I don’t think they’re weird. I think Omegas that go out of their way to discriminate against mixed strategies are weird. A strategy that one-boxes with probability 0.999 never gets a million, while one that one-boxes with probability 1 always gets a million. You could call that a discontinuity.
And I thought 1 was not a probability anyway! Any real rational one-boxing agent will expect to one-box with probability ~1, not with “probability” 1. Does that mean that the agent is using a mixed strategy? On the other hand, any agent that isn’t using quantum randomness will in fact either one-box or two-box, even if it flips coins and stuff. Does that mean the agent is using a pure strategy? I can’t answer this off the top of my head.
I assume the following is the key thing about Eliezer’s original Omega:
Omega has been correct on each of 100 observed occasions so far—everyone who took both boxes has found box B empty and received only a thousand dollars; everyone who took only box B has found B containing a million dollars
I didn’t see Eleizer saying that Omega doesn’t tolerate mixed strategies. If there were coinflippers among that 100, presumably Omega predicted the results of their coinflips and set up box B accordingly. To the extent that I can’t duplicate the conditions perfectly to make sure any coin will land the same way both times, I can’t do that. To the extent that I can, I can.
I don’t think they’re weird. I think Omegas that go out of their way to discriminate against mixed strategies are weird. A strategy that one-boxes with probability 0.999 never gets a million, while one that one-boxes with probability 1 always gets a million. You could call that a discontinuity.
And I thought 1 was not a probability anyway! Any real rational one-boxing agent will expect to one-box with probability ~1, not with “probability” 1. Does that mean that the agent is using a mixed strategy? On the other hand, any agent that isn’t using quantum randomness will in fact either one-box or two-box, even if it flips coins and stuff. Does that mean the agent is using a pure strategy? I can’t answer this off the top of my head.
I assume the following is the key thing about Eliezer’s original Omega:
I didn’t see Eleizer saying that Omega doesn’t tolerate mixed strategies. If there were coinflippers among that 100, presumably Omega predicted the results of their coinflips and set up box B accordingly. To the extent that I can’t duplicate the conditions perfectly to make sure any coin will land the same way both times, I can’t do that. To the extent that I can, I can.
Uh, then my transformation of the problem is better than yours because it “predicts” coinflips perfectly, not just “to the extent that I can” :-)