PIATRA . INSTITUTE

polity coalition attractors

basins of inclusion versus exclusion under stress, norms, and contact

Attractor basins (x₀ vs t₀)

Color shows which attractor dominates from each starting point.

x₀=0.35, t₀=0.55

Inclusive

ExclusionaryClick to set initial conditions.

Trajectory (time series)

x = exclusionary share, t = trust, threat = perceived threat

Phase portrait (x vs t)

Trajectory through state space; attractors appear as endpoints.

Snapshot (final step)

x (exclusionary)1.00

t (trust)0.00

perceived threat0.62

π(E)1.35

π(I)0.12

Δ = π(E)−π(I)1.23

AttractorExclusionary

When Δ is positive, exclusionary support tends to grow (scaled by x(1−x)). Trust can dampen or amplify that growth depending on parameter settings.

Coalition Dynamics Model

Two state variables evolve over time: $x$ (the share of the population supporting an exclusionary coalition) and $t$ (institutional trust / civic confidence). Both are bounded to [0, 1].

\frac{dx}{dt} = \Delta t \cdot x(1-x)(\pi_E - \pi_I) + \Delta t \cdot \text{noise}

\frac{dt}{dt} = \Delta t \cdot (0.55R + 0.45C + 0.25N - 0.55P - 0.65x - 0.45S - 0.2\theta)

The $x(1-x)$ factor ensures replicator dynamics: change is fastest at intermediate shares and stalls near the boundaries. The payoff differential $\pi_E - \pi_I$ determines whether exclusionary or inclusive support grows.

Attractor Classes

Inclusive ( $x < 0.2$ ) — exclusionary support is marginal; trust-building feedbacks dominate.
Mixed ( $0.2 \leq x \leq 0.8$ ) — neither coalition dominates; system is in a contested or transitional zone.
Exclusionary ( $x > 0.8$ ) — exclusionary politics dominate; trust erodes in a self-reinforcing cycle.

Parameters

S (Stress) — economic/security shocks that raise threat salience.
D (Diversity) — salience of group boundaries in this toy model.
P (Polarization) — fragmented information space; amplifies perceived threat.
N (Norms) — rule-of-law / rights constraints that raise the cost of exclusion.
C (Contact) — bridging social capital; reduces perceived threat.
R (Redistribution) — material inclusion; increases trust and inclusive payoff.
O (Opportunism) — elite identity entrepreneurship; strengthens exclusionary narrative feedback.

Notes

This is a toy model. Use it to reason about feedback loops and basins, not to estimate real-world quantities.
Presets are illustrative, not empirically calibrated. For data-grounded presets, map real indicators into S/D/P/N/C/R/O.
The basin map can be computationally expensive at high grid resolutions. Lower the grid setting if interaction feels slow.