Fig 1.
Distribution of the influence factor.
The histograms show the frequency for the influence factor I recorded in the experiment. Percentages stand for the frequencies of answers (rounded to integer values) where the opinion is kept unchanged (I = 0), where the reference opinion is adopted (I = 1), and where a compromise is reached (0 < I < 1). The columns corresponding to I = 0 and I = 1 respectively incorporate the answers with I < 0 and I > 1. A: Individual influence (class A questions). B: Group influence (class B questions).
Fig 2.
Distribution of answers according to opinion and confidence differences.
A: Each dot in the plot corresponds to a pair of answers, with coordinates given by the corresponding opinion and confidence differences, δr and δc. Colors and sizes code the three answer categories, as indicated in the legend. Ellipses give the standard-deviation intervals around the mean value of each category, following the same color coding. B: The frequency of answers corresponding to two categories (keep and adopt) as a function of the confidence difference. Curves are polynomial fittings to the data: fK = 1 − 0.04(5 − δc) − .005(5 − δc)2, and fA = 6.2 × 10−4(5 − δc)3. The least-square regression coefficients are R2 = 0.96 and 0.98, respectively.
Fig 3.
Distribution of changes in the confidence level.
The histogram shows the frequencies for the confidence change between rounds, Δc = c′ − c, for class A questions (see also S2 Table). The frequency is exactly equal to zero for Δc < −2 and Δc > 4. By far, the most frequent value is Δc = 0, with about 71% of the cases. The distribution is biased towards positive values, with a total of 26% and 3% of the cases for Δc > 0 and Δc < 0, respectively.
Table 1.
Frequencies of confidence levels.
First line: as measured in the first round of the experiment. Second line: theoretical stationary values.
Fig 4.
Evolution of the average opinion and the standard deviation.
The plots show simulation results for a population of 104 agents, whose initial opinions where normally distributed and whose confidence is distributed as observed in the first round of the experiment. Results are plotted as functions of the number of events per agent. Straight lines stand for the analytical prediction of exponential slopes (see S3 Text). A: Without opinion leaders. B: With one opinion leader, whose opinion is R = 0.2. The leader’s influence factor is distributed as for any ordinary agent, but the leader is chosen as a reference 100 times more often than any other agent. The insets are close-ups of the initial evolution stage.
Fig 5.
Opinion distributions under the influence of two leaders.
The histograms show simulation results for the stationary distribution of opinions in a population of 104 agents, with the same initial condition as in Fig 4. The leaders have fixed opinions R1 = 0.2 and R2 = −0.1, and they are chosen as references with frequencies α1 = α and α2 = 4α, respectively. The four panels correspond to different values of α, as indicated by the labels. The leaders’ influence is such that, upon interaction with a leader, ordinary agents always adopt the leader’s opinion.