Science Advances

Supplementary Materials

This PDF file includes:

  • section S1. Background on models of decision-making
  • section S2. Study system
  • section S3. Skewness of DSP
  • section S4. Dimensionality and initial conditions
  • section S5. Analogous model of neural decision-making
  • section S6. Derivation of partial differential equations for decision time, error rate, and probability of reaching decision preference
  • section S7. Nash equilibria
  • section S8. A notion of correctness for biological computation
  • section S9. Calculation of mutual information
  • section S10. Most informative measures of consensus
  • section S11. Tuning waiting costs
  • section S12. Comparison of our model to previous studies of animal conflict
  • section S13. War of attrition
  • section S14. Supplementary table
  • section S15. Supplementary figures
  • table S1. Examples of collective computation.
  • fig. S1. Error rate decreases as decision time increases, as long as the initial conditions are not biased toward the correct decision.
  • fig. S2. The mutual information of the power scores computed by a group using Nash thresholds increases as the weight given to decision preference increases, as long as there are nonzero waiting costs.
  • fig. S3. The average skewness of the distribution of eigenvector centrality is maximized at intermediate waiting costs.
  • fig. S4. The best measure of consensus in the decision network depends on the average error rate and the types of errors being made.
  • fig. S5. Schematic of the model.
  • fig. S6. The error rate of a group using Nash thresholds decreases as the weight given to decision preference increases, regardless of the size of the group.
  • fig. S7. Pairs with similar and high abilities always take as long or longer to make a decision than any other pairs do.
  • fig. S8. The mutual information of each consensus algorithm is a decreasing function of the average pairwise error rate.
  • fig. S9. The average skewness of the distribution of unweighted in-degree is maximized at intermediate waiting costs.
  • fig. S10. The average skewness of the distribution of consensus scores from each measure is maximized at intermediate waiting costs.
  • fig. S11. The average skewness of the distribution of consensus scores from each measure is maximized at intermediate waiting costs.
  • fig. S12. When a pair of animals have equal fighting abilities, c = 0.5, there are asymmetric Nash equilibrium thresholds.
  • References (55–59)

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