Most people arrange the grid of assumptions like this:
He squeals. If I squeal, 15 years. If I don't, 25 years. He doesn't. If I squeal, 0 years. If I don't, 1 year.
Viewed this way, the advantage of squealing appears to be guaranteed. Assuming a 50% probability of the variable I don't control, confessing has an expected return of 5.5 more years of freedom than the expected return of staying mum, and a lower risk.
But instead, it can be arranged this way:
Allowed to think about the same problem, we will come up with the same answer. If I squeal, 15 years. If I don't, 1 year. Allowed to think about the same problem, we will come up with different answers. If I squeal, 0 years. If I don't, 25 years.
This is an equally valid way to divide the possibilities. The advantage of one choice is no longer guaranteed. If we assume that there's no way of knowing, and that the probability here is 50% as before, the comparative expected return remains the same, but there are compelling arguments not to treat this like a 50% chance. Hofstadter says that you should assume that your partner is probably as smart as you and therefore will come to the same conclusion as you. Most other people are given to assume that they are probably much smarter than anyone they're paired with. I think the details of the situation will point to which is more likely. In your version, we've just pulled off an epic bank heist together, so it stands to reason that we are comparably clever.
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timeasmymeasure
no subject
He squeals. If I squeal, 15 years. If I don't, 25 years.
He doesn't. If I squeal, 0 years. If I don't, 1 year.
Viewed this way, the advantage of squealing appears to be guaranteed. Assuming a 50% probability of the variable I don't control, confessing has an expected return of 5.5 more years of freedom than the expected return of staying mum, and a lower risk.
But instead, it can be arranged this way:
Allowed to think about the same problem, we will come up with the same answer. If I squeal, 15 years. If I don't, 1 year.
Allowed to think about the same problem, we will come up with different answers. If I squeal, 0 years. If I don't, 25 years.
This is an equally valid way to divide the possibilities. The advantage of one choice is no longer guaranteed. If we assume that there's no way of knowing, and that the probability here is 50% as before, the comparative expected return remains the same, but there are compelling arguments not to treat this like a 50% chance. Hofstadter says that you should assume that your partner is probably as smart as you and therefore will come to the same conclusion as you. Most other people are given to assume that they are probably much smarter than anyone they're paired with. I think the details of the situation will point to which is more likely. In your version, we've just pulled off an epic bank heist together, so it stands to reason that we are comparably clever.