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If interpreted as an expected utility function, a number of delicate details regarding π and its subjective content (beliefs about the probabilities of different states of Y) must be addressed. For example, are beliefs about probabilities correct? Are there impossible (zero probability) events assigned positive weight, or positive probability events ignored altogether? These issues are discussed by Lipman (1991) who demonstrates that subjectivity can in principle be handled using a bounded rationality framework with explicit decision costs. Addressing these issues here, however, distracts from the main objective, which is to characterise environments where optimal ignoring arises with no decision costs whatsoever, simply as a result of the probability and payoff structure of the environment
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If interpreted as an expected utility function, a number of delicate details regarding π and its subjective content (beliefs about the probabilities of different states of Y) must be addressed. For example, are beliefs about probabilities correct? Are there impossible (zero probability) events assigned positive weight, or positive probability events ignored altogether? These issues are discussed by Lipman (1991) who demonstrates that subjectivity can in principle be handled using a bounded rationality framework with explicit decision costs. Addressing these issues here, however, distracts from the main objective, which is to characterise environments where optimal ignoring arises with no decision costs whatsoever, simply as a result of the probability and payoff structure of the environment.
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It may be argued that even when the condition holds, optimisers do not ‘ignore’ information, rather they must carefully analyse all cues in order to determine which can be left out of the optimal action rule. However, this criticism applies only when the payoff function is interpreted as a subjective utility function. When instead the payoff function is viewed as an objective summary of adaptive fitness, then the theorem in this paper says that the environment will reward individuals with decision rules that do not depend on X and penalise those who condition a on X
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It may be argued that even when the condition holds, optimisers do not ‘ignore’ information, rather they must carefully analyse all cues in order to determine which can be left out of the optimal action rule. However, this criticism applies only when the payoff function is interpreted as a subjective utility function. When instead the payoff function is viewed as an objective summary of adaptive fitness, then the theorem in this paper says that the environment will reward individuals with decision rules that do not depend on X and penalise those who condition a on X.
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