Abstract
Human decision makers think categorically when facing a great variety of objects due to their limited information processing capacities. The categorical thinking by Bayesian decision makers is modeled as classifying objects into a small number of categories with respect to their prior probabilities. The classification follows a quantization rule for the prior probabilities. The categorical thinking enables decision makers to handle infinitely many objects but simultaneously causes them to lose precision of prior probabilities and, consequently, of decisions. This chapter considers group decision making by imperfect agents that only knowquantized prior probabilities for use in Bayesian likelihood ratio tests. Global decisions are made by information fusion of local decisions, but information sharing among agents before local decision making is forbidden. The quantization rule of the agents is investigated so as to achieve the minimum mean Bayes risk; optimal quantizers are designed by a novel extension to the Lloyd-Max algorithm. It is proven that agents using identical quantizers are not optimal. Thus diversity in the individual agents’ quantizers leads to optimal performance. In addition, for comparison, it is shown how much their performance gets better when information sharing and collaboration among agents before local decision making is allowed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Brase, G.L., Cosmides, L., Tooby, J.: Individuation, counting, and statistical inference: the role of frequency and whole-object representations in judgment under uncertainty. Journal of Experimental Psychology: General 127(1), 3–21 (1998)
Chugh, D.: Societal and managerial implications of implicit social cognition: Why milliseconds matter. Social Justice Research 17(2), 203–222 (2004)
Cosmides, L., Tooby, J., Kurzban, R.: Perceptions of race. Trends in Cognitive Sciences 7(4), 173–179 (2003)
David, H.A., Nagaraja, H.N.: Order Statistics, 3rd edn. John Wiley & Sons, Hoboken (2003)
Dow, J.: Search decisions with limited memory. Review of Economic Studies 58(1), 1–14 (1991)
Fryer, R., Jackson, M.O.: A categorical model of cognition and biased decision making. The B.E. Journal of Theoretical Economics 8(1) (2008)
Gersho, A., Gray, R.M.: Vector Quantization and Signal Compression. Kluwer Academic Publishers, Norwell (1992)
Glanzer, M., Hilford, A., Maloney, L.T.: Likelihood ratio decisions in memory: Three implied regularities. Psychonomic Bulletin & Review 16(3), 431–455 (2009)
Macrae, C.N., Bodenhausen, G.V.: Social cognition: Thinking categorically about others. Annual Review of Psychology 51, 93–120 (2000)
Miller, G.A.: The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review 63(2), 81–97 (1956)
Piccionea, M., Rubinstein, A.: On the interpretation of decision problems with imperfect recall. Games and Economic Behavior 20(1), 3–24 (1997)
Radner, R.: Team decision problems. The Annals of Mathematical Statistics 33(3), 857–881 (1962)
Radner, R.: Costly and bounded rationality in individual and team decision-making. In: Dosi, G., Teece, D.J., Chytry, J. (eds.) Understanding Industrial and Corporate Change, pp. 3–35. Oxford University Press, Oxford (2005)
Rhim, J.B., Varshney, L.R., Goyal, V.K.: Quantization of prior probabilities for collaborative distributed hypothesis testing. IEEE Trans. Signal Process (to appear)
Rhim, J.B., Varshney, L.R., Goyal, V.K.: Collaboration in distributed hypothesis testing with quantized prior probabilities. In: Proc. IEEE Data Compression Conf., Snowbird, UT, pp. 303–312 (2011)
Rhim, J.B., Varshney, L.R., Goyal, V.K.: Conflict in distributed hypothesis testing with quantized prior probabilities. In: Proc. IEEE Data Compression Conf., Snowbird, UT, pp. 313–322 (2011)
Swets, J.A., Tanner Jr., W.P., Birdsall, T.G.: Decision process in perception. Psychological Review 68(5), 301–340 (1961)
van Trees, H.L.: Detection, Estimation, and Modulation Theory, Part I. John Wiley & Sons, New York (1968)
Varshney, K.R., Varshney, L.R.: Quantization of prior probabilities for hypothesis testing. IEEE Trans. Signal Process. 56(10), 4553–4562 (2008)
Varshney, K.R., Varshney, L.R.: Multilevel minimax hypothesis testing. In: Proc. IEEE/SP Workshop Stat., Nice, France, pp. 109–112 (2011)
Varshney, L.R., Rhim, J.B., Varshney, K.R., Goyal, V.K.: Categorical decision making by people, committees, and crowds. In: Proc. Information Theory and Applications Workshop, La Jolla, CA (2011)
Wilson, A.: Bounded memory and biases in information processing. NajEcon Working Paper Reviews (2003), http://www.najecon.org
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Rhim, J.B., Varshney, L.R., Goyal, V.K. (2013). Distributed Decision Making by Categorically-Thinking Agents. In: Guy, T., Karny, M., Wolpert, D. (eds) Decision Making and Imperfection. Studies in Computational Intelligence, vol 474. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36406-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-36406-8_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36405-1
Online ISBN: 978-3-642-36406-8
eBook Packages: EngineeringEngineering (R0)