utility of one-boxing is computed to be $1,000,000 times p,
utility of two boxing is calculated to be $1,001,000p+$1,000 times (1-p).
If she is confident that she will apply CDT based on past experience, or introspection, she will have previously updated to thinking that p is very low.
Right, I forgot. The reasoning is “I’m a two-boxer because I follow a loser’s logic and Omega knows it, so I may as well two-box.” There is no anticipation of winning $1,001,000. No, that does not sound quite right...
The last bit about p going low with introspection isn’t necessary. The conclusion (two-boxing preferred, or at best indifference between one-boxing and two-boxing if one is certain one will two-box) follows under CDT with the usual counterfactuals for any value of p.
The reasoning is “well, if the world is such that I am going to two-box, then I should two-box, and if the world is such that I am going to one-box, then I should two-box” Optional extension: “hmm, sounds like I’ll be two-boxing then, alas! No million dollars for me...” (Unless I wind up changing my mind or the like, which keeps p above 0).
Right, I forgot. The reasoning is “I’m a two-boxer because I follow a loser’s logic and Omega knows it, so I may as well two-box.” There is no anticipation of winning $1,001,000. No, that does not sound quite right...
The last bit about p going low with introspection isn’t necessary. The conclusion (two-boxing preferred, or at best indifference between one-boxing and two-boxing if one is certain one will two-box) follows under CDT with the usual counterfactuals for any value of p.
The reasoning is “well, if the world is such that I am going to two-box, then I should two-box, and if the world is such that I am going to one-box, then I should two-box” Optional extension: “hmm, sounds like I’ll be two-boxing then, alas! No million dollars for me...” (Unless I wind up changing my mind or the like, which keeps p above 0).