Great post and I agree that conditional probabilities are underrated. In particular I agree that many unconditional predictions should really be interpreted as “default trajectory” predictions, and in some sense “default” predictions are more natural to make for the reasons you give.
However, a very unimportant nitpick: I don't agree that these cases are really paradoxical; that is I think it *is* typically possible to stably predict continuous variables even when your prediction affects the outcome.
Imagine you are predicting some number (say “how much money startup X will raise within a year”) where your stated prediction itself influences the predicted outcome. Then you can imagine the true number as a function of your stated number. Then where (if at all) the function intersects the “true number = stated number” line, that is a fixed point; a point where your stated prediction is consistent with having stated it.
Assuming this is a continuous function over a convex range of values, then there must be at least one such fixed point. This applies under uncertainty, since the number you are guessing could be a probability. And surprisingly it also applies if you are predicting arbitrarily many numbers all at once.
So if you were predicting a discrete/categorical outcome (e.g. just guessing who is most likely to win an election), there are cases where it is impossible to predict correctly. If the function were otherwise discontinuous (e.g. your friend deliberately wants to thwart your prediction for your half marathon time) then sure, it might again be impossible to find a fixed point. But I think these pathological cases are quite unlike e.g. predicting degrees of warming or whatever.
Great post and I agree that conditional probabilities are underrated. In particular I agree that many unconditional predictions should really be interpreted as “default trajectory” predictions, and in some sense “default” predictions are more natural to make for the reasons you give.
However, a very unimportant nitpick: I don't agree that these cases are really paradoxical; that is I think it *is* typically possible to stably predict continuous variables even when your prediction affects the outcome.
Imagine you are predicting some number (say “how much money startup X will raise within a year”) where your stated prediction itself influences the predicted outcome. Then you can imagine the true number as a function of your stated number. Then where (if at all) the function intersects the “true number = stated number” line, that is a fixed point; a point where your stated prediction is consistent with having stated it.
Assuming this is a continuous function over a convex range of values, then there must be at least one such fixed point. This applies under uncertainty, since the number you are guessing could be a probability. And surprisingly it also applies if you are predicting arbitrarily many numbers all at once.
So if you were predicting a discrete/categorical outcome (e.g. just guessing who is most likely to win an election), there are cases where it is impossible to predict correctly. If the function were otherwise discontinuous (e.g. your friend deliberately wants to thwart your prediction for your half marathon time) then sure, it might again be impossible to find a fixed point. But I think these pathological cases are quite unlike e.g. predicting degrees of warming or whatever.