Apologies if this argument has been made before—I’ve had a quick scan through the comments and can’t see it so here goes:
The rational choice is to one-box. The two-boxers are throwing away a critical piece of evidence: in 100 cases out of 100 so far, one-boxing is the right strategy. Therefore, based upon the observable evidence, there’s a less than 1% chance of two-boxing being the correct strategy. It’s irrational to argue that you should two-box.
This argument maps on to the real world. In the real world you are never certain about the mechanism behind the outcomes of your choices, you don’t know what the real probabilities are, and the sample size of evidence you have is too small to make a judgement. To make wise decisions you have to be humble about what you know. To do other is irrational
I’m a big fan of the work of John Vervaeke, particularly the role of Relevance Realisation in helping (and hindering) us make good decisions. In this case, the Prescient alien is just a distraction from the salient facts, which are, in 100 trials, 100% of the time, the best choice is to take the opaque box.
I show you a coin. I tell you that it’s a normal coin. I toss it 100 times. Every time it lands heads. The next time I toss it, what is the chance of it landing tails?
For those of you who said 50%, let me phrase the question another way: Given I have tossed a coin 100 times and it’s landed heads every time, what is the probability that the coin is unbiased?
Apologies if this argument has been made before—I’ve had a quick scan through the comments and can’t see it so here goes: The rational choice is to one-box. The two-boxers are throwing away a critical piece of evidence: in 100 cases out of 100 so far, one-boxing is the right strategy. Therefore, based upon the observable evidence, there’s a less than 1% chance of two-boxing being the correct strategy. It’s irrational to argue that you should two-box. This argument maps on to the real world. In the real world you are never certain about the mechanism behind the outcomes of your choices, you don’t know what the real probabilities are, and the sample size of evidence you have is too small to make a judgement. To make wise decisions you have to be humble about what you know. To do other is irrational
I’m a big fan of the work of John Vervaeke, particularly the role of Relevance Realisation in helping (and hindering) us make good decisions. In this case, the Prescient alien is just a distraction from the salient facts, which are, in 100 trials, 100% of the time, the best choice is to take the opaque box.
In fact. Let’s simplify the thought experiment:
I show you a coin. I tell you that it’s a normal coin. I toss it 100 times. Every time it lands heads. The next time I toss it, what is the chance of it landing tails?
For those of you who said 50%, let me phrase the question another way: Given I have tossed a coin 100 times and it’s landed heads every time, what is the probability that the coin is unbiased?