Will someone strengthen our Goodhart's Law result?
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Apr 1
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We (Thomas Kwa and Drake Thomas) have a Lesswrong post where we make a toy model for Goodhart’s Law, and prove things about the quantity $Q = \lim_{t \to \infty} E[V | X + V > t]$ when X and V are independent variables.

This market resolves YES iff someone other than us (a) substantially strengthens one of our results, or (b) treads nontrivial ground in the nonindependent case. The work must be published by resolution date.

Examples of work that would result in YES resolution:

  • Criterion (a): Weakening “subexponential” to “long-tailed” or “heavy-tailed” in our proof for when Q=0. (This would require some regularity condition.)

  • Criterion (a): Weakening our light-tailed condition in our proof for when Q=infinity

  • Criterion (b): Proving that Q=0 or Q=infinity in any case more general than an explicitly parametrized class of joint distributions, such that Drake and I couldn’t prove it ourselves in 15 minutes.

  • Criterion (b): Proving that Q=0 or Q=infinity in a toy model of AI alignment through oversight that we find insightful, even if the proof is easy.

The resolution criteria may change to keep the spirit of the question, or to discourage manipulation. I will not trade in this market.

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