From Andy Egan.

The Psychopath Button: Paul is debating whether to press the ‘kill all psychopaths’ button. It would, he thinks, be much better to live in a world with no psychopaths. Unfortunately, Paul is quite confident that only a psychopath would press such a button. Paul very strongly prefers living in a world with psychopaths to dying. Should Paul press the button? (Set aside your theoretical commitments and put yourself in Paul’s situation. Would you press the button? Would you take yourself to be irrational for not doing so?)

Newcomb’s Firebomb: There are two boxes before you. Box A definitely contains $1,000,000. Box B definitely contains $1,000. You have two choices: take only box A (call this one-boxing), or take both boxes (call this two-boxing). You will signal your choice by pressing one of two buttons. There is, as usual, an uncannily reliable predictor on the scene. If the predictor has predicted that you will two-box, he has planted an incendiary bomb in box A, wired to the two-box button, so that pressing the two-box button will cause the bomb to detonate, burning up the $1,000,000. If the predictor has predicted that you will one-box, no bomb has been planted – nothing untoward will happen, whichever button you press. The predictor, again, is uncannily accurate.

I would suggest looking at your implicit choice of counterfactuals and their role in your decision theory. Standard causal decision theory involves local violations of the laws of physics (you assign probabilities to the world being such that you'll one-box, or such that you'll one-box, and then ask what miracle magically altering your decision, without any connection to your psychological dispositions, etc, would deliver the highest utility). Standard causal decision theory is a normative principle for action, that says to do the action that would deliver the most utility if a certain kind of miracle happened. But you can get different versions of causal decision theory by substituting different sorts of miracles, e.g. you can say: "if I one-box, then I have a psychology that one-boxes, and likewise for two-boxing" so you select the action such that a miracle giving you the disposition to do so earlier on would have been better. Yet another sort of counterfactual that can be hooked up to the causal decision theory framework would go "there's some mathematical fact about what decision(decisions given Everett) my brain structure leads to in standard physics, and the predictor has access to this mathematical info, so I'll select the action that would be best brought about by a miracle changing that mathematical fact".