Circulation of Elites in an Adaptive Network Model

TL;DR

We study elite circulation using an adaptive network where $N$ agents carry ideological states $\sigma_i$ and form directed power links, with power dynamics governed by local rules. The framework combines cumulative advantage and intra-elite conflict, controlled by $α$ (new colors) and $ε$ (random links), to produce punctuated equilibria and a phase transition toward a disordered elite configuration. Key results include a star-core structural motif, a broad $P(k)$ in-degree distribution for small $ε$, and the proxy $g_{\max}^{\mathrm{top10}}$ that Granger-causes the dominant color fraction and offers predictive early-warning signals via $φ_{\mathrm{in}}$. These findings link microscopic local interactions to macroscopic political stability patterns and suggest observable proxies for real-world elite dynamics, with avenues for extensions such as elite overproduction, wealth coupling, and self-organized criticality.

Abstract

Societies experience politically stable and unstable phases along history, whereas political power is usually passed to new elite groups by these changes. Structural dynamics of the elites in a society have been proposed to be one of the core drivers shaping long term behavior. As current models and data are rather macroscopic, the emergence of macroscopic behavior from microscopic dynamics is largely unclear. Here, we introduce an adaptive network model of directed links representing political power and competing political ideas, based on local dynamical rules, only. The model is based on two socially motivated behaviors: the cumulative advantage effect of political power and intra-elite conflict. We observe punctuated equilibria as an emergent behavior and find a phase transition towards a disordered phase. We define an advance warning measure for elite collapse and find that the states of only a few largest nodes are suitable as a proxy with predictive information.

Figures (6)

• Figure 1: Schematic model description
• Figure 2: Example time series of the dominant color fraction $g_\mathrm{max}$ for a system of $N=10^4$ agents, $\varepsilon=0.2$ and $\alpha=0.13$ close to the transition point $\alpha_\mathrm{c}$. Initially the network starts with a circle of the same color. The model exhibits punctuated equilibria with phases of persisting disunity and unity. Two example subnetworks at $t=1600$ and $t=6820$ contain the 10 nodes with the largest in-degree and a randomly chosen sample of 1% (rounded down) of their in-degree neighbors. A few largest nodes are most influential for the model dynamics with each node trying to build its own star-like structure. Node sizes are logarithmically scaled by their in-degrees in the full network.
• Figure 3: The average order parameter for different parameter values for a system of $N=10^4$ agents and $10^6$ time units. The average is taken after $10^5$ time units. A phase transition appears for $\varepsilon \rightarrow 1$ and is suppressed for a fat tailed degree distribution for smaller $\varepsilon$.
• Figure 4: Finite size scaling of the transition value $\alpha_\mathrm{c}$ for different system sizes $N$ for the phase transition for $\varepsilon=1$. $10^7$ time units were simulated for $N=10^3$, $10^6$ for $N=10^4$ and $10^5$ for larger $N$.
• Figure 5: Example collapse of a dominant color $g_\mathrm{max}$, in-degree weighted color fraction $\phi_\mathrm{in}$ and the dominant color fraction of the 10 largest nodes by in-degree $g_\mathrm{max}^\mathrm{top10}$ for the simulation in Fig. \ref{['fig:example']}. The dominant fraction $g_\mathrm{max}$ lags behind $\phi_\mathrm{in}$ and partially behind $g_\mathrm{max}^\mathrm{top10}$. An example subnetwork for $t=6280$ can be observed in Fig. \ref{['fig:example']}.