The anchoring bias reflects rational use of cognitive resources

  • Falk Lieder
  • Thomas L. Griffiths
  • Quentin J. M. Huys
  • Noah D. Goodman
Theoretical Review

Abstract

Cognitive biases, such as the anchoring bias, pose a serious challenge to rational accounts of human cognition. We investigate whether rational theories can meet this challenge by taking into account the mind’s bounded cognitive resources. We asked what reasoning under uncertainty would look like if people made rational use of their finite time and limited cognitive resources. To answer this question, we applied a mathematical theory of bounded rationality to the problem of numerical estimation. Our analysis led to a rational process model that can be interpreted in terms of anchoring-and-adjustment. This model provided a unifying explanation for ten anchoring phenomena including the differential effect of accuracy motivation on the bias towards provided versus self-generated anchors. Our results illustrate the potential of resource-rational analysis to provide formal theories that can unify a wide range of empirical results and reconcile the impressive capacities of the human mind with its apparently irrational cognitive biases.

Keywords

Bounded rationality Heuristics Cognitive biases Probabilistic reasoning Anchoring-and-adjustment Rational process models 

References

  1. Abbott, J.T., Austerweil, J.L., & Griffiths, T.L. (2015). Random walks on semantic networks can resemble optimal foraging. Psychological Review, 122(3), 558–569.CrossRefPubMedGoogle Scholar
  2. Abbott, J.T., & Griffiths, T.L. (2011). Exploring the influence of particle filter parameters on order effects in causal learning, In Proceedings of the 33rd Annual Conference of the Cognitive Science Society. Austin, Texas: Cognitive Science Society.Google Scholar
  3. Anderson, J.R. (1983). A spreading activation theory of memory. Journal of verbal learning and verbal behavior, 22(3), 261– 295.CrossRefGoogle Scholar
  4. Anderson, J.R. (1990). The adaptive character of thought. Hillsdale, NJ: Psychology Press.Google Scholar
  5. Anderson, J.R. (1991). Is human cognition adaptive? Behavioral and Brain Sciences, 14, 471–485.CrossRefGoogle Scholar
  6. Ariely, D., Loewenstein, G., & Prelec, D. (2003). Coherent arbitrariness: Stable demand curves without stable preferences. The Quarterly Journal of Economics, 118(1), 73–106.CrossRefGoogle Scholar
  7. Beach, L. R., & Mitchell, T. R. (1978). A contingency model for the selection of decision strategies. Academy of Management Review, 3(3), 439–449.Google Scholar
  8. Bonawitz, E., Denison, S., Gopnik, A., & Griffiths, T. L. (2014). Win-stay, lose-sample: A simple sequential algorithm for approximating Bayesian inference. Cognitive Psychology, 74, 35–65.CrossRefPubMedGoogle Scholar
  9. Bonawitz, E., Denison, S., Griffiths, T. L., & Gopnik, A. (2014). Probabilistic models, learning algorithms, and response variability: Sampling in cognitive development. Trends in Cognitive Sciences, 18(10), 497–500.CrossRefPubMedGoogle Scholar
  10. Bourgin, D. D., Abbott, J. T., Griffiths, T. L., Smith, K. A., & Vul, E. (2014). Empirical evidence for markov chain monte carlo in memory search. In Proceedings of the 36th annual meeting of the cognitive science society, (pp. 224–229).Google Scholar
  11. Braine, M. D. (1978). On the relation between the natural logic of reasoning and standard logic. Psychological Review, 85(1), 1.CrossRefGoogle Scholar
  12. Brewer, N. T., & Chapman, G. B. (2002). The fragile basic anchoring effect. Journal of Behavioral Decision Making, 15, 65–77.CrossRefGoogle Scholar
  13. Buesing, L., Bill, J., Nessler, B., & Maass, W. (2011). Neural dynamics as sampling: A model for stochastic computation in recurrent networks of spiking neurons. PLoS Computational Biology, 7(11), e1002211.CrossRefPubMedPubMedCentralGoogle Scholar
  14. Chapman, G. B., & Johnson, E. J. (1994). The limits of anchoring. Journal of Behavioral Decision Making, 7(4), 223–242.CrossRefGoogle Scholar
  15. Chapman, G. B., & Johnson, E. J. (2002). Incorporating the irrelevant: Anchors in judgments of belief and value. In Gilovich, T., Griffin, D., & Kahneman, D. (Eds.), Heuristics and biases: The psychology of intuitive judgment. Cambridge, U.K.: Cambridge University Press.Google Scholar
  16. Chater, N., & Oaksford, M. (2000). The rational analysis of mind and behavior. Synthese, 122(1), 93–131.CrossRefGoogle Scholar
  17. Collins, A. M., & Loftus, E. F. (1975). A spreading-activation theory of semantic processing. Psychological review, 82(6), 407.CrossRefGoogle Scholar
  18. Denison, S., Bonawitz, E., Gopnik, A., & Griffiths, T. (2013). Rational variability in children’s causal inferences: The sampling hypothesis. Cognition, 126(2), 285–300.CrossRefPubMedGoogle Scholar
  19. Diamond, A. (2013). Executive functions. Annual review of psychology, 64, 135.CrossRefPubMedGoogle Scholar
  20. Doucet, A., De Freitas, N., & Gordon, N. (2001). Sequential Monte Carlo methods in practice. New York: Springer.CrossRefGoogle Scholar
  21. Englich, B., Mussweiler, T., & Strack, F. (2006). Playing dice with criminal sentences: The influence of irrelevant anchors on experts’ judicial decision making. Personality and Social Psychology Bulletin, 32(2), 188–200.CrossRefPubMedGoogle Scholar
  22. Epley, N. (2004). A tale of tuned decks? Anchoring as accessibility and anchoring as adjustment. In Koehler, D. J., & Harvey, N. (Eds.), The Blackwell Handbook of Judgment and Decision Making (pp. 240–256). Oxford, UK: Blackwell.CrossRefGoogle Scholar
  23. Epley, N., & Gilovich, T. (2004). Are adjustments insufficient? Personality and Social Psychology Bulletin, 30(4), 447–460.CrossRefPubMedGoogle Scholar
  24. Epley, N., & Gilovich, T. (2005). When effortful thinking influences judgmental anchoring: Differential effects of forewarning and incentives on self-generated and externally provided anchors. Journal of Behavioral Decision Making, 18(3), 199–212.CrossRefGoogle Scholar
  25. Epley, N., & Gilovich, T. (2006). The anchoring-and-adjustment heuristic. Psychological Science, 17(4), 311–318.CrossRefPubMedGoogle Scholar
  26. Epley, N., Keysar, B., Van Boven, L., & Gilovich, T. (2004). Perspective taking as egocentric anchoring and adjustment. Journal of Personality and Social Psychology, 87(3), 327–339.Google Scholar
  27. Fiser, J., Berkes, P., Orbán, G., & Lengyel, M. (2010). Statistically optimal perception and learning: From behavior to neural representations. Trends in Cognitive Sciences, 14(3), 119–130.CrossRefPubMedPubMedCentralGoogle Scholar
  28. Fodor, J. (1975). The language of thought. Cambridge, MA: Harvard University Press.Google Scholar
  29. Frank, M., & Goodman, N. (2012). Predicting pragmatic reasoning in language games. Science, 336(6084), 998.CrossRefPubMedGoogle Scholar
  30. Friedman, M., & Savage, L. J. (1948). The utility analysis of choices involving risk. The Journal of Political Economy, 279–304.Google Scholar
  31. Friston, K. (2009). The free-energy principle: A rough guide to the brain?. Trends in Cognitive Sciences, 13 (7), 293–301.CrossRefPubMedGoogle Scholar
  32. Friston, K., & Kiebel, S. (2009). Predictive coding under the free-energy principle. Philosophical Transactions of the Royal Society B: Biological Sciences, 364(1521), 1211–1221.CrossRefGoogle Scholar
  33. Galinsky, A. D., & Mussweiler, T. (2001). First offers as anchors: The role of perspective-taking and negotiator focus. Journal of Personality and Social Psychology, 81(4), 657.CrossRefPubMedGoogle Scholar
  34. Gershman, S. J., Horvitz, E. J., & Tenenbaum, J. B. (2015). Computational rationality: A converging paradigm for intelligence in brains, minds, and machines. Science, 349(6245), 273–278.CrossRefPubMedGoogle Scholar
  35. Gershman, S. J., Vul, E., & Tenenbaum, J. B. (2012). Multistability and perceptual inference. Neural Computation, 24(1), 1–24.CrossRefPubMedGoogle Scholar
  36. Gigerenzer, G. (2008). Why heuristics work. Perspectives on Psychological Science, 3(1), 20–29.CrossRefPubMedGoogle Scholar
  37. Gigerenzer, G., & Goldstein, D. G. (1996). Reasoning the fast and frugal way: Models of bounded rationality. Psychological Review, 103(4), 650–669.CrossRefPubMedGoogle Scholar
  38. Gigerenzer, G., & Selten, R. (2002) In In Gigerenzer, G., & Selten, R. (Eds.), Bounded rationality: The adaptive toolbox. Cambridge, MA: The MIT Press.Google Scholar
  39. Gilks, W., Richardson, S., & Spiegelhalter, D. (1996). Markov chain Monte Carlo in practice. London: Chapman and Hall.Google Scholar
  40. Good, I. J. (1983). Good thinking: The foundations of probability and its applications. USA: Univ Of Minnesota Press.Google Scholar
  41. Griffiths, T. L., Lieder, F., & Goodman, N. D. (2015). Rational use of cognitive resources: Levels of analysis between the computational and the algorithmic. Topics in Cognitive Science, 7(2), 217–229.CrossRefPubMedGoogle Scholar
  42. Griffiths, T. L., & Tenenbaum, J. B. (2006). Optimal predictions in everyday cognition. Psychological Science, 17(9), 767–773.CrossRefPubMedGoogle Scholar
  43. Griffiths, T. L., & Tenenbaum, J. B. (2011). Predicting the future as Bayesian inference: People combine prior knowledge with observations when estimating duration and extent. Journal of Experimental Psychology: General, 140 (4), 725–743.CrossRefGoogle Scholar
  44. Habenschuss, S., Jonke, Z., & Maass, W. (2013). Stochastic computations in cortical microcircuit models. PLoS Computational Biology, 9(11), e1003311.CrossRefPubMedPubMedCentralGoogle Scholar
  45. Hardt, O., & Pohl, R. (2003). Hindsight bias as a function of anchor distance and anchor plausibility. Memory, 11(4-5), 379–394.CrossRefPubMedGoogle Scholar
  46. Harman, G. (2013). Rationality. In LaFollette, H., Deigh, J., & Stroud, S. (Eds.), International Encyclopedia of Ethics. Hoboken: Blackwell Publishing Ltd.Google Scholar
  47. Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97–109.CrossRefGoogle Scholar
  48. Hedström, P., & Stern, C. (2008). Rational choice and sociology. In Durlauf, S., & Blume, L. (Eds.), The New Palgrave Dictionary of Economics. 2nd edn. Basingstoke, U.K.: Palgrave Macmillan.Google Scholar
  49. Horvitz, E., Suermondt, H., & Cooper, G. (1989). Bounded conditioning: Flexible inference for decisions under scarce resources, Proceedings of the Fifth Workshop on Uncertainty in Artificial Intelligence (pp. 182–193). Mountain View: Association for Uncertainty in Artificial Intelligence.Google Scholar
  50. Jacowitz, K. E., & Kahneman, D. (1995). Measures of anchoring in estimation tasks. Personality and Social Psychology Bulletin, 21(11), 1161–1166.CrossRefGoogle Scholar
  51. Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology, 3(3), 430–454.CrossRefGoogle Scholar
  52. Lewis, R. L., Howes, A., & Singh, S. (2014). Computational rationality: Linking mechanism and behavior through bounded utility maximization. Topics in Cognitive Science, 6(2), 279–311.CrossRefPubMedGoogle Scholar
  53. Lieder, F., Goodman, N. D., & Huys, Q. J. M. (2013). Controllability and resource-rational planning. In Pillow, J., Rust, N., Cohen, M., & Latham, P. (Eds.), Cosyne Abstracts.Google Scholar
  54. Lieder, F., & Griffiths, T. L. (2015). When to use which heuristic: A rational solution to the strategy selection problem. In Noelle, D. C., & et al. (Eds.), Proceedings of the 37th Annual Conference of the Cognitive Science Society Austin. TX: Cognitive Science Society.Google Scholar
  55. Lieder, F., Griffiths, T. L., & Goodman, N. D. (2012). Burn-in, bias, and the rationality of anchoring. In Bartlett, P., Pereira, F. C. N., Bottou, L., Burges, C. J. C., & Weinberger, K. Q. (Eds.), Advances in Neural Information Processing Systems 26.Google Scholar
  56. Lieder, F., Griffiths, T. L., Huys, Q. J. M., & Goodman, N. D. (2017). Empirical evidence for resource-rational anchoring-and-adjustment.Google Scholar
  57. Lieder, F., Hsu, M., & Griffiths, T. L. (2014). The high availability of extreme events serves resource-rational decision-making., In Proceedings of the 36th Annual Conference of the Cognitive Science Society. Austin, TX: Cognitive Science Society.Google Scholar
  58. Lieder, F., Plunkett, D., Hamrick, J. B., Russell, S. J., Hay, N. J., & Griffiths, T. L. (2014). Algorithm selection by rational metareasoning as a model of human strategy selection. Advances in Neural Information Processing Systems 27.Google Scholar
  59. Lohmann, S. (2008). Rational choice and political science. In Durlauf, S., & Blume, L. (Eds.), The New Palgrave Dictionary of Economics. 2nd edn. Basingstoke, U.K.: Palgrave Macmillan.Google Scholar
  60. Marr, D. (1982). Vision: A computational investigation into the human representation and processing of visual information. W. H. Freeman. Paperback.Google Scholar
  61. McKenzie, C. R. (1994). The accuracy of intuitive judgment strategies: Covariation assessment and bayesian inference. Cognitive Psychology, 26(3), 209–239.CrossRefGoogle Scholar
  62. Mengersen, K. L., & Tweedie, R. L. (1996). Rates of convergence of the Hastings and Metropolis algorithms. Annals of Statistics, 24(1), 101–121.CrossRefGoogle Scholar
  63. Mill, J. S. (1882). A system of logic ratiocinative and inductive, 8th edn. New York: Harper and Brothers.Google Scholar
  64. Moreno-Bote, R., Knill, D. C., & Pouget, A. (2011). Bayesian sampling in visual perception. Proceedings of the National Academy of Sciences of the United States of America, 108(30), 12491– 12496.CrossRefPubMedPubMedCentralGoogle Scholar
  65. Mussweiler, T., & Strack, F. (1999). Hypothesis-consistent testing and semantic priming in the anchoring paradigm: A selective accessibility model. Journal of Experimental Social Psychology, 35(2), 136–164.CrossRefGoogle Scholar
  66. Neal, R. (2011) In Brooks, S., Gelman, A., Jones, G., & Meng, X. L. (Eds.), MCMC using Hamiltonian dynamics (Vol. 2, pp. 113–162). FL, USA: CRC Press.Google Scholar
  67. Neely, J. H. (1977). Semantic priming and retrieval from lexical memory: Roles of inhibitionless spreading activation and limited-capacity attention. Journal of experimental psychology: General, 106(3), 226.CrossRefGoogle Scholar
  68. Newell, A., Shaw, J. C., & Simon, H. A. (1958). Elements of a theory of human problem solving. Psychological Review, 65(3), 151–166.CrossRefGoogle Scholar
  69. Nisbett, R. E., & Borgida, E. (1975). Attribution and the psychology of prediction. Journal of Personality and Social Psychology, 32(5), 932–943.CrossRefGoogle Scholar
  70. Nisbett, R. E., & Ross, L. (1980). Human inference: Strategies and shortcomings of social judgment. Englewood Cliffs: Prentice-Hall.Google Scholar
  71. Northcraft, G. B., & Neale, M. A. (1987). Experts, amateurs, and real estate: An anchoring-and-adjustment perspective on property pricing decisions. Organizational Behavior and Human Decision Processes, 39(1), 84–97.CrossRefGoogle Scholar
  72. Oaksford, M., & Chater, N. (2007). Bayesian rationality: The probabilistic approach to human reasoning (Oxford cognitive science series), 1st edn. Oxford: Oxford University Press.CrossRefGoogle Scholar
  73. Payne, J. W., Bettman, J. R., & Johnson, E. J. (1993). The adaptive decision maker: Cambridge University Press.Google Scholar
  74. Pohl, R. F. (1998). The effects of feedback source and plausibility of hindsight bias. European Journal of Cognitive Psychology, 10(2), 191–212.CrossRefGoogle Scholar
  75. Russell, S. J. (1997). Rationality and intelligence. Artificial Intelligence, 94(1-2), 57–77.CrossRefGoogle Scholar
  76. Russell, S. J., & Subramanian, D. (1995). Provably bounded-optimal agents. Journal of Articial Intelligence Research, 2, 575–609.Google Scholar
  77. Russell, S. J., & Wefald, E. (1991). Do the right thing: Studies in limited rationality. Cambridge, MA: The MIT Press.Google Scholar
  78. Russo, J. E., & Schoemaker, P. J. H. (1989). Decision traps: Ten barriers to brilliant decision-making and how to overcome them: Simon and Schuster.Google Scholar
  79. Sanborn, A. N., Griffiths, T. L., & Navarro, D. J. (2010). Rational approximations to rational models: Alternative algorithms for category learning. Psychological Review, 117(4), 1144– 1167.CrossRefPubMedGoogle Scholar
  80. Schwarz, N. (2014). Cognition and communication: Judgmental biases, research methods and the logic of conversation. New York: Psychology Press.Google Scholar
  81. Shafir, E., & LeBoeuf, R. A. (2002). Rationality. Annual Review of Psychology, 53(1), 491–517.CrossRefPubMedGoogle Scholar
  82. Shugan, S. M. (1980). The cost of thinking. Journal of consumer Research, 7(2), 99–111.CrossRefGoogle Scholar
  83. Simmons, J. P., LeBoeuf, R. A., & Nelson, L. D. (2010). The effect of accuracy motivation on anchoring and adjustment: Do people adjust from provided anchors? Journal of Personality and Social Psychology, 99(6), 917–932.CrossRefPubMedGoogle Scholar
  84. Simon, H. A. (1955). A behavioral model of rational choice. The Quarterly Journal of Economics, 69(1), 99–118.CrossRefGoogle Scholar
  85. Simon, H. A. (1956). Rational choice and the structure of the environment. Psychological Review, 63(2), 129.CrossRefPubMedGoogle Scholar
  86. Simon, H. A. (1972). Theories of bounded rationality. Decision and Organization, 1, 161–176.Google Scholar
  87. Simon, H. A. (1976). From substantive to procedural rationality. In Kastelein, T. J., Kuipers, S. K., Nijenhuis, W. A., & Wagenaar, G. R. (Eds.), 25 Years of Economic Theory (pp. 65–86). US: Springer.CrossRefGoogle Scholar
  88. Simonson, I., & Drolet, A. (2004). Anchoring effects on consumers’ willingness-to-pay and willingness-to-accept. Journal of Consumer Research, 31(3), 681–690.CrossRefGoogle Scholar
  89. Slovic, P., Fischhoff, B., & Lichtenstein, S. (1977). Cognitive processes and societal risk taking. In Jungermann, H., & De Zeeuw, G. (Eds.), Decision Making and Change in Human Affairs, (Vol. 16 pp. 7–36). Dordrecht, Netherlands: D. Reidel Publishing Company.Google Scholar
  90. Sosis, C., & Bishop, M. (2014). Rationality. Wiley interdisciplinary reviews: Cognitive Science, 5, 27–37.PubMedGoogle Scholar
  91. Speirs-Bridge, A., Fidler, F., McBride, M., Flander, L., Cumming, G., & Burgman, M. (2010). Reducing overconfidence in the interval judgments of experts. Risk Analysis, 30(3), 512–523.CrossRefPubMedGoogle Scholar
  92. Stewart, N., Chater, N., & Brown, G. D. (2006). Decision by sampling. Cognitive Psychology, 53(1), 1–26.CrossRefPubMedGoogle Scholar
  93. Strack, F., & Mussweiler, T. (1997). Explaining the enigmatic anchoring effect: Mechanisms of selective accessibility. Journal of Personality and Social Psychology, 73(3), 437.CrossRefGoogle Scholar
  94. Sunnåker, M., Busetto, A. G., Numminen, E., Corander, J., Foll, M., & Dessimoz, C. (2013). Approximate bayesian computation. PLoS Computational Biology, 9(1), e1002803.CrossRefPubMedPubMedCentralGoogle Scholar
  95. Thorngate, W. (1980). Efficient decision heuristics. Behavioral Science, 25(3), 219–225.CrossRefGoogle Scholar
  96. Turner, B. M., & Schley, D. R. (2016). The anchor integration model: A descriptive model of anchoring effects. Cognitive Psychology, 90, 1–47.CrossRefPubMedGoogle Scholar
  97. Turner, B. M., & Sederberg, P. B. (2012). Approximate bayesian computation with differential evolution. Journal of Mathematical Psychology, 56(5), 375–385.CrossRefGoogle Scholar
  98. Tversky, A. (1972). Elimination by aspects: A theory of choice. Psychological Review, 79(4), 281.CrossRefGoogle Scholar
  99. Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185(4157), 1124–1131.CrossRefPubMedGoogle Scholar
  100. Van Rooij, I. (2008). The tractable cognition thesis. Cognitive Science, 32(6), 939–984.Google Scholar
  101. Von Neumann, J., & Morgenstern, O. (1944). The theory of games and economic behavior. Princeton: Princeton university press.Google Scholar
  102. Vul, E., Goodman, N. D., Griffiths, T. L., & Tenenbaum, J. B. (2014). One and done? Optimal decisions from very few samples. Cognitive Science, 38, 599–637.CrossRefPubMedGoogle Scholar
  103. Wason, P. C. (1968). Reasoning about a rule. Quarterly Journal of Experimental Psychology, 20(3), 273–281.CrossRefPubMedGoogle Scholar
  104. Wilson, T. D., Houston, C. E., Etling, K. M., & Brekke, N. (1996). A new look at anchoring effects: Basic anchoring and its antecedents. Journal of Experimental Psychology: General, 125(4), 387.CrossRefGoogle Scholar
  105. Wright, W. F., & Anderson, U. (1989). Effects of situation familiarity and financial incentives on use of the anchoring and adjustment heuristic for probability assessment. Organizational Behavior and Human Decision Processes, 44(1), 68–82.CrossRefGoogle Scholar
  106. Zhang, Y. C., & Schwarz, N. (2013). The power of precise numbers: A conversational logic analysis. Journal of Experimental Social Psychology, 49(5), 944–946.CrossRefGoogle Scholar

Copyright information

© Psychonomic Society, Inc. 2017

Authors and Affiliations

  • Falk Lieder
    • 1
    • 2
  • Thomas L. Griffiths
    • 1
    • 5
  • Quentin J. M. Huys
    • 2
    • 4
  • Noah D. Goodman
    • 3
  1. 1.Helen Wills Neuroscience InstituteUniversity of CaliforniaBerkeleyUSA
  2. 2.Translational Neuromodeling Unit, Institute for Biomedical EngineeringUniversity of Zürich and Swiss Federal Institute of Technology (ETH)ZürichSwitzerland
  3. 3.Department of PsychologyStanford UniversityStanfordUSA
  4. 4.Department of Psychiatry, Psychotherapy and Psychosomatics, Hospital of PsychiatryUniversity of ZürichZürichSwitzerland
  5. 5.Department of PsychologyUniversity of CaliforniaBerkeleyUSA

Personalised recommendations