The Tristable Basin

The tristable basin framework developed here stands in direct conversation with several decades of regime transition scholarship. This section situates the model within that literature, identifying where it extends, complements, or departs from existing theory.

Levitsky & Way (2010), Competitive Authoritarianism. The hybrid trap basin provides the strongest formal vindication of Levitsky and Way's central claim: that hybrid regimes are not merely "incomplete transitions" toward democracy but constitute a distinct regime type with its own self-reinforcing logic. Where Levitsky and Way argued qualitatively that competitive authoritarian regimes can persist for decades through manipulated elections and constrained opposition, the tristable model quantifies this persistence: the hybrid basin at L≈47 exhibits 67% ten-year retention, confirming it as a genuine attractor rather than a transient waypoint. The thesis extends their work by formalizing the basin depth (k≈0.05) and identifying the precise liberty-score boundaries (L≈20–70) within which their competitive authoritarian dynamics operate. However, where Levitsky and Way emphasized the role of Western leverage and linkage as exogenous variables determining regime trajectories, the basin model treats these as components of the stochastic shock term ε rather than as structurally determinative—a simplification that future work should address.

Huntington (1991), The Third Wave. Huntington's wave metaphor—democratization proceeding in global surges followed by reverse waves—provides essential historical context for the data patterns underlying this framework. The 91-country, 225-year dataset captures all three of Huntington's waves (1828–1926, 1943–1962, 1974–) and the two reverse waves between them. The tristable model complements Huntington by offering a micro-foundation for his macro-patterns: waves correspond to periods when exogenous shocks (war outcomes, economic crises, demonstration effects) push multiple countries over ridgelines simultaneously, while reverse waves represent coordinated slides back into attractor basins. Critically, however, the basin framework contradicts the implicit linearity of the wave metaphor. Huntington's framing suggests a secular trend toward democracy punctuated by setbacks; the tristable model suggests no such directionality—the tyranny well is deeper than the democratic plateau, implying that the long-run stationary distribution may favor autocracy absent sustained institutional investment.

Diamond (2015), “Facing Up to the Democratic Recession.” Diamond's diagnosis of a global democratic recession since roughly 2006 maps directly onto the velocity analysis in this framework. Where Diamond documented the phenomenon qualitatively—noting stagnation and erosion across multiple democracies—the basin model quantifies the recession as an increase in the rate of countries crossing from the democratic plateau into the hybrid trap. The velocity field analysis shows that post-2006 transition probabilities shifted measurably: the probability of downward movement from Stage 2–3 to Stage 4 increased from a pre-2006 baseline, consistent with Diamond's recession thesis. The framework extends Diamond's analysis by identifying L≈52–55 as the "event horizon"—the critical instability zone where erosion becomes self-accelerating—a threshold that Diamond intuited but could not formalize.

Acemoglu & Robinson (2006), Economic Origins of Dictatorship and Democracy. Acemoglu and Robinson's game-theoretic model treats democratization as a strategic concession by elites facing revolutionary threat—a fundamentally bistable framework (democracy or dictatorship) where transitions are driven by rational actors responding to inequality and mobilization costs. The tristable basin model departs from this framework in two important respects. First, it introduces the hybrid regime as a third equilibrium that Acemoglu and Robinson's binary choice set cannot accommodate: their model predicts either full concession (democracy) or repression (dictatorship), whereas the empirical distribution reveals a large cluster of countries at intermediate liberty scores that are neither. Second, the basin model replaces deterministic game-theoretic transitions with stochastic dynamics driven by aggregate institutional drift and exogenous shocks, capturing the path-dependent, historically contingent nature of actual transitions better than comparative statics can. That said, Acemoglu and Robinson's emphasis on inequality as a driver of regime instability could be incorporated into the basin framework as a variable affecting the depth or location of attractor basins—a promising direction for future work.

Treisman (2020), “Democracy by Mistake.” Treisman's provocative argument—that many democratizations were unintended consequences of miscalculation by authoritarian incumbents—resonates strongly with the stochastic mechanics of the basin model. If transitions were primarily driven by deliberate strategic choice (as in Acemoglu & Robinson), we would expect transitions to cluster at predictable thresholds with low variance. Instead, the high stochastic shock variance (σ≈3–8 depending on stage) and the rarity of recovery from the hybrid trap (3.0% from Stage 5) are consistent with Treisman's view that upward transitions are largely accidental. The basin framework formalizes Treisman's insight: democratization-by-mistake corresponds to a large positive shock ε pushing a country over the ridgeline from the hybrid trap into the democratic basin. The model predicts that such events should be rare, unpredictable, and difficult to sustain—exactly the pattern Treisman documents.