know that cloning is going on. If they are informed which is which, the clone has no incentive to make a rational choice. If they don’t know, they’re both probably unwilling to make a choice at all since doing so involves a 50/50 chance of death.
If the contestant is not informed of the cloning, then the rules of the game are unstated and no choice is more rational than another.
I agree with most of your posts, but this one baffles me since no rational path seems apparent.
No they’re not since like game 3, the rules explained to the contestant(s) is not spelled out. It cannot be the same rules as the OP since what you win is not due to an apparent single choice made.
Freedom to deviate from what? The prediction? Sure, but that almost never happens, so free will isn’t getting the 2B types any more utility than those lacking it. It does not follow from (2) that 2B is the winning strategy.
Depends on what is meant by independent. Causally disconnected, sure, but the correlation is still there, which seems to violate a claim of independence.
I fail to see the relevance of quantum anything in this scenario. Quantum uncertainty doesn’t grant free will, it only grants randomness, not deliberate free choice. Randomness does not yield optimal utility in this scenario.
In all four games the clone believes that he is not the clone.
Every participant (and every clone) knows the rules as spelled out in the four games.
Then let’s say that failure to make a choice guarantees death, whether you’re a clone or not.
Or let’s say that the participants don’t care about living or dying, only about maximising the reward at the end of the game, perhaps because it’s donated to a worthy charity.
Or let’s say that the clone isn’t destroyed, just told after making the choice that they are the clone and that they’re not actually playing the game, only being used to make the prediction.