Let me explain more clearly why this is a circular argument:
a) You want to show that we should take counterfactuals into account when making decisions
b) You argue that this way of making decisions does better on average
c) The average includes the very counterfactuals whose value is in question. So b depends on a already being proven ⇒ circular argument
That isn’t my argument though. My argument is that we ARE thinking ahead about counterfactual mugging right now, in considering the question. We are not misunderstanding something about the situation, or missing critical information. And from our perspective right now, we can see that agreeing to be mugged is the best strategy on average.
We can see that if we update on the value of the coin flip being tails, we would change our mind about this. But the statement of the problem requires that there is also the possibility of heads. So it does not make sense to consider the tails scenario in isolation; that would be a different decision problem (one in which Omega asks us for $100 out of the blue with no other significant backstory).
So we (right now, considering how to reason about counterfactual muggings in the abstract) know that there are the two possibilities, with equal probability, and so the best strategy on average is to pay. So we see behaving updatefully as bad.
So my argument for considering the multiple possibilities is, the role of thinking about decision theory now is to help guide the actions of my future self.
You feel that I’m begging the question. I guess I take only thinking about this counterfactual as the default position, as where an average person is likely to be starting from. And I was trying to see if I could find an argument strong enough to displace this. So I’ll freely admit I haven’t provided a first-principles argument for focusing just on this counterfactual.
I think the average person is going to be thinking about things like duty, honor, and consistency which can serve some of the purpose of updatelessness. But sure, updateful reasoning is a natural kind of starting point, particularly coming from a background of modern economics or bayesian decision theory.
But my argument is compatible with that starting point, if you accept my “the role of thinking about decision theory now is to help guide future actions” line of thinking. In that case, starting from updateful assumptions now, decision-theoretic reasoning makes you think you should behave updatelessly in the future.
Whereas the assumption you seem to be using, in your objection to my line of reasoning, is “we should think of decision-theoretic problems however we think of problems now”. So if we start out an updateful agent, we would think about decision-theoretic problems and think “I should be updateful”. If we start out a CDT agent, then when we think about decision-theoretic problems we would conclude that you should reason causally. EDT agents would think about problems and conclude you should reason evidentially. And so on. That’s the reasoning I’m calling circular.
Of course an agent should reason about a problem using its best current understanding. But my claim is that when doing decision theory, the way that best understanding should be applied is to figure out what decision theory does best, not to figure out what my current decision theory already does. And when we think about problems like counterfactual mugging, the description of the problem requires that there’s both the possibility of heads and tails. So “best” means best overall, not just down the one branch.
If the act of doing decision theory were generally serving the purpose of aiding in making the current decision, then my argument would not make sense, and yours would. Current-me might want to tell the me in that universe to be more updateless about things, but alternate-me would not be interested in hearing it, because alternate-me wouldn’t be interested in thinking ahead in general, and the argument wouldn’t make any sense with respect to alternate-me’s current decision.
So my argument involves a fact about the world which I claim determines which of several ways to reason, and hence, is not circular.
My argument is that we ARE thinking ahead about counterfactual mugging right now, in considering the question
When we think about counterfactual muggings, we naturally imagine the possibility of facing a counterfactual mugging in the future. I don’t dispute the value of pre-committing either to take a specific action or to acting updatelessly. However, instead of imagining a future mugging, we could also imagine a present mugging where we didn’t have time to make any pre-commitments. I don’t think it is immediately obvious that we should think updatelessly, instead I believe that it requires further justification.
The role of thinking about decision theory now is to help guide the actions of my future self
This is effectively an attempt at proof-by-definition
I think the average person is going to be thinking about things like duty, honor, and consistency which can serve some of the purpose of updatelessness. But sure, updateful reasoning is a natural kind of starting point, particularly coming from a background of modern economics or bayesian decision theory
If someone’s default is already updateless reasoning, then there’s no need for us to talk them into it. It’s only people with an updateful default that we need to convince (until recently I had an updateful default).
And when we think about problems like counterfactual mugging, the description of the problem requires that there’s both the possibility of heads and tails
It requires a counterfactual possibility, not an actual possibility. And a counterfactual possibility isn’t actual, it’s counter to the factual. So it’s not clear this has any relevance.
It looks like to me that you’re tripping yourself up with verbal arguments that aren’t at all obviously true. The reason why I believe that the Counterfactual Prisoner’s Dilemma is important is because it is a mathematical result that doesn’t require much in the way of assumptions. Sure, it still has to be interpreted, but it seems hard to find an interpretations that avoids the conclusion that the updateful perspective doesn’t quite succeed on its own terms.
That isn’t my argument though. My argument is that we ARE thinking ahead about counterfactual mugging right now, in considering the question. We are not misunderstanding something about the situation, or missing critical information. And from our perspective right now, we can see that agreeing to be mugged is the best strategy on average.
We can see that if we update on the value of the coin flip being tails, we would change our mind about this. But the statement of the problem requires that there is also the possibility of heads. So it does not make sense to consider the tails scenario in isolation; that would be a different decision problem (one in which Omega asks us for $100 out of the blue with no other significant backstory).
So we (right now, considering how to reason about counterfactual muggings in the abstract) know that there are the two possibilities, with equal probability, and so the best strategy on average is to pay. So we see behaving updatefully as bad.
So my argument for considering the multiple possibilities is, the role of thinking about decision theory now is to help guide the actions of my future self.
I think the average person is going to be thinking about things like duty, honor, and consistency which can serve some of the purpose of updatelessness. But sure, updateful reasoning is a natural kind of starting point, particularly coming from a background of modern economics or bayesian decision theory.
But my argument is compatible with that starting point, if you accept my “the role of thinking about decision theory now is to help guide future actions” line of thinking. In that case, starting from updateful assumptions now, decision-theoretic reasoning makes you think you should behave updatelessly in the future.
Whereas the assumption you seem to be using, in your objection to my line of reasoning, is “we should think of decision-theoretic problems however we think of problems now”. So if we start out an updateful agent, we would think about decision-theoretic problems and think “I should be updateful”. If we start out a CDT agent, then when we think about decision-theoretic problems we would conclude that you should reason causally. EDT agents would think about problems and conclude you should reason evidentially. And so on. That’s the reasoning I’m calling circular.
Of course an agent should reason about a problem using its best current understanding. But my claim is that when doing decision theory, the way that best understanding should be applied is to figure out what decision theory does best, not to figure out what my current decision theory already does. And when we think about problems like counterfactual mugging, the description of the problem requires that there’s both the possibility of heads and tails. So “best” means best overall, not just down the one branch.
If the act of doing decision theory were generally serving the purpose of aiding in making the current decision, then my argument would not make sense, and yours would. Current-me might want to tell the me in that universe to be more updateless about things, but alternate-me would not be interested in hearing it, because alternate-me wouldn’t be interested in thinking ahead in general, and the argument wouldn’t make any sense with respect to alternate-me’s current decision.
So my argument involves a fact about the world which I claim determines which of several ways to reason, and hence, is not circular.
When we think about counterfactual muggings, we naturally imagine the possibility of facing a counterfactual mugging in the future. I don’t dispute the value of pre-committing either to take a specific action or to acting updatelessly. However, instead of imagining a future mugging, we could also imagine a present mugging where we didn’t have time to make any pre-commitments. I don’t think it is immediately obvious that we should think updatelessly, instead I believe that it requires further justification.
This is effectively an attempt at proof-by-definition
If someone’s default is already updateless reasoning, then there’s no need for us to talk them into it. It’s only people with an updateful default that we need to convince (until recently I had an updateful default).
It requires a counterfactual possibility, not an actual possibility. And a counterfactual possibility isn’t actual, it’s counter to the factual. So it’s not clear this has any relevance.
It looks like to me that you’re tripping yourself up with verbal arguments that aren’t at all obviously true. The reason why I believe that the Counterfactual Prisoner’s Dilemma is important is because it is a mathematical result that doesn’t require much in the way of assumptions. Sure, it still has to be interpreted, but it seems hard to find an interpretations that avoids the conclusion that the updateful perspective doesn’t quite succeed on its own terms.