Skip to main content
SpringerLink
Log in

Compressed Environments: Unbounded Optimizers Should Sometimes Ignore Information

  • Published:
Minds and Machines Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Notes

  1. An important theme in the just-noticeable-differences literature is asymmetry of perceptual sensitivity with respect to deviations from the status quo. Allowing for asymmetric τs would add an additional degree of psychological plausibility without changing the main conclusion, namely, that the set of environments in which ignoring is rational is nonempty.

References

  • Berg, N. (2005). Decision-making environments in which unboundedly rational decision makers choose to ignore relevant information. Global Business and Economics Review, 7(1), 59–73.

    Article  Google Scholar 

  • Berg, N., & Hoffrage, U. (2008). Rational ignoring with unbounded cognitive capacity. Journal of Economic Psychology, 29, 792–809.

    Google Scholar 

  • Bookstaber, R., & Langsam, J. (1985). On the optimality of coarse behavior rules. Journal of Theoretical Biology, 116, 161–193.

    Article  MathSciNet  Google Scholar 

  • Brooks, R. A. (1991). New approaches to robotics. Science, 253, 1227–1232.

    Article  Google Scholar 

  • Bullock, S., & Todd, P. M. (1999). Made to measure: Ecological rationality in structured environments. Minds and Machines, 9(4), 497–541.

    Article  Google Scholar 

  • Clarke, D. D., Ward, P., & Truman, W. (2002). In-depth accident causation study of young drivers, Report no. TRL542, TRL Limited, Crowthorne, Berkshire.

  • Connolly, T. (1999). Action as a fast and frugal heuristic. Minds and Machines, 9(4), 479–496.

    Article  Google Scholar 

  • Czerlinski, J., Gigerenzer, G., & Goldstein, D. G. (1999). How good are simple heuristics? In: G. Gigerenzer, P. M. Todd & the ABC Research Group, Simple heuristics that make us smart (pp. 97–118). New York: Oxford University Press.

  • Dobbie, K. (2002). Fatigue-related crashes: An analysis of fatigue-related crashes on Australian roads using an operational definition of fatigue, Australian transport safety bureau report no. OR23.

  • Forster, M. R. (1999). How do simple rules ‘fit to reality’ in a complex world? Minds and Machines, 9(4), 543–564.

    Article  Google Scholar 

  • Gigerenzer, G. & Brighton, H. (2009). Homo heuristicus: Why biased minds make better inferences. Topics in Cognitive Science, 1, 107–143

  • Gigerenzer, G., & Goldstein, D. G. (1996). Reasoning the fast and frugal way: Models of bounded rationality. Psychological Review, 103, 650–669.

    Article  Google Scholar 

  • Gigerenzer, G., Hoffrage, U., & Kleinbölting, H. (1991). Probabilistic mental models: A Brunswikian theory of confidence. Psychological Review, 98, 506–528.

    Article  Google Scholar 

  • Gigerenzer, G., & Selten, R. (Eds.) (2001). Bounded rationality: The adaptive toolbox. Cambridge, MA: MIT Press.

  • Gigerenzer, G., Todd, P. M., & the ABC Research Group. (1999). Simple heuristics that make us smart. New York: Oxford University Press.

    Google Scholar 

  • Goldstein, D. G., & Gigerenzer, G. (2002). Models of ecological rationality: The recognition heuristic. Psychological Review, 109, 75–90.

    Article  Google Scholar 

  • Hansen, M. H., & Bin, Y. (1996). Model selection and minimum description. Journal of the American Statistical Association, 96, 746–774.

    Article  Google Scholar 

  • Hogarth, R. M. (2001). Educating instituition. Chicago: University of Chicago Press.

    Google Scholar 

  • Hogarth, R. M., & Karelaia, N. (2005). Ignoring information in binary choice with continuous variables: When is less “more”? Journal of Mathematical Psychology, 49, 115–124.

    Article  MATH  MathSciNet  Google Scholar 

  • Kahneman, D., & Tversky, A. (1973). On the psychology of prediction. Psychological Review, 80, 237–251.

    Article  Google Scholar 

  • Kahneman, D., Slovic, P., & Tversky, A. (Eds.). (1982). Judgment under uncertainty: Heuristics and biases. Cambridge: Cambridge University Press.

    Google Scholar 

  • Luce, D., & Raiffa, H. (1957). Games and decisions. New York: Wiley.

    MATH  Google Scholar 

  • Mahowald, M. W. (2000). Eyes wide shut: The dangers of sleepy driving. Minnesota Medicine, 83, 25–30.

    Google Scholar 

  • Martignon, L., & Hoffrage, U. (2002). Fast, frugal and fit: Simple heuristics for paired comparison. Theory and Decision, 52, 29–71.

    Article  MATH  Google Scholar 

  • Martignon, L., Katsikopoulos, K. V., & Woike, J. K. (2008). Categorization with limited resources: A family of simple heuristics. Journal of Mathematical Psychology, 52(6), 352–361.

    Google Scholar 

  • Martignon, L., & Schmitt, M. (1999). Simplicity and robustness of fast and frugal heuristics. Minds and Machines, 9(4), 565–593.

    Article  Google Scholar 

  • Mohan, D. (2001). Traffic safety and thirty years of biomechanics research: A personal adventure. In International Research Council on the Biomechanics of Impact Proceedings (pp. 1–12).

  • Pack, A. I., Pack, A. M., Rodgman, E., Cucchiara, A., Dinges, D. F., & Schwab, C. W. (1995). Characteristics of crashes attributed to the driver having fallen asleep. Accident Analysis and Prevention, 27(6), 769–775.

    Article  Google Scholar 

  • Raiffa, H. (1986). Decision analysis: Introductory lectures on choices under uncertainty. New York: Random House.

    Google Scholar 

  • Raiffa, H., & Shlaifer, R. (1961). Applied statistical decision theory. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Schooler, L. J., & Hertwig, R. (2005). How forgetting aids heuristic inference. Psychological Review, 112, 610–628.

    Article  Google Scholar 

  • Simon, H. A. (1982). Models of bounded rationality. Cambridge: MIT Press.

    Google Scholar 

  • Todd, P. M. (1999). Simple inference heuristics versus complex decision machines. Minds and Machines, 9(4), 461–477.

    Article  Google Scholar 

  • Todd, P. M. (2000) The ecological rationality of mechanisms evolved to make up minds. American Behavioral Scientist, 43, 940–956.

    Article  Google Scholar 

  • Tversky, A., & Kahneman, D. (1982). Evidential impact of base rates. In: D. Kahneman, P. Slovic, & A. Tversky (Eds.), Judgment under uncertainty: Heuristics and biases (pp. 153–160). New York: Cambridge University Press.

    Google Scholar 

  • Zellner, A., Keuzenkamp, H., & McAleer, M. (Eds.). (2001). Simplicity, inference and modelling: Keeping it sophisticatedly simple. Cambridge: Cambridge University Press.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Economic, Political, and Policy Sciences (EPPS), University of Texas at Dallas, GR 31 211300, Box 830688, Richardson, TX, 75083-0688, USA

    Nathan Berg

  2. Faculty of Business and Economics, University of Lausanne, Batiment Internef, CH-1015, Lausanne, Switzerland

    Ulrich Hoffrage

Authors
  1. Nathan Berg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ulrich Hoffrage
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nathan Berg.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Berg, N., Hoffrage, U. Compressed Environments: Unbounded Optimizers Should Sometimes Ignore Information. Minds & Machines 20, 259–275 (2010). https://doi.org/10.1007/s11023-009-9167-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11023-009-9167-1

Keywords

Search

Navigation