5 ms·

I guess this boils down to whether you believe in determinism. If you do, then the predictor will always be right, and you have essentially zero chance of fool

by fitter 12y ago

I guess this boils down to whether you believe in determinism. If you do, then the predictor will always be right, and you have essentially zero chance of fooling it by "changing your mind" later for the extra money. If you don't believe in such a thing, then theoretically some nondeterministic volition of yours could allow you to change your mind in a way that the predictor could not have deterministically forseen.

justzisguyuknow 12y ago
It reminds me of the 'Battle of Wits' scene in The Princess Bride: http://c2.com/cgi/wiki?BattleOfWits http://c2.com/cgi/wiki?BattleOfWits
Houshalter 12y ago
That's not really the point of the thought experiment at all. And invoking randomness doesn't make the thought experiment easier, just more complicated. From the link someone posted above: >(Incidentally, don’t imagine you can wiggle out of this by basing your decision on a coin flip! For suppose the Predictor predicts you’ll open only the first box with probability p. Then he’ll put the $1,000,000 in that box with the same probability p. So your expected payoff is 1,000,000p2 + 1,001,000p(1-p) + 1,000(1-p)2 = 1,000,000p + 1,000(1-p), and you’re stuck with the same paradox as before.)
empthought 12y ago
It's not about changing your mind for the money, it's about the fact that causality doesn't (shouldn't) run backwards in time. Consider this: when you are faced with the choice, the allotted money is already under the boxes. How could what you choose now affect this outcome? It can't. You must always take both boxes to get the maximum amount of money possible. Either the $1,000,000 is under the single box, or it is not. If you take both boxes, you will get $1000 regardless of anything else, and possibly $1,001,000. If you take the single box, you will either get $0 or $1,000,000, but your action can't possibly change that, unless you believe somehow that causality runs backwards in time.
- Retric 12y ago
  Your assuming something along the lines of free will. Remember the choice is made independent of what's in the boxes. So, let's consider a deterministic system. If I write a program that uses pure logic to make the choice and it's non random then it always makes the same choice. EX: hard coding chose (A+B). Then that choice has in effect already made based on the algorithm selection making the (A+B) prediction basically fool proof. I could of course then run that program after the fact and see (A+B), but barring a low chance random event it's going to give the result of my prediction. PS: Consider chess, from a math standpoint every possible game already exists with players essentially picking just one game from the set of possible games. So, if you write two deterministic programs and run them the winner is already predetermined based on which algorithms where selected. If you then change one of the programs in such a way that it still chose the same move you know the winner before running the programs.
  - empthought 12y ago
    But that doesn't matter in the slightest. The money is either there or it is not there. It's not put in the boxes after you've made the choice. It's put into the boxes before you even know there's a game. Whether or not there is free will or determinism, picking both boxes always nets the most money of what's on the table.
    - Strilanc 12y ago
      You're using a mathematical model that doesn't apply. The ahead-of-time simulations invalidate the idea that your decision can't affect the outcome, despite the final decision ultimately occurring afterwards. An analogy would be asserting that you can't possibly shoot yourself in the back of the head when firing into the distance, and sticking to that position even after finding out you're in a pac-man-style loop-around world. A much closer but more technical analogy is that you can't solve imperfect information games by recursively solving subtrees in isolation. Optimal play can involve purposefully losing in some subtrees, so that bluffs are more effective in other subtrees. The fact that you are doing worse by two-boxing, leaving with a thousand dollars instead of a million, despite following logic that's supposed to maximize how well you do, should be a huge red flag.
Retra 12y ago
That is not the issue at all. There are two main ways of seeing the problem: 1. If the predictor really has such an awesome predicting talent, you have to wonder why. How much information must she have the means to process in order to make such successful predictions? Do you really think you could outperform her? 2. It doesn't matter what she predicts, because the result is independent of her prediction. This is a problem about determining what is more important to rational decision-making: newly discovered information advantages, or previously known truths. Do you bet on the powerful new technology, or the tried and true past solution? Do you hire the person with a proven track-record of reliable success, or the unproven one with the ground-breaking earth-shattering new idea?

by fitter 12y ago

justzisguyuknow 12y ago

It reminds me of the 'Battle of Wits' scene in The Princess Bride: http://c2.com/cgi/wiki?BattleOfWits http://c2.com/cgi/wiki?BattleOfWits

Houshalter 12y ago

That's not really the point of the thought experiment at all. And invoking randomness doesn't make the thought experiment easier, just more complicated. From the link someone posted above: >(Incidentally, don’t imagine you can wiggle out of this by basing your decision on a coin flip! For suppose the Predictor predicts you’ll open only the first box with probability p. Then he’ll put the $1,000,000 in that box with the same probability p. So your expected payoff is 1,000,000p2 + 1,001,000p(1-p) + 1,000(1-p)2 = 1,000,000p + 1,000(1-p), and you’re stuck with the same paradox as before.)

empthought 12y ago

It's not about changing your mind for the money, it's about the fact that causality doesn't (shouldn't) run backwards in time. Consider this: when you are faced with the choice, the allotted money is already under the boxes. How could what you choose now affect this outcome? It can't. You must always take both boxes to get the maximum amount of money possible. Either the $1,000,000 is under the single box, or it is not. If you take both boxes, you will get $1000 regardless of anything else, and possibly $1,001,000. If you take the single box, you will either get $0 or $1,000,000, but your action can't possibly change that, unless you believe somehow that causality runs backwards in time.

Retric 12y ago
Your assuming something along the lines of free will. Remember the choice is made independent of what's in the boxes. So, let's consider a deterministic system. If I write a program that uses pure logic to make the choice and it's non random then it always makes the same choice. EX: hard coding chose (A+B). Then that choice has in effect already made based on the algorithm selection making the (A+B) prediction basically fool proof. I could of course then run that program after the fact and see (A+B), but barring a low chance random event it's going to give the result of my prediction. PS: Consider chess, from a math standpoint every possible game already exists with players essentially picking just one game from the set of possible games. So, if you write two deterministic programs and run them the winner is already predetermined based on which algorithms where selected. If you then change one of the programs in such a way that it still chose the same move you know the winner before running the programs.
- empthought 12y ago
  But that doesn't matter in the slightest. The money is either there or it is not there. It's not put in the boxes after you've made the choice. It's put into the boxes before you even know there's a game. Whether or not there is free will or determinism, picking both boxes always nets the most money of what's on the table.
  - Strilanc 12y ago
    You're using a mathematical model that doesn't apply. The ahead-of-time simulations invalidate the idea that your decision can't affect the outcome, despite the final decision ultimately occurring afterwards. An analogy would be asserting that you can't possibly shoot yourself in the back of the head when firing into the distance, and sticking to that position even after finding out you're in a pac-man-style loop-around world. A much closer but more technical analogy is that you can't solve imperfect information games by recursively solving subtrees in isolation. Optimal play can involve purposefully losing in some subtrees, so that bluffs are more effective in other subtrees. The fact that you are doing worse by two-boxing, leaving with a thousand dollars instead of a million, despite following logic that's supposed to maximize how well you do, should be a huge red flag.

Retra 12y ago

That is not the issue at all. There are two main ways of seeing the problem: 1. If the predictor really has such an awesome predicting talent, you have to wonder why. How much information must she have the means to process in order to make such successful predictions? Do you really think you could outperform her? 2. It doesn't matter what she predicts, because the result is independent of her prediction. This is a problem about determining what is more important to rational decision-making: newly discovered information advantages, or previously known truths. Do you bet on the powerful new technology, or the tried and true past solution? Do you hire the person with a proven track-record of reliable success, or the unproven one with the ground-breaking earth-shattering new idea?