Compressed environments: Unbounded optimizers should sometimes ignore information
Given free information and unlimited processing power, should decision algorithms use as much information as possible? A formal model of the decision making environment is developed to address this question and provide conditions under which informationally frugal algorithms, without any information or processing costs whatsoever, are optimal. One cause of compression that allows optimal algorithms to rationally ignore information is inverse movement of payoffs and probabilities (e.g., high payoffs occur with low probably and low payoffs occur with high probability). If inversely related payoffs and probabilities cancel out, then predictors that correlate with payoffs and consequently condition the probabilities associated with different payoffs will drop out of the expected-payoff objective function, severing the link between information and optimal action rules. Stochastic payoff processes in which rational ignoring occurs are referred to as compressed environments, because optimal action depends on a reduced-dimension subset of the environmental parameters. This paper considers benefits and limitations of economic models versus other methods for studying links between environmental structure and the real-world success of simple decision procedures. Different methods converge on the normative proposition of ecological rationality, as opposed to axiomatic rationality based on informational efficiency and internal consistency axioms, as a superior framework for comparing the effectiveness of decision strategies and prescribing decision algorithms in application.
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- Berg, Nathan & Hoffrage, Ulrich, 2008. "Rational ignoring with unbounded cognitive capacity," Journal of Economic Psychology, Elsevier, vol. 29(6), pages 792-809, December.
- Nathan Berg, 2005. "Decision-making environments in which unboundedly rational decision makers choose to ignore relevant information," Global Business and Economics Review, Inderscience Enterprises Ltd, vol. 7(1), pages 59-73.
- Laura Martignon & Ulrich Hoffrage, 2002. "Fast, frugal, and fit: Simple heuristics for paired comparison," Theory and Decision, Springer, vol. 52(1), pages 29-71, February.
- Robin Hogarth & Natalia Karelaia, 2004. "Ignoring information in binary choice with continuous variables: When is less 'more'?," Economics Working Papers 742, Department of Economics and Business, Universitat Pompeu Fabra, revised Oct 2004.
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