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Luke_A_Somers comments on How to offend a rationalist (who hasn't thought about it yet): a life lesson - Less Wrong Discussion
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Those are good examples that you need to be really careful applying math to society.
If you come up with a short list of axioms for a social group, and then use them to formulate policy, you're probably going to end up leaving the domain over which those axioms are valid. If you have a lot of power, this can be a really bad thing.