Figure 1.
Schematic representation of the model.
Individuals receive pieces of information from the media (1) and from their peers (2). Each piece of information k is given a weight by the individual i and stored in his or her memory (3). The collection of weighted information an individual i owns is finally used to determine the level of risk perception ri (4). Circled numbers indicate different steps of the elaboration of the model as described in the main text. All model parameters and variables are summarized in tables 1 and 2, respectively.
Table 1.
Description of model parameters and the corresponding values used in the numerical simulations.
Table 2.
Description of model variables and their initial values as used in the numerical simulations.
Figure 2.
Graphical representation of the risk perception function
. The function indicates the perception of risk of an individual owning a total amount of information
and
indicating the danger and the safety of the situation, respectively. The function parameters are set to
= 0.8, and
= 0.2. In the absence of any information, the risk perception level is 0, whereas large and well-balanced amounts of information for both sides yield a risk level of 0.5. The function always returns a value between 0 and 1.
Figure 3.
Three representative examples of the model predictions.
(a) With low levels of independent search and social influence
, opposed judgments coexist in the population but the clustering level is low. (b) As the weight of social influence increases, clusters of neighboring people with similar views emerge. (c) When the levels of independent search and social influence are both high, individuals tend to converge towards a global consensus with a risk perception close to 0.5, corresponding to a well-balance judgment. Simulations were conducted with N = 2500 agents (i.e. grid size of 50×50).
Figure 4.
Collective dynamics of the system as a function of the weight of independent search , and the weight of social influence
.
(a) The polarization level indicates how much the views of individuals in the population differ. It is measured as the standard deviation of opinion distribution. A polarization of 0 indicates a global consensus while high values indicate a divergence of opinions in the population. (b) The local difference is the average absolute difference between an individuals’ opinion and his or her direct neighbors. Low values can indicate a global consensus (such as the example shown Fig. 2c, which lies in the upper right corner of the maps), or local clustering (such as the example show Fig. 2b, which lies in the lower right corner of the map). (c) The clustering level is the polarization of the population divided by the local difference. Therefore, the clustering is high when different opinions coexist in the population and a strong agreement is found among neighboring people. (d) The average percentage of all available information that are known by individuals. Results are averaged over 50 simulations with model parameters identical to those used in figure 3.
Figure 5.
Three representative examples of the search patterns emerging from the model.
The three examples correspond to the same set of parameters as in Figure 3. (a) With low levels of independent search and social influence
, the search volume is constant and low. (b) A spiky search pattern followed by a slow relaxation is visible when
= 0.1 and
= 1. (c) When both variables are high, the search volume stays high during a certain amount of time, until all individuals become inactive almost simultaneously. The search volume corresponds to the number of individuals who engaged in an independent search per unit of time.
Figure 6.
The dynamics of information flow as observed during simulations.
(a) Illustrative example of how one particular piece of information k spreads in the population. The color-coding shows the local information flow, measured as the number of time the information k has been communicated to an individual i. Dark blue zones indicate individuals how have never heard of information k, whereas those who received the information 20 times are colored in dark red. (b) Distribution of the local flow over all pieces of information. The skewed distribution indicates that information spreads unequally in the population. (c) The risk perception of individuals as a function of the average number of information they have received. The grey zone indicates the standard deviation of the average. The visible reverse-U shape indicates that individuals expressing extreme opinions are on average less informed than those having a moderate risk judgment. Results are averaged over 50 simulations with parameters = 0.1 and
= 0.9, corresponding to the bottom right corner of the maps presented in figure 4.