Optimising a proxy can still maximise the true goal when both are light tailed, but a heavy-tailed discrepancy makes the goal collapse at a rate set by the tail shape.
Monetary relationships : a view from threadneedle street
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The Strong, Weak and Benign Goodhart's law. An independence-free and paradigm-agnostic formalisation
Optimising a proxy can still maximise the true goal when both are light tailed, but a heavy-tailed discrepancy makes the goal collapse at a rate set by the tail shape.