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wedrifid comments on A Voting Puzzle, Some Political Science, and a Nerd Failure Mode - Less Wrong
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I affirm Desrtopa's interpretation, as well as Eliezer's reminder about how conjunction works.
To reiterate: When you encounter "!(A AND B)" it does not mean "Let X equal whichever of !A and !B is most objectionable and claim that !(A AND B) is equivalent to X".