That is a possible and likely model, but it seems to me that we should not stop the analysis here.
Let’s assume that rationality works mostly by preventing failures. As a simple mathematical model, we have a biased coin that generates values “success” and “failure”. For a typical smart but not rational person, the coin generates 90% “success” and 10% “failure”. For an x-rationalist, the coin generates 99% “success” and 1% “failure”. If your experiment consists of doing one coin flip and calculating the winners, most winners will not be x-rationalists, simply because of the base rates.
But are these coin flips always taken in isolation, or is it possible to create more complex games? For example, if the goal is to flip the coin 10 times and have 10 “successes”, then the players have total chances of 35% vs 90%. That seems like a greater difference, although the base rates would still dwarf this.
My point is, if your magical power is merely preventing some unlikely failures, you should have a visible advantage in situations which are complex in a way that makes hundreds of such failures possible. A person without the magical power would be pretty likely to fail at some point, even if each individual failure would be unlikely.
I just don’t know what (if anything) in the real world corresponds to this. Maybe the problem is that preventing hundreds of different unlikely failures would simply take too much time for a single person.
Also, rationality might mostly work by making disaster less common—it’s not so much that the victories are bigger as that fewer of them are lost.
That is a possible and likely model, but it seems to me that we should not stop the analysis here.
Let’s assume that rationality works mostly by preventing failures. As a simple mathematical model, we have a biased coin that generates values “success” and “failure”. For a typical smart but not rational person, the coin generates 90% “success” and 10% “failure”. For an x-rationalist, the coin generates 99% “success” and 1% “failure”. If your experiment consists of doing one coin flip and calculating the winners, most winners will not be x-rationalists, simply because of the base rates.
But are these coin flips always taken in isolation, or is it possible to create more complex games? For example, if the goal is to flip the coin 10 times and have 10 “successes”, then the players have total chances of 35% vs 90%. That seems like a greater difference, although the base rates would still dwarf this.
My point is, if your magical power is merely preventing some unlikely failures, you should have a visible advantage in situations which are complex in a way that makes hundreds of such failures possible. A person without the magical power would be pretty likely to fail at some point, even if each individual failure would be unlikely.
I just don’t know what (if anything) in the real world corresponds to this. Maybe the problem is that preventing hundreds of different unlikely failures would simply take too much time for a single person.
I suspect rationality does a lot to prevent likely failures as well as unlikely failures.