Free Will Philosophy Problem

[gasgod]

Let me paraphrase what you have been saying in this thread:

"You must accept the premise that the alien will successfully predict your action to a high degree of accuracy. Randomizing your play is forbidden, even though this is a central idea in game theory, because that would obviously defeat the premise."

Given the conditions you put on the game, it's just plain rigged. You might as well say: "Assuming that if you pick only box 2 that it will always contain a million, and further assuming that if you pick both, box 2 will always be empty, which would you pick?"

You would have a valid point if somebody proposed to use a time machine to determine whether box 2 was empty. This has never been done, and we don't have any reason to believe it could ever be done. But randomizing one's play is done every day millions of times all over the world. Forbidding it equivalent to forbidding a bridge player to double, or a chess player to castle.

GG

[FishAndChips]

Let's play it like a poker hand:

Since there is no point to doing this if you don't accept the premise, let's agree that the Alien is able to predict your actions almost 100% correctly (let's just say 99%)

So lets break it down say over 100 trials.

1) If you "decide" to take both boxes every time you get $1000 99 times and once you will win $1,001,000 when it (does our alien have a gender?) has guessed wrong. Thus you earn: $1,100,000 by taking both boxes.

2) If you "decide" to only take box 2 then you win 1,000,000 (99 times) + $0 (once) = $99,000,000

2 is clearly larger than 1. Pick only 2 and live like a high roller.

If it wasn't stated in the premise that the Alien was able to predict your decisions with high accuracy, then it might be different, but assuming that premise true, you have to pick box two. [img]/images/graemlins/smile.gif[/img]

I find it interesting that so many poker players demand the sure thing of $1,000 when the chance for a million is so high. It may be a gamble, but look at giving up the "sure" thousand as a buy-in to the World Series of Alien Prediction Poker. Grand prize $1,000,000.

[PairTheBoard]

GG: "Given the conditions you put on the game, it's just plain rigged. You might as well say: "Assuming that if you pick only box 2 that it will always contain a million, and further assuming that if you pick both, box 2 will always be empty, which would you pick?" "

Exactly. That's exactly what I understood the premise to be - the alien Could accurately predict your choice if you actually make the choice. As another poster said, the problem is sometimes stated that the alien can predict your action with 100% accuracy. The puzzle Could be further defined by assuming that if you avoid making the choice yourself by letting something else choose for you then the game is null and void. The alien will predict your action and no money will be in either box. Under those assumptions the game Will appear rigged to you. Like magic your choice will always coincide with the box contents. The apparent rigging of the game will offend your sensibilities. But those are the assumptions.

However, upon further reflection I'm now thinking that the KEY PHRASE of the scenario as stated by edthayer is "AS ACCURATE AS POSSIBLE". That's the Phrase that should be discussed Up Front by anyone answering the question. That's the real issue. Your box choice strategy Depends on your opinion of that Phrase. btw, that's what I focused on in my first post on this thread.

http://forumserver.twoplustwo.com/sh...;o=14&vc=1


PairTheBoard

[gasgod]

It has been an enjoyable discussion, and I think we have both said all that can be said for our respective points of view.

BTW, I firmly believe that "free will" is a meaningless concept. "Determinism" might also be meaningless, but that's material for another thread.

GG

[edthayer]

For those people that think taking only Box 2 is correct, I have a new way to approach this problem.

Forget the alien for a moment. Consider the same situation regarding the boxes, minus the alien. In this new situation, it should be painfully obvious that it is correct to take both boxes.

Okay, now bring the alien back into it. Does the fact that the alien put those boxes there really have anything to do with it?

The alien cannot predict with perfect accuracy: he is not God. Newcomb could have made it very clear if he intended the alien to have God powers, but he didn't. He says the alien has a perfect history, and that he can use all the physical evidence at his disposal to make a prediction.

For all the people who still consider this a gamble, you need to realize that the boxes and their contents are already set IN STONE when you make your choice. It's superstition that causes you to chose only Box 2, and it will cost you a grand every single time you make it.

[ZeeJustin]

Fact: the alien has already made his decision.
Fact: nothing you do now can change the decision he made.

Take both boxes, hope he's wrong. It seems simple to me.

[ZeeJustin]

The free-will people obviously make the right decision and take both boxes. The determinism people seem to be taking only box 2 which makes no sense.

Determinism means that it is possible to predict your future actions. It does not mean that your future actions can change the past. The alien has made his mind up already, you choosing only box 2 won't change his PAST decision, so you take both boxes anyway.

[TStoneMBD]

dont you guys think that it is possible that the alien has a time machine and therefore will know what decision you will make 100% of the time? you therefore cannot beat him with a coin flip, not that you would want to reduce the million dollars to a 50/50 chance anyway.

isnt it also possible that you can predetermine your future actions by a decision you have already made? what if you made the predecision that you are definitely going to take box 2? what if the alien can read your thoughts? you get all the money.

what if you predetermine that you are going to flip a coin/take both boxes or whatever? what if the alien knows this? you only get $1,000.

what if you predetermine that you are going to subconciously pretend to have predetermined to take box 2, but in reality you are going to take both boxes? what if the alien knows this? you only get $1,000.


its so silly that you guys are willing to risk 1 million dollars on a potential gain of $1,000 when you really dont know the alien's powers or what he is capable of. you guys are trying to outsmart the alien, which is silly. predetermine that you are going to only pick box 2 and you will then receive the million a hell of alot more than if you decided to take both boxes.

[ZeeJustin]

[ QUOTE ]
its so silly that you guys are willing to risk 1 million dollars on a potential gain of $1,000

[/ QUOTE ]

It's a philisophical question. Don't focus on the amounts so much. What if box 1 was $100,000? Think of it that way.

[TStoneMBD]

the amounts matter a great deal, because we have to look at this from an ev perspective. if the first box was $100,000 then you would have to do math to determine what choice is most profitable. there are variables that cannot be determined so an accurate estimate is not possible. also, the alien might realize that 100,000 is alot more money than 1,000 and therefore will rarely ever put a million in the second box.

so yes, if there was $100,000 in the first box i would take both boxes. however, im not sure if that is correct.