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How social information can improve estimation accuracy in human groups

  1. Guy Theraulazb,e,1
  1. aLaboratoire de Physique Théorique, CNRS, Université de Toulouse (Paul Sabatier), 31062 Toulouse, France;
  2. bCentre de Recherches sur la Cognition Animale, Centre de Biologie Intégrative, CNRS, Université de Toulouse, 31062 Toulouse, France;
  3. cDepartment of Behavioral Science, Hokkaido University, 060-0810 Sapporo, Japan;
  4. dToulouse School of Economics, Institut National de la Recherche Agronomique (INRA), Université de Toulouse (Capitole), 31000 Toulouse, France;
  5. eInstitute for Advanced Study in Toulouse, 31015 Toulouse, France;
  6. fToulouse School of Economics, Université de Toulouse (Capitole), 31000 Toulouse, France;
  7. gDepartment of Social Psychology, The University of Tokyo, 113-0033 Tokyo, Japan
  1. Edited by Burton H. Singer, University of Florida, Gainesville, FL, and approved October 2, 2017 (received for review March 5, 2017)

  1. Fig. 2.

    (A) Mean sensitivity to social influence <mml:math><mml:mi>S</mml:mi></mml:math>S against the distance <mml:math><mml:mrow><mml:mpadded width="+1.7pt"><mml:mi>D</mml:mi></mml:mpadded><mml:mo>=</mml:mo><mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mo>?</mml:mo><mml:mi>M</mml:mi></mml:mrow></mml:mrow></mml:math>D=Xp?M between personal estimate <mml:math><mml:msub><mml:mi>X</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:math>Xp and social information <mml:math><mml:mi>M</mml:mi></mml:math>M (group estimate). Black circles correspond to experimental data, while red open circles are simulations of the model. Note that only about <mml:math><mml:mrow><mml:mpadded width="+1.7pt"><mml:mn>14</mml:mn></mml:mpadded><mml:mo>%</mml:mo></mml:mrow></mml:math>14% of data are beyond three orders of magnitude. (B) Fraction of subjects keeping (maroon), adopting (pink), and being in the Gaussian-like part of the distribution of <mml:math><mml:mi>S</mml:mi></mml:math>S (mostly compromisers; purple) against <mml:math><mml:mi>D</mml:mi></mml:math>D.

  2. Fig. 3.

    Collective performance, defined as the absolute value of the median of estimates (A) and width of the distribution of estimates (B), for all <mml:math><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>ρ</mml:mi><mml:mo>,</mml:mo><mml:mi>τ</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>(ρ,τ) before (blue) and after (red) social influence. Both improve with <mml:math><mml:mi>ρ</mml:mi></mml:math>ρ after social influence, except for the collective performance at <mml:math><mml:mrow><mml:mpadded width="+1.7pt"><mml:mi>ρ</mml:mi></mml:mpadded><mml:mo>=</mml:mo><mml:mrow><mml:mpadded width="+1.7pt"><mml:mn>0</mml:mn></mml:mpadded><mml:mo>%</mml:mo></mml:mrow></mml:mrow></mml:math>ρ=0%. Full circles correspond to experimental data, while open circles represent the predictions of the full model. The black lines are the predictions of the simple solvable model presented in SI Appendix. For <mml:math><mml:mrow><mml:mpadded width="+1.7pt"><mml:mi>ρ</mml:mi></mml:mpadded><mml:mo>=</mml:mo><mml:mrow><mml:mpadded width="+1.7pt"><mml:mn>60</mml:mn></mml:mpadded><mml:mo>%</mml:mo></mml:mrow></mml:mrow></mml:math>ρ=60%, only model predictions are available.

  3. Fig. 4.

    Collective accuracy (median distance to the truth of individual estimates) before (blue) and after (red) social influence against <mml:math><mml:mi>ρ</mml:mi></mml:math>ρ for the five behavioral categories identified in Fig. 1B and for the whole group (all). Adopting leads to the sharpest improvement and the best accuracy for <mml:math><mml:mrow><mml:mpadded width="+1.7pt"><mml:mi>ρ</mml:mi></mml:mpadded><mml:mo>≥</mml:mo><mml:mrow><mml:mpadded width="+1.7pt"><mml:mn>40</mml:mn></mml:mpadded><mml:mo>%</mml:mo></mml:mrow></mml:mrow></mml:math>ρ≥40%. Full circles correspond to experimental data, while open circles represent the predictions of the model (including for <mml:math><mml:mrow><mml:mpadded width="+1.7pt"><mml:mi>ρ</mml:mi></mml:mpadded><mml:mo>=</mml:mo><mml:mn>60</mml:mn></mml:mrow></mml:math>ρ=60%, a case not tested experimentally).

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