When the measure
misses the mechanism.

A theory predicts a boundary. A dataset contains a percentage. A graph bends. Connecting those three things can produce an apparently compelling explanation, even when the percentage measures something different from the variable that drives the theory.

My research, Paying the Guards: Coup Insurance, Coercive Capacity, and the Measurement of Repression, examines that connection in political economy. It asks what researchers can learn from counts of security organisations, personnel shares and recorded protest responses, and what evidence would be needed to test a mechanism about loyalty and resistance.

The contribution joins formal modelling to an empirical measurement audit. Its value is in making the route from a political argument to an observable test explicit enough to inspect.

Three outcomes require three explanations

A coup attempt, success conditional on that attempt, and the use of force against civilians are different events. An institution might affect one without moving the others in the same direction.

The model begins with a force that can serve the incumbent, defect towards civilian opposition, or attempt to seize power. Its compensation must satisfy competing loyalty constraints. A separate capacity to resist a coup changes the seizure option under the maintained assumptions; it does not automatically change the attraction of civilian defection.

This creates a conditional boundary. In the costless benchmark, additional resistance eventually stops changing the upper boundary between the ruler’s modelled repression and redistribution choices, because the other loyalty constraint becomes decisive. Charging for a necessary protective capacity changes that conclusion about exact recovery of the benchmark.

These results depend on enforceable contingent wages, the specified payoffs and technologies, and a fixed civilian environment. They describe an institutional mechanism, rather than a universal country percentage or a welfare ranking of political choices.

What does the recorded percentage measure?

The theoretical variable is effective resistance available against a particular force attempting seizure. A count of separate organisations records command structure. A personnel share records reported numbers within selected formations. Neither, by itself, measures the relevant relationship between potential actors.

The paper makes this gap visible through an organisational crosswalk for 2010. It links security-force records with personnel reporting across 68 countries. Of 116 records identified as counterweights, 56 can be linked to a personnel figure; 60 cannot.

That is a statement about information availability among identified records. It does not imply that roughly half of real guards exist, or that an unmatched organisation has no resisting capacity. Names, aggregation, organisational change and reporting coverage can all interrupt a link.

The practical implication is important for research design: a carefully transcribed number can still be an incomplete measure of the institution a theory requires.

An index can erase direction

The paper also examines the effective-number index calculated from personnel shares. With two forces, exchanging their shares leaves the index unchanged.

Consider an illustrative division of 80 per cent and 20 per cent. The index gives the same answer when the army is the larger force as when the counterforce is larger. It summarises how evenly personnel are divided, while discarding which organisation occupies which position.

That is an algebraic property of every two-force configuration. Improving transcription cannot restore information the formula removes. The article therefore keeps a directional personnel-share measure separate from an organisational count share, while recognising that both remain distinct from effective capacity.

Put the apparent threshold under pressure

The personnel-share analysis uses 384 country-years from 63 countries over 2010–2020. Only 25 countries change the exposure during the observed period. The outcome is the share of reported protest events recorded as receiving state intervention.

That outcome is itself constructed from event sources with different coverage and definitions. It describes recorded responses among reported protests, rather than a complete census of repression. A national change could reflect a change in conduct, a transfer between acting organisations, or a change in what becomes visible.

The analysis searches for a change in slope while accounting for country and year effects. Against a linear baseline, the personnel specification selects a location of 8.85 per cent and reports an unknown-location, country-block bootstrap p-value of 0.039.

But a smooth curve also departs from a straight line. A broken-line fit can gain explanatory power by approximating curvature, without locating a sharp institutional boundary.

The paper therefore repeats the search while allowing the baseline to bend smoothly. Adding a quadratic term moves the selected location to 33.33 per cent and the p-value to 0.095. With a cubic term, the location is 26.32 per cent and the p-value is 0.819.

Interpret the sensitivity at the right level

This comparison weakens the claim that the design has located a stable theoretical threshold. It does not prove that the true relationship has no kink, uniquely establish a particular smooth curve, or refute the conditional model.

The broader evidence also matters. The initial 0.039 result does not survive the paper’s adjustment across four outcome-and-exposure tests. Alternative event sources and specifications select different locations. Around a typical admissible personnel-share candidate, only six countries are observed on both sides.

Those facts make the information supporting a location much clearer. A selected percentage can look precise on a graph while depending on limited within-country movement and consequential decisions about the comparison model.

The organisational analysis uses a different period and sample, so its results cannot be read as a controlled contest between two measurement technologies. Keeping their populations visible is part of making the audit useful.

Build the empirical bridge

A more direct test would connect specific organisations, their compensation and outside options, the resistance relevant to them, and comparable civilian challenges. It would also record which actor used force, when no force was used, and how event visibility changed.

This is where the paper’s mathematical and empirical work reinforce one another. The model specifies which relationship matters. The data audit shows which parts are observed and which are being assumed. The specification checks reveal how an attractive numerical threshold can outrun that evidence.

The general lesson for institutional research is to preserve the meaning of the variable all the way from theory to table. A successful test needs more than a measurable proxy and a bend in the data. It needs evidence that the bend addresses the mechanism the research set out to explain.