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Corrected math

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edited Jun 7, 2015 at 15:16

I think their strategy is wrong.

When they collaborate, they should designate either Alice or Bob, but not both, as a presser, and the other as a non-presser. Suppose Alice is the designated presser; Bob is no longer part of the consideration, since we know he can't have any effect on the net payout. There is then a 50% chance that Alice makes \$5000, and a 50% chance she loses \$2000, for an expected payout of $\frac{\\\$5000-\\\$2000}{2}$ = \$1500, which is better than the $500 expectation of the "both press" situation. This doesn't resolve the paradox, but unless I made a mistake, it does show that the paradox shouldn't even be considered, because it resulted from a strategy that never should've been followed in the first place.

EDIT: Ouch, I did bad math.

There is a 25% chance she alone is selected, and a 50% chance they're both selected, reducing the expected payout of a designated presser to $\frac{\\\$5000-$2000 -\\\$2000}{4}$ = \$250. But by symmetry, shouldn't a "both press" situation result in a \$500 gain?

I think their strategy is wrong.

When they collaborate, they should designate either Alice or Bob, but not both, as a presser, and the other as a non-presser. Suppose Alice is the designated presser; Bob is no longer part of the consideration, since we know he can't have any effect on the net payout. There is then a 50% chance that Alice makes \$5000, and a 50% chance she loses \$2000, for an expected payout of $\frac{\\\$5000-\\\$2000}{2}$ = \$1500, which is better than the $500 expectation of the "both press" situation. This doesn't resolve the paradox, but unless I made a mistake, it does show that the paradox shouldn't even be considered, because it resulted from a strategy that never should've been followed in the first place.

I think their strategy is wrong.

When they collaborate, they should designate either Alice or Bob, but not both, as a presser, and the other as a non-presser. Suppose Alice is the designated presser; Bob is no longer part of the consideration, since we know he can't have any effect on the net payout. There is then a 50% chance that Alice makes \$5000, and a 50% chance she loses \$2000, for an expected payout of $\frac{\\\$5000-\\\$2000}{2}$ = \$1500, which is better than the $500 expectation of the "both press" situation. This doesn't resolve the paradox, but unless I made a mistake, it does show that the paradox shouldn't even be considered, because it resulted from a strategy that never should've been followed in the first place.

EDIT: Ouch, I did bad math.

There is a 25% chance she alone is selected, and a 50% chance they're both selected, reducing the expected payout of a designated presser to $\frac{\\\$5000-$2000 -\\\$2000}{4}$ = \$250. But by symmetry, shouldn't a "both press" situation result in a \$500 gain?

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created Jun 7, 2015 at 15:04

Jeff

I think their strategy is wrong.

When they collaborate, they should designate either Alice or Bob, but not both, as a presser, and the other as a non-presser. Suppose Alice is the designated presser; Bob is no longer part of the consideration, since we know he can't have any effect on the net payout. There is then a 50% chance that Alice makes \$5000, and a 50% chance she loses \$2000, for an expected payout of $\frac{\\\$5000-\\\$2000}{2}$ = \$1500, which is better than the $500 expectation of the "both press" situation. This doesn't resolve the paradox, but unless I made a mistake, it does show that the paradox shouldn't even be considered, because it resulted from a strategy that never should've been followed in the first place.