Measuring Ideologies by Their Statistical Prerequisites

Abstract

There is a political dimension that rarely gets named directly: how much homogeneity an ideology requires in order to function at all. This paper identifies seven statistical assumptions — stationarity, ergodicity, equilibrium, linearity, reversibility, normality, and exchangeability — that ideologies depend on to varying degrees, and proposes that this dependence is measurable, consequential, and a better predictor of political behavior under stress than position on a left-right spectrum. COVID and climate breakdown are adversarial stress tests that reveal which ideologies depend on assumptions the world no longer satisfies.

1. The Hidden Dimension

Most political analysis places ideologies on spectra: left-right, libertarian-authoritarian, progressive-conservative. These spectra capture differences in values, preferences, and policy positions. They do not capture a more fundamental question: what does the ideology need the world to be like in order for its reasoning to work?

Some ideologies only function if the world behaves the same way everywhere. Others can tolerate difference, drift, rupture, and unevenness without losing coherence. This difference shows up not only in moral language or policy preferences but in the statistical and dynamical assumptions the ideology quietly depends on.

These assumptions are not incidental. They are the load-bearing structure. When they hold, the ideology produces coherent policy, plausible predictions, and stable institutions. When they fail, the ideology either adapts or resorts to coercion or denial. Characterizing ideologies by their statistical prerequisites — rather than by their stated values — reveals fault lines that conventional political analysis misses.

2. Seven Assumptions

Each of the following assumptions reduces heterogeneity in a specific way, smoothing the world so that planning, optimization, and universal claims remain possible. Together they enable governance by summary: growth rates, cost-benefit analyses, risk bands, incentive structures, “best practices.”

2.1 Stationarity

Definition. A process is stationary when the probability distribution generating its behavior does not change over time. Yesterday’s distribution is a good guide to tomorrow.

What it enables. Historical baselines, trend extrapolation, precedent-based law, institutional learning that assumes the future resembles the past.

Who depends on it. Any ideology that argues “in the long run” or “historically” or “based on evidence” without asking whether the evidence-generating process has changed. Milly et al. (2008) showed that stationarity is no longer a defensible assumption in water resource management; the same applies to any governance system calibrated to historical data.

2.2 Ergodicity

Definition. A system is ergodic when the time average of a single trajectory converges to the ensemble average across all possible trajectories. What happens to one person over time matches what happens to all people at a moment.

What it enables. Population-level policy justified by individual-level outcomes. “On average, people benefit” treated as equivalent to “each person benefits eventually.”

Who depends on it. Expected utility theory (Peters 2019), insurance logic, most welfare economics. Peters argues that the failure to distinguish ergodic from non-ergodic dynamics underlies fundamental errors in economic theory — expected value maximization is rational only in ergodic systems, and most real human economic situations are non-ergodic.

2.3 Equilibrium

Definition. A system is in equilibrium when, after a perturbation, it returns to a stable baseline.

What it enables. Policy as correction: intervene, wait for the system to restabilize, measure the result. Market-clearing models, homeostatic governance, the assumption that crises are temporary.

Who depends on it. General equilibrium theory (Arrow & Debreu 1954), most macroeconomic policy, any framework that assumes shocks are followed by recovery.

2.4 Linearity

Definition. Inputs scale proportionally to outputs. Doubling the cause doubles the effect.

What it enables. Cost-benefit analysis, marginal reasoning, the assumption that small interventions produce small effects and large interventions produce large ones.

Who depends on it. Any ideology that reasons in terms of proportional response, marginal improvement, or scalable policy. Nonlinear systems produce disproportionate effects, cascades, and tipping points that linear reasoning cannot predict.

2.5 Reversibility

Definition. Damage can be undone. The system’s trajectory can be reversed to a prior state.

What it enables. The assumption that mistakes are correctable, that harms can be compensated, that “we can always fix it later.”

Who depends on it. Any ideology whose policy framework assumes future remediation: carbon capture to offset present emissions, reparations to reverse historical injustice, deregulation followed by re-regulation. Irreversible harms — species extinction, climate tipping points, intergenerational trauma — break this assumption.

2.6 Normality

Definition. Outcomes are distributed according to a Gaussian (bell curve) distribution. Extremes are rare and safely ignorable.

What it enables. Risk management by standard deviation, confidence intervals, the assumption that outliers are noise rather than signal.

Who depends on it. Financial regulation, public health policy, infrastructure design — any system that treats “normal” as a meaningful baseline and “extreme” as exceptional. Taleb (2007) argues that the most consequential events in complex systems are precisely the ones that Gaussian models treat as negligibly improbable.

2.7 Exchangeability

Definition. Units can be treated as interchangeable without moral or functional loss. One person, one community, one ecosystem can be substituted for another in aggregate calculations.

What it enables. Utilitarian aggregation, GDP as welfare proxy, the assumption that “a life saved is a life saved” regardless of context.

Who depends on it. Classical utilitarianism, welfare economics, any framework that aggregates across persons. De Finetti (1937) formalized exchangeability in probability; Sen (1999) argued that treating persons as exchangeable units erases the capabilities and contexts that make their lives incommensurable.

3. The Homogeneity Metric

These seven assumptions form a rough metric. An ideology that depends on all seven requires maximum homogeneity — it can only function in a world that is stationary, ergodic, equilibrial, linear, reversible, normal, and exchangeable. An ideology that depends on none can function in a world of drift, path-dependence, irreversibility, fat tails, and incommensurable difference.

No ideology occupies the extremes. But the profile matters. Consider:

Assumption	Neoliberalism	Fascism	Mutual aid	Indigenous land ethics
Stationarity	High	High	Low	Low
Ergodicity	High	High	Low	Low
Equilibrium	High	Moderate	Low	Low
Linearity	High	Low	Low	Low
Reversibility	High	Low	Low	Low
Normality	High	Low	Low	Low
Exchangeability	High	High	Low	Low

Neoliberalism requires nearly all seven: it governs by aggregate, assumes markets clear, treats persons as interchangeable utility-maximizers, and relies on historical data remaining predictive. Fascism requires stationarity (the mythic past) and exchangeability (the interchangeable Volk member) but actively breaks linearity, reversibility, and normality through crisis, permanent mobilization, and the embrace of extremes. Mutual aid and Indigenous land ethics operate with minimal assumptions about homogeneity — they rely on local judgment, ongoing relationship, and the expectation that the world will not stay the same.

This table is illustrative, not definitive. The point is that the profile of assumptions matters more than any single dimension, and that the profile predicts behavior under stress better than stated values do.

4. Stress Tests

COVID and climate breakdown function as adversarial stress tests that probe whether an ideology’s hidden assumptions hold.

COVID exposed the cost of assuming exchangeability and ergodicity. Population averages masked wildly unequal exposure, vulnerability, and consequence. “Everyone faces the same risk” was false. “On average, people recover” was meaningless to those whose losses were permanent. Ideologies that governed by population summary — “the death rate is only X percent” — failed the people who were not exchangeable with the average.

Climate breakdown exposes the cost of assuming stationarity, reversibility, and equilibrium. Past data stops being predictive. Damages compound rather than recover. There is no stable “after” to return to. The companion paper Why Staying Under 2°C Was Never Physically Plausible demonstrates this in detail: climate policy assumed a stationary forcing trajectory and reversible overshoot, and both assumptions were structurally violated.

Ideologies that depend on the failing assumptions respond by trying to force reality back into shape. Disruption is treated as anomaly. Inequality is treated as temporary. Extreme outcomes are reframed as acceptable deviations from a working average. Homogeneity becomes an operational requirement, enforced through normalization, discipline, or abandonment.

By contrast, ideologies that accept non-stationarity, non-ergodicity, irreversibility, and path-dependence sound messier and less reassuring. They rely on local judgment, redundancy, care, and ongoing revision. They resist universal claims because they do not assume a universal substrate. They are harder to summarize, harder to scale, and harder to sell — precisely because they do not promise that the world will smooth itself out.

5. Ethical Fault Lines

Many political disagreements that appear to be about values are actually about how much sameness is being assumed.

When someone argues that a policy “works in the long run,” the question is: under what assumptions of stationarity and reversibility? When someone argues that “on average” things improve, the question is: ergodic over which lives, and at what cost? When someone argues that harms can be compensated, the question is: reversible for whom?

These are not technical quibbles. They are ethical fault lines. The statistical assumptions are doing moral work: deciding whose losses count, whose futures are foreclosed, and whose experiences are averaged away. An ideology that assumes exchangeability treats the death of one person as compensable by the survival of another. An ideology that rejects exchangeability cannot.

6. Related Work and Positioning

Peters (2019) argues that the ergodicity assumption underlies fundamental errors in economic theory. Taleb (2007) argues that Gaussian assumptions in risk management produce catastrophic blindness to fat-tailed events. Milly et al. (2008) showed that stationarity is dead in hydrology. Sen (1999) argued that treating persons as exchangeable erases capability and context. Scott (1998) showed that state legibility requires the violent simplification of complex social reality.

Each of these critiques targets one or two assumptions. The contribution of this paper is to collect them into a single framework and propose that the profile of assumptions — which ones an ideology depends on, and how it responds when they fail — is a measurable, consequential political dimension that conventional spectra do not capture.

7. Conclusion

The hidden metric is not where an ideology sits on a spectrum, but how much difference it can survive — and what it is willing to do when the world refuses to be averaged.

References

• Arrow, K., & Debreu, G. (1954). “Existence of an Equilibrium for a Competitive Economy.” Econometrica, 22(3), 265–290.
• de Finetti, B. (1937). “La prévision: ses lois logiques, ses sources subjectives.” Annales de l’Institut Henri Poincaré, 7(1), 1–68.
• Milly, P. C. D., et al. (2008). “Stationarity Is Dead: Whither Water Management?” Science, 319(5863), 573–574.
• Peters, O. (2019). “The Ergodicity Problem in Economics.” Nature Physics, 15, 1216–1221.
• Scott, J. C. (1998). Seeing Like a State. Yale University Press.
• Sen, A. (1999). Development as Freedom. Oxford University Press.
• Taleb, N. N. (2007). The Black Swan: The Impact of the Highly Improbable. Random House.