lessdazed comments on Existential Risk - Less Wrong
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"Willing" can be unpacked.
Having the other party believe you are operating under a mixed strategy would be optimal, so long as: a) each side values the other side winning more than mutual destruction, which as humans they probably do, and b) accidental/irrational launches are possible but not significantly higher when facing a perceived mixed strategy.
If, say, the USSR and the USA were willing to strike first to win, but not willing to incur a 95% risk of mutual destruction for a 5% chance of total victory, the optimal retaliatory strategy is to (have the other believe you will) retaliate based on a roll of 1d20 - a roll of a natural one has one refrain from retaliating. That way, an accidental launch has a 5% chance of not destroying the world.
In practice, declaring a mixed strategy will probably be seen as setting up an excuse to update one's actions based on the expected payoff considering the circumstances that have happened - i.e. to use CDT rather than TDT. Declaring an updateless strategy is a good way to convey one is operating under a mixed one.