Newcomb's Problem Solved By Quantum Mechanics

Revisiting Newcomb’s Problem again, because I had a cold when I first wrote about it and at one point crawled into bed thinking that there was something about Quantum Mechanics that made perfect predictors impossible. It turns out there is.

On Monday our Perfect Predictor says what I’m going to do and acts accordingly (it doesn’t matter how). On Tuesday, I make my decision. With the aid of a Schrodinger box. No cats are harmed in this box, I press the button and after a while either a red or a green light shines. If it’s red, I take Box B, otherwise I take both boxes. This turns the Perfect Predictor’s prediction into a perfect prediction about the result from the Schrodinger box, and that’s the contradiction, because the behaviour of Schrodinger boxes is not predictable. There are no Perfect Predictors and in that case, you take both boxes.

One of my colleagues presented this problem as the warm-up brain teaser in our team meeting this week. The reason she liked it was because, she said, it showed that two different conclusions could be reached by what seem like equally plausible logical arguments. Some people like the idea that reason can’t draw conclusions. I was amazed at how some people bought straight into the inductive fallacy - that previous success meant future success for the Perfect Predictor - or indeed how people thought only taking Box B might even be a good idea. What was noticeable was that anyone whose job had “analyst” in the title went for taking both boxes.

Problems like these, and trolley problems, arise for the same reason that the problem of "what happens when an irresistible force meets and immovable object” arises. There is a contradiction or subtle falsehood in the premises. In the case of the force and object, the question posits a contradiction: there can’t be irresistible forces if there are immovable objects and vice versa. Trolley problems rob you of morally-relevant information about the people that you would usually have in real life. Newcomb’s Problem posits something impossible according to our best theories, or slyly hints that it’s okay to be an inductivist, or to believe in causality that runs backwards in time, or some other mistake.

Beware of American Philosophers bearing paradoxes.