Fig. 2.

Results of two hypothetical studies of collective decision making. (A–C) Predicted observations made from a symmetric experimental setup ($x=0$). (D–F) Predicted observations from an experiment in which option A is superior by an amount typical in the habitual environment ($x=\sqrt{2/\pi }$). (A and D) The probability, from the perspective of an external observer, that a focal agent will choose option A, conditioned on the number of agents, $n_A,n_B$, previously choosing options A and B, respectively. (B and E) The probability of the focal agent selecting option A against the proportion of previous agents selecting A. Red circles indicate the average across all possible sequences of previous choices, while black circles indicate probabilities conditioned on specific sequences (discretized to intervals of 0.05), with larger points indicating more likely sequences. The average trend shows the relationship that would be observed in an experiment where sequence information was discarded. (C and F) The probability of possible aggregate outcomes, defined as the number of agents in total that will select option A, showing the high probability of consensus decisions and of collectively choosing the higher-utility option in the asymmetric scenario.