In the classic form of Newcomb's Problem, you receive two boxes, one (Box A) clear with $1,000, or one (Box B) opaque with either $0 or $1,000,000. You can take either both boxes or only Box B. Omega, the superintelligence who has been right 99% of the time (some phrase it as 100%), will put $0 in Box B if they think you will take both boxes, and puts $1,000,000 in Box B if they think you will take only Box B.
People have argued constantly over which option is better. "Take both," some say, "because they are already filled, and either way, you will get $1,000 instead of $0, or $1,001,000 instead of $1,000,000." "Take only B," others say, "for you must be the type of person who will take only B, and if you are the type of person who wants to take both, if that is your decision, then Box B will be empty.
And people say that these are rational arguments.
Back in the days before Galileo, people argued constantly over how gravity works. "Heavier objects fall faster!" said one person. "No, size is what matters, larger fall faster!" said another. "No, denser objects fall faster!" said another. "No, things blessed by mysterious rituals fall faster!"
And then Galileo came, and he was the one who figured it out, because he stopped arguing over philosophy, did an experiment, and actually looked at the way the world was.
The reason that Galileo's theory of "The weight of an object does not affect how fast it falls" was correct was not because of some philosophical truth. It was because he looked at the world, and that was what he saw!
So let's go back to Newcomb's problem, and solve it through scientific experiment. 200 people do the problem- 100 one-boxers, 100 two-boxers. Omega is right 99% of the time, so 99 one-boxers get $1,000,000, one one-boxer gets $0, 99 two-boxers get $1,000, and one two-boxer gets $1,001,000.
This means that on average, a one-boxer gets $990,000, and a two-boxer gets $11,000. Our goal as rationalists is to win. We want as much money as possible, and through scientific experiment we have found that the option that gives us the most money- 90 times as much money, in fact- is to take Box B and only Box B.
So people will continue their debates on Omega's strength and our ability to change the future and whether we should choose Box A. But those of us who follow the scientific method, the basis of all rationality, know our decision.
And the two-boxers will be proud of how they managed to grab $1,000+0 instead of just $0, while we receive $1,000,000.