Wednesday, April 19, 2023

Avoiding regrets

I’ve recently been troubled by cases where you are sure to regret your decision, but the decision still seems reasonable. Some of these cases involve reasonable-seeming violations of expected utility maximization, but there is also the Cable Guy paradox, though admittedly I think I can probably exclude the Cable Guy paradox with causal finitism.

I shared Cable Guy with Clare Pruss, and she said that the principle of avoiding future regrets is false, and should be modified to a principle of avoiding final future regrets, because there are ordinary cases where you expect to regret something temporarily. For instance, you volunteer to do something onerous, and you expect that while volunteering, you will be regreting your choice, but you will be glad afterwards.

In all the cases that I’ve been interested in, while you are sure that there will be regret at some point in the future, you are not sure that there will be regret at the end (half the time the Cable Guy comes at the time you bet on him coming, after all).


IanS said...

In the last example in your post ‘Problems with Neglecting Small Probabilities’, the regret can be turned into a Dutch book. (If the die lands 1 or 2, the bookie offers to cancel the original bet for a suitably small extra payment.) For Cable Guy, and for your Brownian motion example, it can’t.

As far as I can see (by a quick look at Google Scholar), all commenters reject or modify Hájek’s regret principle, as does Hájek himself. They are surely right to do so – it has to be wrong, the question is precisely how and why.

It’s not so easy to dismiss the Dutch book. That’s a bullet you have to bite if you want to reject standard EU maximization. Of course, there are standard responses to Dutch book arguments. But some response must be made. Buchak’s response to criticisms of her Risk-weighted Expected Utility gives an idea of how this might go (section 5 in the ungated draft I looked at):

Alexander R Pruss said...


Unconditional Dutch Books, where one is offered a predetermined sequence of wagers, are not hard to get out of. Buchak's approach (note that neglecting small probabilities, if done right, is a special case of REU) is to make the decisions be global. Then there is no unconditional DB.

Conditional DBs are trickier. I think the solution (I don't know if Buchak does this) has to be some form of binding, where you choose the best strategy (where a strategy specifies what you will do in each epistemically possible future state) by your lights, and then stick to that strategy come what may. If you choose the best strategy by means of a strictly monotonic prevision, you are guaranteed not to be dominated by another strategy, and hence there will be no DBs against you.

Unfortunately, in the case of neglecting small probabilities, one can set things up so that sticking to the strategy can look extremely dangerous.