On the more philosophical points. My position is perhaps similar to Daniel K’s. But anyway...
Of course, I agree that problems that punish the agent for using a particular theory (or using float multiplication or feeling a little wistful or stuff like that) are “unfair”/”don’t lead to interesting theory”. (Perhaps more precisely, I don’t think our theory needs to give algorithms that perform optimally in such problems in the way I want my theory to “perform optimally” Newcomb’s problem. Maybe we should still expect our theory to say something about them, in the way that causal decision theorists feel like CDT has interesting/important/correct things to say about Newcomb’s problem, despite Newcomb’s problem being designed to (unfairly, as they allege) reward non-CDT agents.)
But I don’t think these are particularly similar to problems with predictions of the agent’s distribution over actions. The distribution over actions is behavioral, whereas performing floating point operations or whatever is not. When randomization is allowed, the subject of your choice is which distribution over actions you play. So to me, which distribution over actions you choose in a problem with randomization allowed, is just like the question of which action you take when randomization is not allowed. (Of course, if you randomize to determine which action’s expected utility to calculate first, but this doesn’t affect what you do in the end, then I’m fine with not allowing this to affect your utility, because it isn’t behavioral.)
I also don’t think this leads to uninteresting decision theory. But I don’t know how to argue for this here, other than by saying that CDT, EDT, UDT, etc. don’t really care whether they choose from/rank a set of distributions or a set of three discrete actions. I think ratificationism-type concepts are the only ones that break when allowing discontinuous dependence on the chosen distribution and I don’t find these very plausible anyway.
To be honest, I don’t understand the arguments against predicting distributions and predicting actions that you give in that post. I’ll write a comment on this to that post.
On the more philosophical points. My position is perhaps similar to Daniel K’s. But anyway...
Of course, I agree that problems that punish the agent for using a particular theory (or using float multiplication or feeling a little wistful or stuff like that) are “unfair”/”don’t lead to interesting theory”. (Perhaps more precisely, I don’t think our theory needs to give algorithms that perform optimally in such problems in the way I want my theory to “perform optimally” Newcomb’s problem. Maybe we should still expect our theory to say something about them, in the way that causal decision theorists feel like CDT has interesting/important/correct things to say about Newcomb’s problem, despite Newcomb’s problem being designed to (unfairly, as they allege) reward non-CDT agents.)
But I don’t think these are particularly similar to problems with predictions of the agent’s distribution over actions. The distribution over actions is behavioral, whereas performing floating point operations or whatever is not. When randomization is allowed, the subject of your choice is which distribution over actions you play. So to me, which distribution over actions you choose in a problem with randomization allowed, is just like the question of which action you take when randomization is not allowed. (Of course, if you randomize to determine which action’s expected utility to calculate first, but this doesn’t affect what you do in the end, then I’m fine with not allowing this to affect your utility, because it isn’t behavioral.)
I also don’t think this leads to uninteresting decision theory. But I don’t know how to argue for this here, other than by saying that CDT, EDT, UDT, etc. don’t really care whether they choose from/rank a set of distributions or a set of three discrete actions. I think ratificationism-type concepts are the only ones that break when allowing discontinuous dependence on the chosen distribution and I don’t find these very plausible anyway.
To be honest, I don’t understand the arguments against predicting distributions and predicting actions that you give in that post. I’ll write a comment on this to that post.