Like I noted earlier, your choice has already caused Omega to appear, but it has not, and cannot, affect what the envelope contains.
The nature of my decision procedure affects the conditions under which Omega can appear.
When I first confront this problem, I have not thought it through, but I know that Omega has appeared. So I ask: given that fact, what is the probability that the envelope contains the £1000000?
Without any knowledge of what my decision procedure is, the probability that the envelope contains the £1000000 is .5.
If I am a determined £10-taker, then the probability that the envelope contains the £1000000 is zero. If I am a determined £10-refuser, then the probability that the envelope contains the £1000000 is one.
But I am neither of those things. I am some more complicated decision-making system which is capable of either taking or refusing the £10, depending on which act is to my advantage. And I can see that if I refuse the £10, then there must be £1000000 in the envelope, which I get to keep. So, I refuse the £10.
Now it might be argued that I just got lucky. If I was as rational as you and Vladimir, then Omega would only ever appear when there was no money in the envelope. But because I hadn’t thought things through, it is possible for Omega to show up when there is money in the envelope, and in that case the right thing to do is what I did.
Basically, if you are already an entity which has reflectively optimized its decision procedure for Alpha-Omega situations, then you and Vladimir are making the right choice. But I was not such an entity, and so my choice was the right one for me.
Basically, if you are already an entity which has reflectively optimized its decision procedure for Alpha-Omega situations, then you and Vladimir are making the right choice. But I was not such an entity, and so my choice was the right one for me.
Actually, not. Like I said, your choice there doesn’t affect what the envelope contains. If you were rational like me and Vladimir, you wouldn’t meet Omega. You’d just receive an envelope with £1 000 000 in it. Funny thing with this envelope-puzzle is that Omega makes refursers and accepters to live in different conditionals. If you end up answering “refuse”, you’re in the conditional “Alpha decided to send you money”. If you answer “accept”, you’re in the conditional “Alpha decided not to send you money”. However, your choice doesn’t have any power over these conditionals, regardless of what you’d choose, Alpha’s coin toss wouldn’t be affected.
And because your choice doesn’t affect what the envelope contains, you’re not actually winning anything by refusing £10. Your refusal is simply a-causally making Omega appear in front of you after you got £1 000 000 from Alpha. Just like it is making a-causally Omega appear in front of me and Vladimir after we didn’t get anything. It doesn’t say anything about our chances to win £1 000 000, which were 50-50. And like I noted earlier, because of this, occasionally we receive enveloped that hold 1 000 000, while you occasionally receive empty envelopes.
If I am a determined £10-taker, then the probability that the envelope contains the £1000000 is zero. If I am a determined £10-refuser, then the probability that the envelope contains the £1000000 is one.
But I am neither of those things. I am some more complicated decision-making system which is capable of either taking or refusing the £10, depending on which act is to my advantage. And I can see that if I refuse the £10, then there must be £1000000 in the envelope, which I get to keep. So, I refuse the £10.
No. If you knowably refuse the £10 in this situation that makes you a determined £10-refuser. The fact that you personally did not know that you are a determined £10-refuser even though Omega did does not have any magical consequences.
Basically you can’t simultaneously take the fact that you have a choice and the fact that Omega is actually standing before you as given.
The nature of my decision procedure affects the conditions under which Omega can appear.
When I first confront this problem, I have not thought it through, but I know that Omega has appeared. So I ask: given that fact, what is the probability that the envelope contains the £1000000?
Without any knowledge of what my decision procedure is, the probability that the envelope contains the £1000000 is .5.
If I am a determined £10-taker, then the probability that the envelope contains the £1000000 is zero. If I am a determined £10-refuser, then the probability that the envelope contains the £1000000 is one.
But I am neither of those things. I am some more complicated decision-making system which is capable of either taking or refusing the £10, depending on which act is to my advantage. And I can see that if I refuse the £10, then there must be £1000000 in the envelope, which I get to keep. So, I refuse the £10.
Now it might be argued that I just got lucky. If I was as rational as you and Vladimir, then Omega would only ever appear when there was no money in the envelope. But because I hadn’t thought things through, it is possible for Omega to show up when there is money in the envelope, and in that case the right thing to do is what I did.
Basically, if you are already an entity which has reflectively optimized its decision procedure for Alpha-Omega situations, then you and Vladimir are making the right choice. But I was not such an entity, and so my choice was the right one for me.
Actually, not. Like I said, your choice there doesn’t affect what the envelope contains. If you were rational like me and Vladimir, you wouldn’t meet Omega. You’d just receive an envelope with £1 000 000 in it. Funny thing with this envelope-puzzle is that Omega makes refursers and accepters to live in different conditionals. If you end up answering “refuse”, you’re in the conditional “Alpha decided to send you money”. If you answer “accept”, you’re in the conditional “Alpha decided not to send you money”. However, your choice doesn’t have any power over these conditionals, regardless of what you’d choose, Alpha’s coin toss wouldn’t be affected.
And because your choice doesn’t affect what the envelope contains, you’re not actually winning anything by refusing £10. Your refusal is simply a-causally making Omega appear in front of you after you got £1 000 000 from Alpha. Just like it is making a-causally Omega appear in front of me and Vladimir after we didn’t get anything. It doesn’t say anything about our chances to win £1 000 000, which were 50-50. And like I noted earlier, because of this, occasionally we receive enveloped that hold 1 000 000, while you occasionally receive empty envelopes.
No. If you knowably refuse the £10 in this situation that makes you a determined £10-refuser. The fact that you personally did not know that you are a determined £10-refuser even though Omega did does not have any magical consequences.
Basically you can’t simultaneously take the fact that you have a choice and the fact that Omega is actually standing before you as given.
Apparently someone thinks there is something wrong with this. Could they please explain?