Anthropic has yet to make a principled case that their efforts are risk-reducing on net. An analysis supporting such a claim would include a quantified estimate of the risk to society they are currently causing, weighed against the risk reduction they estimate from their activities. Anthropic has, to our knowledge, published no such analysis. We suspect that an honest accounting would suggest an unacceptable level of absolute incurred risk.
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Now that we have the mechanics spelled out, let’s take r = 1/4 and analyze the optimal solutions for some initial values of b: