emr comments on Open thread, Jan. 26 - Feb. 1, 2015 - Less Wrong Discussion
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Sometimes when one learns something it makes many other things "click" by making them all make sense in a broader framework. Moreover, when this happens I will be astounded I hadn't learned about the thing in the first place. One very memorable such occasion is when I learned about categories and how many different mathematical structures could be thought of in that context. Do people have other examples where they have been "Wow. That makes so much sense. Why didn't anyone previously say that?"
Basic game theory: Nash equilibriums and the idea of evolutionary game theory.
An unbelievable number of human problems map onto the property that a particular Nash equilibrium or evolutionarily stable strategy isn't guaranteed to be socially desirable (or even Pareto-efficient, or even when compared only to other Nash equilibrium).
Likewise, you really can't do non-trivial consequentialist reasoning without accounting for the impact of your proposed strategy on the strategies of other agents.
Once you've seen the patterns, you can avoid painstakingly deriving or arguing for the general picture over and over again, which probably consumes about a third of all policy and ethics debate. And more critically, you can avoid missing the importance of interlocking strategies in cases where it does matter: Another third of public debate is reserved for wondering why people are acting in the way that the actions of other people encourage them to act; or for helpfully suggesting that some group should move unilaterally along a moral gradient, and then blindly assuming that this will lead to a happier equilibrium once everything adjusts.
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