Late to the party but want to say this post is quite on point with the analysis. Just want to add my—as a supporter of CDT—reading to the problem, which has a different focus.
I agree the assumption that every person would make the same decision as I do is deeply problematic. It may seem intuitive if the others are “copies of me”, which is perhaps why this problem is first brought up in an anthropic context. CDT inherently treats the decision maker as an agent apart from his surrounding world, outside of the casual analysis scope. Assuming “other copies of me” giving the same decision as I do put the entire analysis into a self-referential paradox.
In contrast the analysis of this post is the way to go. I shall just regard the others as part of the environment, their “decision” are nothing special but parameters I shall considered as input to the only decision-making in question—my decision making. It cuts off the feed back loop.
While CDT treating the decision maker as separate-from-the-world agent outside the analysis scope is often regarded as it’s Achille’s heel, I think that is precisely why it is correct. For decision is inherently a first-person concept, where the free-will resides. If we cannot imagine reasoning from a certain thing’s perspective, then whatever that thing outputs are mere mechanical products. The concept of decision never applies.
I diverge from this post in the sense that instead of ascribing this reflective inconsistency paradox to the above mentioned assumption, I think its cause is something deeper. In particular, for the F(p) graph, it shows that IF all others sticks to the plan of p=0.9355 then there is no difference for me to take or reject the bet (so there is no incentive to deviate from the pregame plan.) However, how solid is it to assume that they will stick to the plan? It cannot be said that’s the only rational scenario. And according to the graph if I think they deviated from the plan then there so must I. Notice in this analysis there is no forcing others’ decisions so they must be same as mine, and our strategies could well be different. So the notion that the reflective inconsistency resolves itself by rejecting the assumption of everyone makes the same decision only works in the limited case if we take an alternative assumption that the others all stick to the pregame plan (or all others reject the bet.) Even in that limited case, my pregame strategy was to take the bet with p=0.9355 while the in game strategy was anything goes (as they do not make a difference to the reward). Sure there is no incentive to deviate from the pregame plan but I am hesitant to call it a perfect resolution of the problem.
Late to the party but want to say this post is quite on point with the analysis. Just want to add my—as a supporter of CDT—reading to the problem, which has a different focus.
I agree the assumption that every person would make the same decision as I do is deeply problematic. It may seem intuitive if the others are “copies of me”, which is perhaps why this problem is first brought up in an anthropic context. CDT inherently treats the decision maker as an agent apart from his surrounding world, outside of the casual analysis scope. Assuming “other copies of me” giving the same decision as I do put the entire analysis into a self-referential paradox.
In contrast the analysis of this post is the way to go. I shall just regard the others as part of the environment, their “decision” are nothing special but parameters I shall considered as input to the only decision-making in question—my decision making. It cuts off the feed back loop.
While CDT treating the decision maker as separate-from-the-world agent outside the analysis scope is often regarded as it’s Achille’s heel, I think that is precisely why it is correct. For decision is inherently a first-person concept, where the free-will resides. If we cannot imagine reasoning from a certain thing’s perspective, then whatever that thing outputs are mere mechanical products. The concept of decision never applies.
I diverge from this post in the sense that instead of ascribing this reflective inconsistency paradox to the above mentioned assumption, I think its cause is something deeper. In particular, for the F(p) graph, it shows that IF all others sticks to the plan of p=0.9355 then there is no difference for me to take or reject the bet (so there is no incentive to deviate from the pregame plan.) However, how solid is it to assume that they will stick to the plan? It cannot be said that’s the only rational scenario. And according to the graph if I think they deviated from the plan then there so must I. Notice in this analysis there is no forcing others’ decisions so they must be same as mine, and our strategies could well be different. So the notion that the reflective inconsistency resolves itself by rejecting the assumption of everyone makes the same decision only works in the limited case if we take an alternative assumption that the others all stick to the pregame plan (or all others reject the bet.) Even in that limited case, my pregame strategy was to take the bet with p=0.9355 while the in game strategy was anything goes (as they do not make a difference to the reward). Sure there is no incentive to deviate from the pregame plan but I am hesitant to call it a perfect resolution of the problem.