Are you sure at the critical point in the plan EDT really would choose to take randomly from the lighter pair than the heavier pair? She’s already updated from knowing the weights of the pairs, and surely a random box from the more heavy pair has more money in expectation than a random box from the less heavy pair, the expected value of it is just half the total weight? If it was a tie (as it certainly will be) it wouldn’t matter. If there’s not a tie somehow one Host made an impossible mistake: if she chooses from the lighter she can expect the Hosts mistake was not putting money in since that would have been optimal (so the boxes have 301, 301, 301, 201, and choosing from the lighter has expected value 251), but if she chooses from the heavier the Hosts mistake was putting money in when it shouldn’t have (so the boxes weigh 101, 101, 101, 1), and choosing from the heavier guarantees 101, which would be less? Actually okay yeah I’m persuaded that this works. I imagined when I first wrote this that weighing a group of boxes lets you infer the total value, so she’d defect on the plan and choose from the heavier pair expecting more returns that way, but so long as she only knows which pair of boxes is heavier (a comparative weighing) instead of how much each pair of boxes actually weighs exactly (from which she would infer the amount on money in each pair total) she can justify choosing the lighter and get 301, I think?
Are you sure at the critical point in the plan EDT really would choose to take randomly from the lighter pair than the heavier pair? She’s already updated from knowing the weights of the pairs, and surely a random box from the more heavy pair has more money in expectation than a random box from the less heavy pair, the expected value of it is just half the total weight?
If it was a tie (as it certainly will be) it wouldn’t matter. If there’s not a tie somehow one Host made an impossible mistake: if she chooses from the lighter she can expect the Hosts mistake was not putting money in since that would have been optimal (so the boxes have 301, 301, 301, 201, and choosing from the lighter has expected value 251), but if she chooses from the heavier the Hosts mistake was putting money in when it shouldn’t have (so the boxes weigh 101, 101, 101, 1), and choosing from the heavier guarantees 101, which would be less?
Actually okay yeah I’m persuaded that this works. I imagined when I first wrote this that weighing a group of boxes lets you infer the total value, so she’d defect on the plan and choose from the heavier pair expecting more returns that way, but so long as she only knows which pair of boxes is heavier (a comparative weighing) instead of how much each pair of boxes actually weighs exactly (from which she would infer the amount on money in each pair total) she can justify choosing the lighter and get 301, I think?