How networks shape diversity for better or worse

TL;DR

It is found that pronounced inequalities in the distribution of connections obstruct socio-diversity, and the prevalence of close-knit communities, a scarcity of long-range connections, and a significant tie density tend to promote it.

Abstract

Socio-diversity, the variety of human opinions, ideas, behaviors and styles, has profound implications for social systems. While it fuels innovation, productivity, and collective intelligence, it can also complicate communication and erode trust. So what mechanisms can influence it? This paper studies how fundamental characteristics of social networks can support or hinder socio-diversity. It employs models of cultural evolution, mathematical analysis, and numerical simulations. We find that pronounced inequalities in the distribution of connections obstruct socio-diversity. In contrast, the prevalence of close-knit communities, a scarcity of long-range connections, and a significant tie density tend to promote it. These results open new perspectives for understanding how to change social networks to sustain more socio-diversity and, thereby, societal innovation, collective intelligence, and productivity.

Figures (5)

• Figure 1: Illustration of the random social exploration game (A-C) and the progression of cultural evolution in a small social network (D-F). The network features six individuals: Alice ($a$), Bob ($b$), Carla ($c$), Darcy ($d$), Elon ($e$), and Frank ($f$). (A-C) In the random social exploration game, letters sent by Alice and Bob are randomly forwarded through the network until they meet in a mailbox (see main text for details). In this illustration, the letters' journeys are marked by highlighted edges, converging at Elon's mailbox. (D-F) These panels illustrate cultural evolution within our social network in three time steps. Each panel depicts both the present meme distribution and its imminent evolution by colors. An individual's current meme is reflected by the color of their vertex, whereas upcoming changes are represented by the color and direction of arrows pointing toward their vertex. For instance, Alice's red meme in Panel D, transforms into Frank's magenta meme (see Panel E), as indicated by the magenta arrow pointing from Frank to Alice. It is noteworthy that in Panel D, no arrows point towards Elon, suggesting he does not mimic others at $t=1$, but instead introduces a new meme (the black meme).
• Figure 2: Correlation of expected socio-diversity $D_{\infty}$ with the structural diversity index $\Delta(G)$. We simulated the cultural evolution model across various real-world social networks $G$ to determine $D_{\infty}$. Each dot represents a simulation for a distinct social network. The red line depicts the curve $1 - e^{-2\Delta(G)}$, our theoretical estimate for $D_{\infty}$ derived from Eq. (\ref{['eq:duality_short']}) using $\alpha = 1$ (or $r = 1/\lvert V(G) \rvert)$. Remarkably, the structural diversity index predicts expected socio-diversity levels quite accurately, as evidenced by observations scattering around the red line. See Methods for simulation parameters and descriptions of the social networks.
• Figure 3: Numerical simulation (dots) and analytical estimates (red lines) of the structural diversity index of (A) scale-free and (B) Watts-Strogatz networks. These are plotted against (A) the power-law exponent $\gamma$ and (B) the rewiring probability $s$. In (A), the red lines show the equation $\Delta(G_{\gamma}) = b \cdot \lvert V(G_{\gamma}) \rvert^{-a \cdot (3-\gamma)/(\gamma-1)}$ where $a$ and $b$ are obtained by ordinary least squares fit. In (B), the red line represents the approximation in Eq. (\ref{['eq:deltag_ws']}). Scale-free networks tend to suppress socio-diversity ($\Delta(G_{\gamma}) < 1$). Specifically, greater heterogeneity in the degree distribution (i.e., a smaller exponent $\gamma$) induces greater suppression of socio-diversity (i.e., smaller values of $\Delta(G_{\gamma})$). Conversely, Watts-Strogatz networks tend to amplify socio-diversity ($\Delta(W_s) > 1$). However, socio-diversity amplification is reduced as more long-range connections are established or/and more randomness is inserted (i.e., as the rewiring probability $s$ increases). Supplementary Movie 1 offers a visual comparison of cultural evolution on scale-free and Watts-Strogatz networks (see Section F.1 of the SI for the movie's caption). See Methods for simulation parameters.
• Figure 4: Relationship between the structural diversity index and (A) the degree-heterogeneity $\kappa(G)$, (B) the Wiener index $W(G)$, (C) the edge density $e(G)$, (D) the clustering coefficient $c(G)$, and (E) the size $\lvert V(G) \rvert$ of a network $G$ (see main text for definitions). Analyzing a variety of social networks we find that high degree-heterogeneity tends to suppress socio-diversity. In contrast, high clustering, Wiener index and edge density tend to amplify it. The effect of network size is more intricate (see text for details). See Methods for descriptions of the networks.
• Figure 5: Removing links to highly connected individuals may increase the structural diversity index. (A) Illustration of a simple strategy to raise the structural diversity index: each individual in the network $G$ (top) removes links to her $h = 1$ most connected neighbors (tie sorting is random), resulting in the network $G_h$ (bottom). (B) Percentage change $(\Delta(G_h)-\Delta(G))/\Delta(G)$ in the structural diversity index after applying the procedure outlined in (A) to a network $G$. This simple procedure leads to remarkable increases of the structural diversity index, even when the number of removed connections per individual is small. On average, increasing $h$ by one leads to a $10\%$ increase in the index. See Methods for details about network data, box plots and regression values.