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Microscopic modeling and analysis of collective decision making: equality bias leads suboptimal solutions. (English) Zbl 1408.91060

Summary: We discuss a novel microscopic model for collective decision-making interacting multi-agent systems. In particular we are interested in modeling a well known phenomena in the experimental literature called equality bias, where agents tend to behave in the same way as if they were as good, or as bad, as their partner. We analyze the introduced problem and we prove the suboptimality of the collective decision-making in the presence of equality bias. Numerical experiments are addressed in the last section.

MSC:

91B06 Decision theory
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[1] Albi, G., Pareschi, L.: Modeling of self-organized systems interacting with a few individuals: from microscopic to macroscopic dynamics. Appl. Math. Lett. 26(4), 397-401 (2013) · Zbl 1257.92048 · doi:10.1016/j.aml.2012.10.011
[2] Albi, G., Herty, M., Pareschi, L.: Kinetic description of optimal control problems and applications to opinion consensus. Commun. Math. Sci. 13(6), 1407-1429 (2015) · Zbl 1325.49001 · doi:10.4310/CMS.2015.v13.n6.a3
[3] Albi, G.; Pareschi, L.; Toscani, G.; Zanella, M.; Bellomo, N. (ed.); Degond, P. (ed.); Tadmor, E. (ed.), Recent advances in opinion modeling: control and social influence (2017), Berlin
[4] Albi, G., Pareschi, L., Zanella, M.: Boltzmann-type control of opinion consensus through leaders. Philos. Trans. R. Soc. Lond. A: Math. Phys. Eng. Sci. 372(2028), 20140138 (2014) · Zbl 1353.91038 · doi:10.1098/rsta.2014.0138
[5] Albi, G., Pareschi, L., Zanella, M.: Uncertainty quantification in control problems for flocking models. Math. Probl. Eng. 2015, 14 (2015) · Zbl 1394.93074 · doi:10.1155/2015/850124
[6] Albi, G., Pareschi, L., Zanella, M.: Opinion dynamics over complex networks: kinetic modelling and numerical methods. Kinet Relat Models 10(1), 1-32 (2017) · Zbl 1352.35195
[7] Bahrami, B., Olsen, K., Latham, P.E., Roepstorff, A., Rees, G., Frith, C.D.: Optimally interacting minds. Science 329(5995), 1081-1085 (2010) · doi:10.1126/science.1185718
[8] Brugna, C., Toscani, G.: Kinetic models of opinion formation in the presence of personal conviction. Phys. Rev. E 92(5), 052818 (2015) · doi:10.1103/PhysRevE.92.052818
[9] Cañizo, J.A., Carrillo, J.A., Rosado, J.: A well-posedness theory in measures for some kinetic models of collective behavior. Math. Models Methods Appl. Sci. 21(3), 515-539 (2011) · Zbl 1218.35005 · doi:10.1142/S0218202511005131
[10] Carrillo, J.A., Fornasier, M., Rosado, J., Toscani, G.: Asymptotic flocking dynamics for the kinetic Cucker-Smale model. SIAM J. Math. Anal. 42(1), 218-236 (2010) · Zbl 1223.35058 · doi:10.1137/090757290
[11] Carrillo, JA; Fornasier, M.; Toscani, G.; Vecil, F.; Naldi, G. (ed.); Pareschi, L. (ed.); Toscani, G. (ed.), Particle, kinetic and hydrodynamic models of swarming, 297-336 (2010), Boston · Zbl 1211.91213 · doi:10.1007/978-0-8176-4946-3_12
[12] Castellano, C., Fortunato, S., Loreto, V.: Statistical physics of social dynamics. Rev. Mod. Phys. 81(2), 591 (2009) · doi:10.1103/RevModPhys.81.591
[13] Chakraborti, A., Chakrabarti, B.K.: Statistical mechanics of money: how saving propensity affects its distribution. Eur. Phys. J. B-Condens. Matter Complex Syst. 17(1), 167-170 (2000) · doi:10.1007/s100510070173
[14] Cristiani, E., Piccoli, B., Tosin, A.: Multiscale Modeling of Pedestrian Dynamics, MS&A: Modeling, Simulation and Applications, vol. 12. Springer, Berlin (2014) · Zbl 1314.00081
[15] Cucker, F., Smale, S.: Emergent behavior in flocks. IEEE Trans. Autom. Control 52(5), 852-862 (2007) · Zbl 1366.91116 · doi:10.1109/TAC.2007.895842
[16] D’Orsogna, M.R., Chuang, Y.L., Bertozzi, A.L., Chayes, L.S.: Self-propelled particles with soft-core interactions: patterns, stability and collapse. Phys. Rev. Lett. 96(10), 104-302 (2006)
[17] Düring, B., Markowich, P., Pietschmann, J.F., Wolfram, M.-T.: Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders. Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci. 465(2112), 3687-3708 (2009) · Zbl 1195.91127 · doi:10.1098/rspa.2009.0239
[18] Galam, S.: Rational group decision making: a random field Ising model at T=0. Phys. A. Stat. Mech. Appl. 238((1-4)), 66-80 (1997) · doi:10.1016/S0378-4371(96)00456-6
[19] Galam, S., Zucker, J.-D.: From individual choice to group decision-making. Phys. A. Stat. Mech. Appl. 287, 644-659 (2000) · doi:10.1016/S0378-4371(00)00399-X
[20] Galton, F.: One vote, one value. Nature 75, 414-414 (1907) · JFM 38.0288.03 · doi:10.1038/075414a0
[21] Harvey, N., Fischer, I.: Taking advice: accepting help, improving judgment, and sharing responsibility. Organ. Behav. Hum. Decis. Process. 70(2), 117-133 (1997) · doi:10.1006/obhd.1997.2697
[22] Herty, M., Zanella, M.: Performance bounds for the mean-field limit of constrained dynamics. Discrete Contin. Dyn. Syst. A 37(4), 2023-2043 (2017) · Zbl 1366.35203 · doi:10.3934/dcds.2017086
[23] Kruger, J., Dunning, D.: Unskilled and unaware of it: how difficulties in recognizing one’s incompetence lead to inflated self-assessments. J. Pers. Soc. Psychol. 77(6), 1121-1134 (1999) · doi:10.1037/0022-3514.77.6.1121
[24] Mahmoodi, A., Bang, D., Olsen, K., Zhao, Y.A., Shi, Z., Broberg, K., Safavi, S., Han, S., Ahmadabadi, M.N., Frith, C.D., Roepstorff, A., Rees, G., Bahrami, B.: Equality bias impairs collective decision-making across cultures. Proc. Natl. Acad. Sci. 112(12), 3835-3840 (2015)
[25] Motsch, S., Tadmor, E.: Heterophilious dynamics enhances consensus. SIAM Rev. 56(4), 577-621 (2014) · Zbl 1310.92064 · doi:10.1137/120901866
[26] Motsch, S., Tadmor, E.: A new model for self-organized dynamics and its flocking behavior. J. Stat. Phys. 144(5), 923-947 (2011) · Zbl 1230.82037 · doi:10.1007/s10955-011-0285-9
[27] Pareschi, L., Toscani, G.: Wealth distribution and collective knowledge: a Boltzmann approach. Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 372(2028), 20130396 (2014) · Zbl 1353.91036 · doi:10.1098/rsta.2013.0396
[28] Pareschi, L., Toscani, G.: Interacting Multiagent Systems: Kinetic Equations and Monte Carlo Methods. Oxford University Press, Oxford (2013) · Zbl 1330.93004
[29] Pareschi, L., Vellucci, P., Zanella, M.: Kinetic models of collective decision-making in the presence of equality bias. Phys. A. Stat. Mech. Appl. 467, 201-217 (2017) · Zbl 1400.91141 · doi:10.1016/j.physa.2016.10.003
[30] Shen, J.: Cucker-Smale flocking under hierarchical leadership. SIAM J. Appl. Math. 68(3), 694-719 (2007) · Zbl 1311.92196 · doi:10.1137/060673254
[31] Toscani, G.: Kinetic models of opinion formation. Commun. Math. Sci. 4(3), 481-496 (2006) · Zbl 1195.91128 · doi:10.4310/CMS.2006.v4.n3.a1
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