In the spirit of Blackwell (1951), we analyze how two fundamental mistakes in information processing - incorrect beliefs about the world and misperception of information - affect the expected utility ranking of information experiments. We explore their individual and combined influence on welfare and provide necessary and sufficient conditions when mistakes alter and possibly reverse the ranking of information experiments.
Both mistakes by themselves reduce welfare in a model where payoff relevant actions also generate informative signals. This is true for naive decision-makers, unaware of any errors, as well as for sophisticated decision-makers, who account for the possibility of mistakes. However, mistakes can interact in non-obvious ways and an agent might be better off suffering from both, rather than just one. We provide a characterization when such positive interactions are possible. Surprisingly, this holds true only for naive decision-makers and thus naivete can be beneficial.
We discuss implications for information acquisition and avoidance, welfare-improving belief manipulation, and policy interventions in general.