Conflict-Averse Centrism Dynamics

• Conflict-averse centrism is defined as a strategy to minimize polarization by favoring moderate, consensus-driven decisions through mechanisms like social-balance rewiring and external deradicalizing fields.
• Key findings reveal that system dynamics display phase transitions with metastable states, quantifiable via critical field strengths and equilibrium analyses.
• Applications include voter models with committed centrists and algorithmic preference aggregation, demonstrating measurable effects on political conflict and consensus evolution.

Conflict-averse centrism denotes both a behavioral and a formal strategy set in group decision processes, ideological dynamics, and evolutionary conflicts, whereby individuals, institutions, or algorithmic agents seek to minimize overt conflict by gravitating toward moderate, consensus-seeking positions—either through intrinsic aversion to polarization or via active deradicalization mechanisms. Technically, conflict-averse centrism encompasses social-balance rewiring, quasi-stationary stabilization of centrist states, logic-based compromise constructions, and evolutionary game-theoretic regimes suppressing extremes. Its unique properties and system-level effects are demonstrated in opinion dynamics (Singh et al., 2015), constrained voter models (Mobilia, 2012), logic-based preference aggregation (George et al., 13 Aug 2025), evolutionary simulations of asymmetric contest (Topaz, 6 Dec 2025), and critical analyses of deradicalization strategies (Marvel et al., 2012).

1. Mechanisms of Conflict-Aversion in Social Balance Models

In triadic social networks, conflict-aversion is formalized by rewiring unbalanced triads toward friendly interactions. In the canonical three-state model—leftist (L), rightist (R), and centrist (C)—links between feuding extremists (L–R) are marked as unfriendly (–), while all other links are friendly (+). A triangle L–R–C is unbalanced if it has an odd number of unfriendly edges. Social-balance rewiring proceeds as follows: with probability 1–p, an unbalanced triangle is "repaired" by converting one node's opinion—either the centrist becomes an extremist (probability α), or (with 1–α) an extremist becomes a centrist, both chosen uniformly (Singh et al., 2015).

The external deradicalizing field, with strength p, models exogenous efforts (media, campaigns, sanctions) that, with probability p per step, convert an extremist directly into a centrist. The composite dynamics yield a mean-field rate equation:

$\frac{dx}{dt} = -px + 3(2\alpha-1)(1-p)x y z$

$\frac{dy}{dt} = -py + 3(2\alpha-1)(1-p)x y z$

$\frac{dz}{dt} = -(dx/dt + dy/dt)$

Here, balance and field terms compete; the parameter α quantifies whether social repair favors extremism (α > ½) or centrism (α < ½). Introduction of u = x + y (total extremists) and v = x – y leads to a one-dimensional equation for the evolution of extremist density (Singh et al., 2015).

2. Metastable Mixed States and Phase Transition to Consensus

The critical field strength

$p_c = \frac{3(2\alpha-1)}{8 + 3(2\alpha-1)}$

separates two regimes. For p < p_c, the system possesses a metastable fixed point (balanced coexistence of extremists and centrists), alongside a saddle point; the system can remain in this configuration for exponentially long time in population size N (consensus time T_c ∼ exp[β(p)N], with β(p) ∝ |p_c – p|^ν, ν ≈ 1.6). For p > p_c, only the all-centrist absorbing state exists, and consensus time grows at most polynomially in N (T_c ∼ N log N) (Singh et al., 2015).

The metastable point lies at

$$x_{meta} = \frac{1}{4} + \frac{1}{4}\sqrt{1 - \frac{8p}{3(2\alpha-1)(1-p)}}$$

$z^* = 1 - 2x_{meta}$

As p approaches p_c from below, the nontrivial fixed points coalesce and vanish, indicating a sharp phase transition from persistent polarization/coexistence to rapid centrism consensus.

3. Anchoring Effects of Centrist Commitment in Voter Models

In multi-agent voter frameworks, committed centrists ("zealots") (Cz) act as conflict-averse anchors. The model comprises persuasive extremists (A,B), susceptible centrists (C), and zealot centrists (Cz) who never change state. The persuasion bias parameters δ_A, δ_B quantitate extremist attractiveness, while zealot fraction ζ = ℓₓ⁄N (N = total agents) governs commitment (Mobilia, 2012).

Mean-field equations show a continuous transition at ζ_c = δ_A⁄(1+δ_A). Below this critical density, extremist–centrist coexistence persists (metastable), with mean consensus time τ ~ N^{–1/2}e^{Nγ}; above, the system flows rapidly to centrism (τ ~ ln N). Thus, sufficient centrist commitment suppresses polarization, while insufficient commitment allows exponentially long persistence of conflict.

4. Logic-Based Construction of Middle Grounds in Preference Aggregation

Conflict-averse centrism can be encoded as the pursuit of formal compromise sets—middle grounds (MGs)—in preference aggregation over multi-attribute alternatives. Let each stakeholder submit a set of preference statements (Φ₁,…,Φₙ) over alternatives. An MG Φ must satisfy:

• Non-triviality (P1): Φ is both satisfiable and falsifiable.
• Union-preservation (P2): If the union ∪Φᵢ is consistent, Φ = ∪Φᵢ.
• Compatibility (P3): No Φ statement outright contradicts any stakeholder base.
• Justification (P4): Every Φ statement is entailed by some stakeholder.
• Maximality (P5): No strictly stronger compatible compromise exists (George et al., 13 Aug 2025).

MG existence is guaranteed if ∪Φᵢ is consistent; otherwise, it may not exist, or may be non-unique. Algorithms for MG construction are combinatorial (general hierarchical models) or tractable for lexicographic orders. In practice, MG articulates a conflict-averse centrist position that avoids provoking any stakeholder while preserving maximal agreeable core (George et al., 13 Aug 2025).

<table> <thead> <tr><th>Model Type</th><th>MG Existence</th><th>Computational Complexity</th></tr> </thead> <tbody> <tr><td>General hierarchical</td><td>coNP-hard (may fail)</td><td>Exponential</td></tr> <tr><td>Lexicographic</td><td>Efficient test</td><td>Polynomial (existence)</td></tr> </tbody> </table>

5. Evolutionary Game Theory: Centrism in Asymmetric Political Conflict

Conflict-averse centrism materially reorganizes evolutionary dynamics in clash-of-values games involving resistance (R), authoritarianism (F), and centrism (C). The payoff structure determines long-run global outcomes as follows (Topaz, 6 Dec 2025):

• Heteroclinic cycle (cyclic resurgence): Under payoffs F ≻ C ≻ R ≻ F, trajectories spiral out from a repelling interior fixed point to boundary cycling; if the eigenvalue ratio ρ_F is maximal, asymptotically most time is spent near the authoritarian vertex (F). Conflict aversion via centrists punishing resistance (high a_R, b_C) secures authoritarian resurgence, even if resistance would otherwise dominate F head-to-head.
• Centrist–authoritarian coalition: For payoff parameters enabling mutual benefit between C and F (c_C, c_F), the system approaches a globally attracting equilibrium (x_R = 0, x_C = c_C/(c_C+c_F), x_F = c_F/(c_C+c_F)), with resistance excluded. The coalition is uninvadable if c_C > b_R, that is, centrists’ benefit from alliance exceeds resistance’s competitive edge.

In both regimes, greater conflict aversion systematically impedes resistance, allowing either recurrent authoritarian surges or a stable exclusion of protest actors.

6. Deradicalization Strategies: Comparative Model Analysis

Systematic study of seven deradicalization interventions identifies only one robust path to stable, conflict-averse centrism: nonsocial deradicalization, i.e., uniform external "cooling" that suppresses extremist persistence independently of local social contacts. Mechanisms relying on stubbornness of moderates, evangelical persuasion, extremist infighting, balanced zealotry, or moderate zealots all produce critical thresholds beyond which moderation collapses, or paradoxical vulnerabilities (Marvel et al., 2012).

The governing rate equations are

$\dot{x} = (p + x)(1 - p - x - y) - x y - u x$

$\dot{y} = y(1 - p - x - y) - (p + x)y - u y$

Here, u > 0 ensures asymptotic stability of the moderate-only equilibrium for all u, eliminating saddle-node or bifurcation events that might erase moderation. External deradicalizing "field" (e.g., education, legislation) that universally saps extremist fervor is mathematically and empirically the only conflict-averse strategy that always expands centrism without risking extinction.

7. Strategic Implications and Limitations

Conflict-averse centrism—whether driven by individual disposition, institutional intervention, or algorithmic compromise—can reliably stabilize moderate consensus and suppress polarization when external influence or centrist commitment exceeds system thresholds. However, excessive focus on civility or avoidance of conflict can also inadvertently enable exclusionary coalitions or recurrent authoritarian dominance, as shown in evolutionary models (Topaz, 6 Dec 2025). Logic-based compromise construction may fail for structurally incompatible preference sets, and combinatorial complexity limits scalability in large or multidimensional decision contexts (George et al., 13 Aug 2025). A plausible implication is that effective deradicalization and centrism require careful calibration of external influences, structural design of decision protocols, and explicit attention to asymmetric effects in polarized domains. The literature provides rigorous timescales, equilibrium structures, and stability criteria for evaluating the feasibility and resilience of conflict-averse centrist regimes.