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Giles comments on The Doubling Box - Less Wrong Discussion
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Suppose instead of multiplying the utility by 2 each day, the box multiplied the utility by 1. Would it look like this?
Day 1: Curing cancer
Day 2: Curing cancer
Day 3: Curing cancer ...
Probably not - each of those "curing cancer" outcomes is not identical (cancer gets cured on a different day) so you'd assign them different utilities. In order to conform to the specification, the box would have to add an extra sweetener each day in order to make up for a day's worth of cancer deaths.