In his paper 'Why Ain'cha Rich?', David Lewis considers a flipped Newcomb's problem in which the predictor tries to reward irrationality according to evidential decision theory (which one-boxers adopt). He's arguing against the one-boxing argument of 'if I'm wrong, why am I the one with the money?', and defending the view that the predictor rewards irrationality. He shows that this flipped scenario is impossible. But surely this would support the one-boxer's view that rationality does always coincide with getting more money. I'm not sure how it supports his view.
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Lewis's PW realism counterfactuals are grounded only in worlds constrained by causal structure as our action cannot change the predictor. While counterpossible semantics where even logically impossible alternatives are considered includes pure logical dependence such as contemplating different deterministic decision functions to reach an updateless fixed point from clustered nearby worlds avoiding the causal conditional acting trap. There's a deep shift from “What happens if I act differently?” to “What happens if the computation I implement outputs differently across all its instances?”...Double Knot– Double Knot2026-04-05 00:01:42 +00:00Commented Apr 5 at 0:01
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The context here is that Newcomb's problem can be thought of as having two different solutions depending on whether one follows evidential decision theory (what Lewis calls V-rationality) or whether one follows causal decision theory (what Lewis calls U-rationality). The evidential approach leads to the one-box solution; the causal approach leads to the two-box solution. Lewis holds that the causal approach is correct and so two-boxing is the rational thing to do.
However, the two-boxer faces a challenge from the one-boxer. Assuming we accept the preconditions of the problem, one-boxers will (mostly) find the closed box to contain the big prize money, while the two-boxers will (mostly) find it empty. So the challenge from the one-boxers is: if your two-box solution is correct, why is it that we are rich and you are not?
Lewis' response is that the game is rigged. In effect, the controller of the game has predetermined that they will reward irrational behaviour. Specifically, they will reward U-irrational behaviour, which Lewis holds is the correct kind. If you play a game in which the controller rewards irrational decision-making then there is no rational way to win: you just have to accept that irrational behaviour will be rewarded.
But the challenge remains that since V-rational behaviour wins the big money, is that not itself a sufficient condition for saying that V-rational decision-making is correct after all? Lewis concedes that there is no convincing answer to this. The V-theorist may consistently claim that they are acting rationally by their own lights.
So Lewis is not so much arguing against his two-box solution, but rather accepting that he has no way to prove that the one-box solution is irrational. It is rational on the basis of a rival theory of rationality.
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2Indeed. The core sentence in Lewis' paper is: "So it's a standoff. We may consistently go on thinking that it proves nothing that the one-boxers are richly pre-rewarded and we are not. But they may consistently go on thinking otherwise." (But who wants to be consistent if you can be rich -- without moral qualms?)mudskipper– mudskipper2026-04-04 15:29:22 +00:00Commented Apr 4 at 15:29
