An immediate regret principle

Here’s a plausible immediate regret principle:

1. It is irrational to make a decision such that learning that you’ve made this decision immediately makes it rational to regret that you didn’t make a different decision.

The regret principle gives an argument for two-boxing in Newcomb’s Paradox, since if you go for one box, as soon as you have made your decision to do that, you will regret you didn’t make the two-box decision—there is that clear box with money staring at you, but if you go for two boxes, you will have no regrets.

Interestingly, though, one can come up with predictor stories where one has regrets no matter what one chooses. Suppose there are two opaque boxes, A and B, and you can take either box but not both. A predictor put a thousand dollars in the box that they predicted you won’t take. Their prediction need not be very good—all we need for the story is that there is a better than even probability of their having predicted you choosing A conditionally on your choosing A and a better than even probability of their having predicted you choosing B conditionally on your choosing B. But now as soon as you’ve made your decision, and before you opened the chosen box, you will think the other box is more likely to have the money, and so your knowledge of your decision will make it rational to regret that decision. Note that while the original Newcomb problem is science-fictional, there is nothing particularly science-fictional about my story. It would not be surprising, for instance, if someone were able to guess with better than even chance of correctness about what their friends would choose.

Is this a counterexample to the immediate regret principle (1), or is this an argument that there are real rational dilemmas, cases where all options are irrational?

I am not sure, but I am inclined to think that it’s a counterexample to the regret principle.

Can we modify the immediate regret principle to save it? Maybe. How about this?

2. No decision is such that learning that you’ve rationally made this decision immediately makes it rationally required to regret that you didn’t make a different decision.

On this regret principle, regret is compatible with non-irrational decision making but not with (known) rational decision making.

In my box story, it is neither rational nor irrational to choose A, and it is neither rational nor irrational to choose B. Then there is no contradiction to (2), since (2) only applies to decisions that are rationally made. And applying (2) to Newcomb’s Paradox no longer yields an argument for two-boxing, but only an argument that it is not rational to one-box. (For if it were rational to one-box, one could rationally decide to one-box, and one would then regret that.)

The “rationally” in (2) can be understood in a weaker way or a stronger way (the stronger way reads it as “out of rational requirement”). On either reading, (2) has some plausibility.