Research ArticleCOMPUTATIONAL BIOLOGY

Polya’s bees: A model of decentralized decision-making

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Science Advances  18 Sep 2015:
Vol. 1, no. 8, e1500253
DOI: 10.1126/sciadv.1500253
  • Fig. 1 Pareto frontiers of mistake probability and expected waiting time with 2 and 4 options.

    The optimal choice has quality vc* = 2, whereas the suboptimal choices have quality vc = 1 for all cc*. As an artifact of specifying recruitment (that is, choice quality) so precisely, there are thresholds for which the decision is both slower and less accurate than for a threshold one unit smaller. The corresponding points on the graph are clearly not on the Pareto frontier, but they are shown for completeness.

  • Fig. 2 Pareto frontiers of mistake probability and expected waiting time with varying choice quality.

    Left: Varying optimal choice quality. There are C = 2 possible choices, and the quality of the suboptimal choice is v~c* = 1. Right: Varying suboptimal choice quality. There are C = 2 possible choices, and the quality of the optimal choice is vc* = 4.

  • Fig. 3 Probability of selecting the safe option over a risky option with the same expected quality for a fixed quorum threshold of 100.

    There are C = 2 options. The safe option has quality vSafe = 2. The riskiness of the risky option is indexed by the potential reward R such that the quality of the risky option is Embedded Image that is, it has expected quality 2 and variance R − 2.

  • Fig. 4 Pareto frontiers of mistake probability and expected waiting time with varying rates of discovery, recruitment, and disruption.

    There are C = 2 options. The optimal choice has quality vc* = 2, and the suboptimal choice has quality v~c* = 1. The rate of discovery βc is the same for both options, and it varies across the columns. The agents’ hazard rate of disruption δ varies across the rows. The agents’ rate of recruitment λ varies within each panel.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/1/8/e1500253/DC1

    Fig. S1. Mistake probability and expected waiting time as a function of the quorum threshold with 2 and 4 possible options.

    Fig. S2. Mistake probability and expected waiting time as a function of the quorum threshold, varying the quality of the optimal choice.

    Fig. S3. Mistake probability and expected waiting time as a function of the quorum threshold, varying the quality of the suboptimal choice.

    Fig. S4. Mistake probability and expected waiting time as a function of the quorum threshold in noisy and noiseless environments.

    Fig. S5. Probability of selecting a safe option with quality vSafe = 2 over a risky one with quality vRisky = {1,50%;3,50%}, as a function of the quorum threshold.

    Fig. S6. Probability of selecting a safe option with quality vSafe = 1 over a risky one with quality Formula for a quorum threshold of τ = R + 1.

    Fig. S7. Mistake probability and expected waiting time as a function of the quorum threshold, with varying rates of discovery, recruitment, and disruption.

    An Ancillary Result

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Mistake probability and expected waiting time as a function of the quorum threshold with 2 and 4 possible options.
    • Fig. S2. Mistake probability and expected waiting time as a function of the quorum threshold, varying the quality of the optimal choice.
    • Fig. S3. Mistake probability and expected waiting time as a function of the quorum threshold, varying the quality of the suboptimal choice.
    • Fig. S4. Mistake probability and expected waiting time as a function of the quorum threshold in noisy and noiseless environments.
    • Fig. S5. Probability of selecting a safe option with quality vSafe = 2 over a risky one with quality vRisky = {1,50%;3,50%}, as a function of the quorum threshold.
    • Fig. S6. Probability of selecting a safe option with quality vSafe = 1 over a risky one with quality see PDF for equation for a quorum threshold of t = R + 1.
    • Fig. S7. Mistake probability and expected waiting time as a function of the quorum threshold, with varying rates of discovery, recruitment, and disruption.
    • An Ancillary Result

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