Some clarifications on my intentions writing this story.
Omega being dead and Irene having taken the money from one box before having the conversation with Rachel are both not relevant to the core problem. I included them as a literary flourish to push people’s intuitions towards thinking that Irene should open the second box, similar to what Eliezer was doing here.
Omega was wrong in this scenario, which departs from the traditional Newcomb’s problem. I could have written an ending where Rachel made the same arguments and Irene still decided against doing it, but that seemed less fun. It’s not relevant whether Omega was right or wrong, because after Irene has made her decision, she always has the “choice” to take the extra money and prove Omega wrong. My point here is that leaving the $1000 behind falls prey to the same “rational agents should win” problem that’s usually used to justify one-boxing. After taking the $1,000,000 you can either have some elaborate justification for why it would be irrational to open the second box, or you could just… do it.
Here’s another version of the story that might demonstrate this more succinctly:
Irene wakes up in her apartment one morning and finds Omega standing before her with $1,000,000 on her bedside table and a box on the floor next to it. Omega says “I predicted your behavior in Newcomb’s problem and guessed that you’d take only one box, so I’ve expedited the process and given you the money straight away, no decision needed. There’s $1000 in that box on the floor, you can throw it away in the dumpster out back. I have 346 other thought experiments to get to today, so I really need to get going.”
I think you have to consider what winning means more carefully.
A rational agent doesn’t buy a lottery ticket because it’s a bad bet. If that ticket ends up winning, does that contradict the principle that “rational agents win”?
An Irene who acts like your model of Irene will win slightly more when omega makes an incorrect prediction (she wins the lottery), but will be given the million dollars far less commonly because Omega is almost always correct. On average she loses. And rational agents win on average.
By average I don’t mean average within a particular world (repeated iteration), but on average across all possible worlds.
Updateless Decision Theory helps you model this kind of thing.
I think you have to consider what winning means more carefully.
A rational agent doesn’t buy a lottery ticket because it’s a bad bet. If that ticket ends up winning, does that contradict the principle that “rational agents win”?
That doesn’t seem at all analogous. At the time they had the opportunity to purchase the ticket, they had no way to know it was going to win.
An Irene who acts like your model of Irene will win slightly more when omega makes an incorrect prediction (she wins the lottery), but will be given the million dollars far less commonly because Omega is almost always correct. On average she loses. And rational agents win on average.
By average I don’t mean average within a particular world (repeated iteration), but on average across all possible worlds.
I agree with all of this. I’m not sure why you’re bringing it up?
I don’t see how winning can be defined without making some precise assumptions about the mechanics...How Omega’s predictive abilities work, whether you have free will anyway, and so on. Consider trying to determine what the winning strategy is by writing a programme
Why would you expect one decision theory to work in any possible universe?
Eliezer’s alteration of the conditions very much strengthens the prisoner’s dilemma. Your alterations very much weaken the original problem in both reducing the strength of evidence for Omega’s hidden prediction, and in allowing a second decision after (apparently) receiving a prize.
Whether Omega ended up being right or wrong is irrelevant to the problem, since the players only find out if it was right or wrong after all decisions have been made. It has no bearing on what decision is correct at the time; only our prior probability of whether Omega will be right or wrong matters.
the players only find out if [Omega] was right or wrong after all decisions have been made
If you observe Omega being wrong, that’s not the same thing as Omega being wrong in reality, because you might be making observations in a counterfactual. Omega is only stipulated to be a good predictor in reality, not in the counterfactuals generated by Omega’s alternative decisions about what to predict. (It might be the right decision principle to expect Omega being correct in the counterfactuals generated by your decisions, even though it’s not required by the problem statement either.)
It is extremely relevant to the original problem. The whole point is that Omega is known to always be correct. This version weakens that premise, and the whole point of the thought experiment.
In particular, note that the second decision was based on a near-certainty that Omega was wrong. There is some ordinarily strong evidence in favour of it, since the agent is apparently in possession of a million dollars with nothing to prevent getting the thousand as well. Is that evidence strong enough to cancel out the previous evidence that Omega is always right? Who knows? There is no quantitative basis given on either side.
And that’s why this thought experiment is so much weaker and less interesting than the original.
This variant is known as Transparent Newcomb’s Problem (cousin_it alluded to this in his comment). It illustrates different things, such as the need to reason so that the counterfactuals show the outcomes you want them to show because of your counterfactual behavior (or as I like to look at this, taking the possibility of being in a counterfactual seriously), and also the need to notice that Omega can be wrong in certain counterfactuals despite the stipulation of Omega always being right holding strong, with there being a question of which counterfactuals it should still be right in. Perhaps it’s not useful for illustrating some things the original variant is good at illustrating, but that doesn’t make it uninteresting in its own right.
Some clarifications on my intentions writing this story.
Omega being dead and Irene having taken the money from one box before having the conversation with Rachel are both not relevant to the core problem. I included them as a literary flourish to push people’s intuitions towards thinking that Irene should open the second box, similar to what Eliezer was doing here.
Omega was wrong in this scenario, which departs from the traditional Newcomb’s problem. I could have written an ending where Rachel made the same arguments and Irene still decided against doing it, but that seemed less fun. It’s not relevant whether Omega was right or wrong, because after Irene has made her decision, she always has the “choice” to take the extra money and prove Omega wrong. My point here is that leaving the $1000 behind falls prey to the same “rational agents should win” problem that’s usually used to justify one-boxing. After taking the $1,000,000 you can either have some elaborate justification for why it would be irrational to open the second box, or you could just… do it.
Here’s another version of the story that might demonstrate this more succinctly:
I think you have to consider what winning means more carefully.
A rational agent doesn’t buy a lottery ticket because it’s a bad bet. If that ticket ends up winning, does that contradict the principle that “rational agents win”?
An Irene who acts like your model of Irene will win slightly more when omega makes an incorrect prediction (she wins the lottery), but will be given the million dollars far less commonly because Omega is almost always correct. On average she loses. And rational agents win on average.
By average I don’t mean average within a particular world (repeated iteration), but on average across all possible worlds.
Updateless Decision Theory helps you model this kind of thing.
That doesn’t seem at all analogous. At the time they had the opportunity to purchase the ticket, they had no way to know it was going to win.
I agree with all of this. I’m not sure why you’re bringing it up?
I’m showing why a rational agent would not take the 1000 dollars, and that doesn’t contradict “rational agents win”
I don’t see how winning can be defined without making some precise assumptions about the mechanics...How Omega’s predictive abilities work, whether you have free will anyway, and so on. Consider trying to determine what the winning strategy is by writing a programme
Why would you expect one decision theory to work in any possible universe?
Eliezer’s alteration of the conditions very much strengthens the prisoner’s dilemma. Your alterations very much weaken the original problem in both reducing the strength of evidence for Omega’s hidden prediction, and in allowing a second decision after (apparently) receiving a prize.
Whether Omega ended up being right or wrong is irrelevant to the problem, since the players only find out if it was right or wrong after all decisions have been made. It has no bearing on what decision is correct at the time; only our prior probability of whether Omega will be right or wrong matters.
If you observe Omega being wrong, that’s not the same thing as Omega being wrong in reality, because you might be making observations in a counterfactual. Omega is only stipulated to be a good predictor in reality, not in the counterfactuals generated by Omega’s alternative decisions about what to predict. (It might be the right decision principle to expect Omega being correct in the counterfactuals generated by your decisions, even though it’s not required by the problem statement either.)
It is extremely relevant to the original problem. The whole point is that Omega is known to always be correct. This version weakens that premise, and the whole point of the thought experiment.
In particular, note that the second decision was based on a near-certainty that Omega was wrong. There is some ordinarily strong evidence in favour of it, since the agent is apparently in possession of a million dollars with nothing to prevent getting the thousand as well. Is that evidence strong enough to cancel out the previous evidence that Omega is always right? Who knows? There is no quantitative basis given on either side.
And that’s why this thought experiment is so much weaker and less interesting than the original.
This variant is known as Transparent Newcomb’s Problem (cousin_it alluded to this in his comment). It illustrates different things, such as the need to reason so that the counterfactuals show the outcomes you want them to show because of your counterfactual behavior (or as I like to look at this, taking the possibility of being in a counterfactual seriously), and also the need to notice that Omega can be wrong in certain counterfactuals despite the stipulation of Omega always being right holding strong, with there being a question of which counterfactuals it should still be right in. Perhaps it’s not useful for illustrating some things the original variant is good at illustrating, but that doesn’t make it uninteresting in its own right.