Kinetic models of collective decision-making in the presence of equality bias

We introduce and discuss kinetic models describing the influence of the competence in the evolution of decisions in a multi-agent system. The original exchange mechanism, which is based on the human tendency to compromise and change opinion through self-thinking, is here modified to include the role of the agents’ competence. In particular, we take into account the agents’ tendency to behave in the same way as if they were as good, or as bad, as their partner: the so-called equality bias. This occurred in a situation where a wide gap separated the competence of group members. We discuss the main properties of the kinetic models and numerically investigate some examples of collective decision under the influence of the equality bias. The results confirm that the equality bias leads the group to suboptimal decisions.

[1]  Jonathan D. Cohen,et al.  The physics of optimal decision making: a formal analysis of models of performance in two-alternative forced-choice tasks. , 2006, Psychological review.

[2]  Lara Trussardi,et al.  A kinetic equation for economic value estimation with irrationality and herding , 2016, 1601.03244.

[3]  Giuseppe Toscani,et al.  Kinetic models of opinion formation in the presence of personal conviction. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Bikas K. Chakrabarti,et al.  Statistical mechanics of money: how saving propensity affects its distribution , 2000, cond-mat/0004256.

[5]  L Pareschi,et al.  Wealth distribution and collective knowledge: a Boltzmann approach , 2014, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[6]  Lorenzo Pareschi,et al.  Opinion dynamics over complex networks: kinetic modeling and numerical methods , 2016, ArXiv.

[7]  P. Markowich,et al.  Boltzmann and Fokker–Planck equations modelling opinion formation in the presence of strong leaders , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[8]  T. Lorenzi,et al.  Asymptotic analysis of continuous opinion dynamics models under bounded confidence , 2012 .

[9]  Bikas K. Chakrabarti,et al.  Sociophysics: An Introduction , 2014 .

[10]  Sébastien Motsch,et al.  Heterophilious Dynamics Enhances Consensus , 2013, SIAM Rev..

[11]  Bikas K. Chakrabarti,et al.  Opinion Formation in the Kinetic Exchange Models , 2011 .

[12]  I Poulakakis,et al.  Coupled stochastic differential equations and collective decision making in the Two-Alternative Forced-Choice task , 2010, Proceedings of the 2010 American Control Conference.

[13]  Mattia Zanella,et al.  Performance bounds for the mean-field limit of constrained dynamics , 2015, 1511.08364.

[14]  Lorenzo Pareschi,et al.  An introduction to Monte Carlo method for the Boltzmann equation , 2001 .

[15]  N. Harvey,et al.  Taking Advice: Accepting Help, Improving Judgment, and Sharing Responsibility☆☆☆ , 1997 .

[16]  Lorenzo Pareschi,et al.  Kinetic description of optimal control problems and applications to opinion consensus , 2014, 1401.7798.

[17]  Lorenzo Pareschi,et al.  Reviews , 2014 .

[18]  Roz Dixon,et al.  Ostracism , 2007 .

[19]  Marie-Therese Wolfram,et al.  Opinion dynamics: inhomogeneous Boltzmann-type equations modelling opinion leadership and political segregation , 2015, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[20]  G Albi,et al.  Boltzmann-type control of opinion consensus through leaders , 2014, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[21]  M. Tsige,et al.  Thermodynamics of a stochastic three level elevator model , 2015 .

[22]  Eitan Tadmor,et al.  A New Model for Self-organized Dynamics and Its Flocking Behavior , 2011, 1102.5575.

[23]  P. Latham,et al.  References and Notes Supporting Online Material Materials and Methods Figs. S1 to S11 References Movie S1 Optimally Interacting Minds R�ports , 2022 .

[24]  J. Kruger,et al.  Unskilled and unaware of it: how difficulties in recognizing one's own incompetence lead to inflated self-assessments. , 1999, Journal of personality and social psychology.

[25]  Katarzyna Sznajd-Weron,et al.  Opinion evolution in closed community , 2000, cond-mat/0101130.

[26]  Jean-Daniel Zucker,et al.  From Individual Choice to Group Decision Making , 2000 .

[27]  F. Galton.  One Vote, One Value , 1907, Nature.

[28]  S. Galam.  Rational group decision making: A random field Ising model at T = 0 , 1997, cond-mat/9702163.

[29]  Giuseppe Toscani,et al.  The Grazing Collision Limit of the Inelastic Kac Model around a Lévy-type Equilibrium , 2011, SIAM J. Math. Anal..

[30]  Nigel Harvey,et al.  Confidence in judgment , 1997, Trends in Cognitive Sciences.

[31]  Giuseppe Carbone,et al.  Model of human collective decision-making in complex environments , 2015, The European Physical Journal B.

[32]  R. Hogarth,et al.  Confidence in judgment: Persistence of the illusion of validity. , 1978 .

[33]  Massimo Fornasier,et al.  Fluid dynamic description of flocking via the Povzner–Boltzmann equation , 2011 .

[34]  C. Frith,et al.  Equality bias impairs collective decision-making across cultures , 2015, Proceedings of the National Academy of Sciences.

[35]  G. Toscani,et al.  Kinetic models of opinion formation , 2006 .

[36]  H. Lau,et al.  How to measure metacognition , 2014, Front. Hum. Neurosci..