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Vulture comments on Mechanism Design: Constructing Algorithms for Strategic Agents - Less Wrong
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Thanks for catching that!
I did introduce a lot here. Now that I've thrown all the pieces of the model out on the table, I'll include refreshers as I go along so it can actually sink in.
Oh, and now that I'm going over it more carefully, another nitpick: You don't seem to actually define the notation Π_i before using it in the definition of a social choice function, and it isn't clear (to me) from context what it's supposed to mean.
That's an indexed Cartesian product, analogous to sigma notation for indexed summation, so
is the set of all vectors of agent types.
Oh, okay. Hah, here I was trying to fight my instinct to automatically interpret capital-pi as a product. Thanks!