Criticality triggers the emergence of collective intelligence in groups

A spinlike model mimicking human behavior in groups is employed to investigate the dynamics of the decision-making process. Within the model, the temporal evolution of the state of systems is governed by a time-continuous Markov chain. The transition rates of the resulting master equation are defined in terms of the change of interaction energy between the neighboring agents (change of the level of conflict) and the change of a locally defined agent fitness. Three control parameters can be identified: (i) the social interaction strength $\beta J$ measured in units of social temperature, (ii) the level of confidence ${\beta }^{\prime }$ that each individual has on his own expertise, and (iii) the level of knowledge $p$ that identifies the expertise of each member. Based on these three parameters, the phase diagrams of the system show that a critical transition front exists where a sharp and concurrent change in fitness and consensus takes place. We show that at the critical front, the information leakage from the fitness landscape to the agents is maximized. This event triggers the emergence of the collective intelligence of the group, and in the end it leads to a dramatic improvement in the decision-making performance of the group. The effect of size $M$ of the system is also investigated, showing that, depending on the value of the control parameters, increasing $M$ may be either beneficial or detrimental.

Figure 1

The multiplex network utilized to build up the model. Observe that on each decision layer the structure of the social network (blue links) may be different. Blue links identify those spins (on a given layer) that interact through an Ising-like interaction energy. Red dashed links connect the different decision layers. These types of links identify, for any given member, the interaction among spins on the different decision layer, leading to an additional energy term that provides the fitness of each single member of the group.

Figure 2

The stationary values of the normalized averaged fitness $V_{\infty }$ (a) and of the statistically averaged consensus ${\chi }_{\infty }$ (b) as a function of $\beta J$. Results are presented for ${\beta }^{\prime }=10$, $p=1$, $N=15$, and $K=14$, and for three different team sizes $M=7$, 21, and 100.

Figure 3

The stationary values of the normalized averaged fitness $V_{\infty }$ (a) and of the statistically averaged consensus ${\chi }_{\infty }$ (b) as a function of $\beta J$. Results are presented for ${\beta }^{\prime }=5$, $p=1$, $N=15$, and $K=14$, and for three different team sizes: $M=7$, 21, and 100.

Figure 4

The stationary values of the normalized averaged fitness $V_{\infty }$ (a) and of the statistically averaged consensus ${\chi }_{\infty }$ (b) as a function of $\beta J$ and ${\beta }^{\prime }$. The phase diagram is represented in (c). Results are presented for $p=1$, $N=15$, $K=14$, and $M=7$.

Figure 5

The stationary values of the normalized averaged fitness $V_{\infty }$ (a) and of the statistically averaged consensus ${\chi }_{\infty }$ (b) as a function of $\beta J$ and ${\beta }^{\prime }$. The phase diagram is represented in (c). Results are presented for $p=1$, $N=15$, $K=14$, and $M=21$.

Figure 6

The critical critical transition fronts for $M=7$ (blue line) and $M=21$ (red line). Results are presented for $p=1$, $N=15$, and $K=14$. On the thick part of the lines, the critical transition is sharp and is associated with a very large step from low to high fitness. On the thin line, the critical transition is smeared and the step change in fitness is smaller. It even decreases as one moves along the line to increase ${\beta }^{\prime }$. Note that increasing $M$ from 7 to 21 makes the point $P_{min}$ move to $Q_{min}$, thus ${\beta }_{min}^{\prime }$ decreases significantly whereas ${\left(\beta J\right)}_{min}$ increases slightly.

Figure 7

The mutual information $\text{MI}\left({\chi }_{\infty },V_{\infty }\right)$, in color scale (blue for low values, red for high values), between the consensus ${\chi }_{\infty }$ and the group fitness $V_{\infty }$, $M=7$ (a) and $M=21$ (b). Results are presented for $p=1$, $N=15$, and $K=14$. Notice that $\text{MI}\left({\chi }_{\infty },V_{\infty }\right)$ is small everywhere but close to the critical front, where it takes higher values. The highest mutual information is obtained for ${\beta }^{\prime }<{\beta }_{min}^{\prime }$.

Figure 8

The stationary values of the normalized averaged fitness $V_{\infty }$ as a function of $\beta J$ and ${\beta }^{\prime }$. Results are presented for $p=0.3$ (a), $p=0.7$ (b), $p=1$ (c), and for $N=15$, $K=14$, and $M=7$.

Figure 9

The critical transition fronts for different levels of knowledge of the agents: $p=0.3$, 0.7, and 1. Results are presented for $N=15$, $K=14$, and $M=21$. Note that decreasing $p$ reduces ${\beta }_{min}^{\prime }$ and increases ${\left(\beta J\right)}_{min}$.

Figure 10

The stationary values of the normalized averaged fitness $V_{\infty }$ as a function of $\beta J$ and $\alpha$. Results are presented for $p=1$, $N=15$, $K=14$, $M=7$, and ${\beta }_L^{\prime }=5$ (a), ${\beta }_L^{\prime }=10$ (b).

Figure 11

The occurrence of groupthink. Far from the critical threshold, i.e., for high values of the social interaction strength (high level of trust), the pressure for consensus seeking makes the members completely overlook the effect of their decision on their own perceived fitness. The dynamics of the system resemble the classical dynamics of a pure Ising-like system. This leads to a high value of consensus ${\chi }_{\infty }$ (b) but to a very low value of group fitness $V_{\infty }$ (a). Results are presented for $p=1$, $N=15$, $K=14$, $M=7$, and for ${\beta }^{\prime }=5$ and 10.