But with Vladimir’s assumptions, he gets the £1000000 zero percent of the time! I quote:
the money-maximizing agents will only be visited by Omega when the envelope is empty
The description “money-maximizing” is wrong, but he is talking about a type of agent which does indeed make it impossible for Omega to ever show up while the £1000000 is there.
To return to your own comment,
our choice only affects whether or not Omega comes and offers you £10 or not,
correct
and you maximize your expected value there by being the kinda guy who takes £10 that’s offered.
You’re missing the fact that Alpha sending a letter happened regardless of Omega, and thus regardless of what you choose, you’d get £1 000 000 from Alpha 50% of time. You can’t choose so that you’d get £1 000 000 zero percent of the time simply because your choice doesn’t affect that.
I repeat that, since that seems to be the key problem here. Alpha flipped a coin to decide whether or not to send you £1 000 000. Your past or future actions don’t have any control over Alpha doing this, and sending you £1 000 000. In particular, your actions, upon receiving the envelope don’t have any, direct or indirect, entanglement with what does the envelope contain.
Your actions however are entangled with whether or not Omega comes along to offer you £10. If you’re the kinda guy to accept the £10, Omega makes this deal only when Alpha didn’t sent you £1 000 000. If you’re the kinda guy that refuses £10, Omega comes only when Alpha sent you £1 000 000.
So to maximize the expected value, you should accept the £10. That way, you get 50% time £1 000 000 and 50% £10. Otherwise you get 50% time £1 000 000 and 50% time £0
You can’t choose so that you’d get £1 000 000 zero percent of the time simply because your choice doesn’t affect that.
Vladimir (and you!) get £1000000 zero percent of the time on those occasions when Omega appears, and by hypothesis this is one of those occasions! You are committing a higher-order version of the two-box mistake.
Vladimir (and you!) get £1000000 zero percent of the time on those occasions when Omega appears
Exactly. Which is our purpose here. We want Omega to give £10 when we can accept it, not when we have to reject it. Which brings us back to my earlier statement:
So to maximize the expected value, you should accept the £10. That way, you get 50% time £1 000 000 and 50% £10. Otherwise you get 50% time £1 000 000 and 50% time £0
If you accept the £10, you get £10, and envelope will be empty. However, just as often(I’m assuming for simplicity that Omega appears always when possible) you receive envelope with £1 000 000 in it.
If you refuse £10, you find that the envelope holds £1 000 000. However, just as often you receive empty envelopes. Your expected value here is £500 000, whereas by accepting your expected value would be £500 005.
Your choice doesn’t affect what the envelope holds. It will just as often hold £1 000 000 and be empty. Only thing you can affect here is when does the Omega appear. This is very much unlike the Newcombs problem, where your choice actually affects what the boxes contain.
So effectively, only thing we do here is shift Omega-appearances to the times when we can accept the £10. Like I noted earlier, your choice has already caused Omega to appear, but it has not, and cannot, affect what the envelope contains.
Edit: I should clarify that Omega appearing is a double conditional, if you won, you won regardless. If you lost, you lost regardless. For Omega to appear, your choice, given Omega appearing, has to be the right kind, and result of Alpha coin toss has to be the right kind. If you’re the kinda guy to turn down the £10, for Omega to appear envelope has to contain the £1 000 000. Regardless of what you choose, you won anyway. This way however, if you didn’t win, Omega wouldn’t appear, offering you £10.
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.
So Omega said, if you accept the ten pounds, I predict that Alpha gave you a bag of air. You accept the ten, and it turns out that Alpha still sends you ten million. So Omega is wrong. But Omega is never wrong. But he is. But he can’t be. But he is!
But he did. He’s in front of you. You’re the winner. And you’re going to tell him that you’d rather have ten pounds.
I understand that it’s more profitable to mop bathrooms in a public school than to buy lottery tickets, but if somebody tells you, “if you turn down this job, I will give you a winning ticket,” don’t go to work.
But with Vladimir’s assumptions, he gets the £1000000 zero percent of the time! I quote:
The description “money-maximizing” is wrong, but he is talking about a type of agent which does indeed make it impossible for Omega to ever show up while the £1000000 is there.
To return to your own comment,
correct
wrong!
You’re missing the fact that Alpha sending a letter happened regardless of Omega, and thus regardless of what you choose, you’d get £1 000 000 from Alpha 50% of time. You can’t choose so that you’d get £1 000 000 zero percent of the time simply because your choice doesn’t affect that.
I repeat that, since that seems to be the key problem here. Alpha flipped a coin to decide whether or not to send you £1 000 000. Your past or future actions don’t have any control over Alpha doing this, and sending you £1 000 000. In particular, your actions, upon receiving the envelope don’t have any, direct or indirect, entanglement with what does the envelope contain.
Your actions however are entangled with whether or not Omega comes along to offer you £10. If you’re the kinda guy to accept the £10, Omega makes this deal only when Alpha didn’t sent you £1 000 000. If you’re the kinda guy that refuses £10, Omega comes only when Alpha sent you £1 000 000.
So to maximize the expected value, you should accept the £10. That way, you get 50% time £1 000 000 and 50% £10. Otherwise you get 50% time £1 000 000 and 50% time £0
Vladimir (and you!) get £1000000 zero percent of the time on those occasions when Omega appears, and by hypothesis this is one of those occasions! You are committing a higher-order version of the two-box mistake.
Exactly. Which is our purpose here. We want Omega to give £10 when we can accept it, not when we have to reject it. Which brings us back to my earlier statement:
If you accept the £10, you get £10, and envelope will be empty. However, just as often(I’m assuming for simplicity that Omega appears always when possible) you receive envelope with £1 000 000 in it.
If you refuse £10, you find that the envelope holds £1 000 000. However, just as often you receive empty envelopes. Your expected value here is £500 000, whereas by accepting your expected value would be £500 005.
Your choice doesn’t affect what the envelope holds. It will just as often hold £1 000 000 and be empty. Only thing you can affect here is when does the Omega appear. This is very much unlike the Newcombs problem, where your choice actually affects what the boxes contain.
So effectively, only thing we do here is shift Omega-appearances to the times when we can accept the £10. Like I noted earlier, your choice has already caused Omega to appear, but it has not, and cannot, affect what the envelope contains.
Edit: I should clarify that Omega appearing is a double conditional, if you won, you won regardless. If you lost, you lost regardless. For Omega to appear, your choice, given Omega appearing, has to be the right kind, and result of Alpha coin toss has to be the right kind. If you’re the kinda guy to turn down the £10, for Omega to appear envelope has to contain the £1 000 000. Regardless of what you choose, you won anyway. This way however, if you didn’t win, Omega wouldn’t appear, offering you £10.
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?
Click.
Thanks!
So Omega said, if you accept the ten pounds, I predict that Alpha gave you a bag of air. You accept the ten, and it turns out that Alpha still sends you ten million. So Omega is wrong. But Omega is never wrong. But he is. But he can’t be. But he is!
No.
If Alpha sends you 10m and you would accept the ten, Omega doesn’t make the stated prediction.
But he did. He’s in front of you. You’re the winner. And you’re going to tell him that you’d rather have ten pounds.
I understand that it’s more profitable to mop bathrooms in a public school than to buy lottery tickets, but if somebody tells you, “if you turn down this job, I will give you a winning ticket,” don’t go to work.