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The Non-Monotonicity of Wrongness

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In addition to being perhaps the happiest statistician in the history of statistics, George said it best. Perhaps he was so happy because he accepted the inherent flaws in all models. Acceptance is very powerful. Of course, correlation, causation, ... But, George's statement is intriguing. If all models are wrong and only a subset are useful, how do we know which of the incorrect models are, in fact, useful? One criteria that might be (implicitly) used in empirical research is based on a simple accounting exercise: If one is choosing between two competing models, the one with fewer errors is preferred. We can summarize this thought process in the following claim: "The usefulness of a model is (weakly?) diminishing in its wrongness" where 'wrongness' is measured by the number of errors. While I don't have specific examples off the top of my head (and wouldn't want to throw specific papers under the bus even if I did), an implicit or exp