Thanks for posting. Your analysis is an improvement over the LW conventional wisdom, but you still doesn't get it right, where right, to me, means the way it is analyzed by the guys who won all those Nobel prizes in economics. You write:
First, let's note that there definitely are possible cases where it would be "beneficial to be irrational".
But in every example you supply, what you really want is not exactly to be irrational; rather it is to be believed irrational by the other player in the game. But you don't notice this because in each of your artificial examples, the other player is effectively omniscient, so the only way to be believed irrational is to actually be irrational. But then, once the other player really believes, his strategies and actions are modified in such a way the your expected behavior (which would have been irrational if the other player had not come to believe you irrational) is now no longer irrational!
But, better yet, lets Taboo the word irrational. What you really want him to believe is that you will play some particular strategy. If he does, in fact, believe, then he will choose a particular strategy, and your own best response is to use the strategy he believes you are going to use. To use the technical jargon, you two are in a Nash equilibrium.
So, the standard Game Theory account is based on the beliefs each player has about the other player's preferences and strategies. And, because it deals with (Bayesian) belief, it is an incredibly flexible explanatory framework. Pick up a standard textbook or reference and marvel at the variety of applications that are covered rigorously, quantitatively, and convincingly.
I suspect that the LW interest in scenarios involving omniscient agents arises from considerations of one AI program being able to read another program's source code. However, I don't understand why there is an assumption of determinism. For example, in a Newcomb-type problem, suppose I decide to resolve the question of one box or two by flipping a coin? Unless I am supposed to believe that Omega can foretell the results of future coin flips, I think the scenario collapses. Has anyone written anything on LW about responding to Omega by randomizing? [Edited several times for minor cleanups]
But in every example you supply, what you really want is not exactly to be irrational; rather it is to be believed irrational by the other player in the game.
I don't think that's the real problem: after all, Parfit's Hitchhiker and Newcomb's problem also eliminate this distinction by positing an Omega that will not be wrong in its predictions.
The real problem is that Chappell has delineated a failure mode that we don't care about. TDT/UDT are optimized for situations in which the world only cares about what you would do, not why you decide to do so. ...
A common background assumption on LW seems to be that it's rational to act in accordance with the dispositions one would wish to have. (Rationalists must WIN, and all that.)
E.g., Eliezer:
And more recently, from AdamBell:
Within academic philosophy, this is the position advocated by David Gauthier. Derek Parfit has constructed some compelling counterarguments against Gauthier, so I thought I'd share them here to see what the rest of you think.
First, let's note that there definitely are possible cases where it would be "beneficial to be irrational". For example, suppose an evil demon ('Omega') will scan your brain, assess your rational capacities, and torture you iff you surpass some minimal baseline of rationality. In that case, it would very much be in your interests to fall below the baseline! Or suppose you're rewarded every time you honestly believe the conclusion of some fallacious reasoning. We can easily multiply cases here. What's important for now is just to acknowledge this phenomenon of 'beneficial irrationality' as a genuine possibility.
This possibility poses a problem for the Eliezer-Gauthier methodology. (Quoting Eliezer again:)
The problem, obviously, is that it's possible for irrational agents to receive externally-generated rewards for their dispositions, without this necessarily making their downstream actions any more 'reasonable'. (At this point, you should notice the conflation of 'disposition' and 'choice' in the first quote from Eliezer. Rachel does not envy Irene her choice at all. What she wishes is to have the one-boxer's dispositions, so that the predictor puts a million in the first box, and then to confound all expectations by unpredictably choosing both boxes and reaping the most riches possible.)
To illustrate, consider (a variation on) Parfit's story of the threat-fulfiller and threat-ignorer. Tom has a transparent disposition to fulfill his threats, no matter the cost to himself. So he straps on a bomb, walks up to his neighbour Joe, and threatens to blow them both up unless Joe shines his shoes. Seeing that Tom means business, Joe sensibly gets to work. Not wanting to repeat the experience, Joe later goes and pops a pill to acquire a transparent disposition to ignore threats, no matter the cost to himself. The next day, Tom sees that Joe is now a threat-ignorer, and so leaves him alone.
So far, so good. It seems this threat-ignoring disposition was a great one for Joe to acquire. Until one day... Tom slips up. Due to an unexpected mental glitch, he threatens Joe again. Joe follows his disposition and ignores the threat. BOOM.
Here Joe's final decision seems as disastrously foolish as Tom's slip up. It was good to have the disposition to ignore threats, but that doesn't necessarily make it good idea to act on it. We need to distinguish the desirability of a disposition to X from the rationality of choosing to do X.