category boundaries should be drawn for epistemic and not instrumental reasons
Sounds very wrong to me. In my view, computationally unbounded agents don’t need categories at all ; categories are a way for computationally bounded agents to approximate perfect Bayesian reasoning, and how to judge the quality of the approximation will depend on the agent goals — different agents with different goals will care differently about a similar error.
(It’s actually somewhat interesting; the logarithmic score doesn’t work as a measure of category-system goodness because it can only reward you for the probability you assign to the exact answer, but we want “partial credit” for almost-right answers, so the expected squared error is actually better here, contrary to what you said in the “Technical Explanation” about what Bayesian statisticians do)
Yes, exactly. When you’re at the point when you’re deciding between log-loss and MSE, you’re no longer doing pure epistemics, you’re entering the realm of decision theory ; you’re crafting a measure of how good your approximation is, a measure that can and should be tailored to your specific goals as a rational agent. log-loss and MSE are only two possibilities in a vast universe of possible such measures, ones that are quite generic and therefore not optimal for a given agent goals.
Sounds very wrong to me. In my view, computationally unbounded agents don’t need categories at all ; categories are a way for computationally bounded agents to approximate perfect Bayesian reasoning, and how to judge the quality of the approximation will depend on the agent goals — different agents with different goals will care differently about a similar error.
Yes, exactly. When you’re at the point when you’re deciding between log-loss and MSE, you’re no longer doing pure epistemics, you’re entering the realm of decision theory ; you’re crafting a measure of how good your approximation is, a measure that can and should be tailored to your specific goals as a rational agent. log-loss and MSE are only two possibilities in a vast universe of possible such measures, ones that are quite generic and therefore not optimal for a given agent goals.
MSE can also be seen as a special-case of log-loss for a Gaussian distribution with constant variance.
This can only be true if they do not ever have to interact with computationally bounded agents.