La Bourse / Volume VI / Nº VI.08 / Ten concept briefs

A team seated around a white table in a meeting, one woman standing to speak, a board of sketches behind them. — Plate VI.08 · Ten concept briefsThe Two Maps on One Table.Every argument about who decides is, underneath, an argument about whether the boundary of the decision matches the boundary of its consequences. Put the two maps on one table and most of the argument goes quiet.

TEN CONCEPT BRIEFS · Chapter VI.08 — Federation and Subsidiarity

One page each. A reader who reads only these ten pages has the chapter.

BRIEF 1 — The Assignment Problem

The idea. There is no such thing as deciding how centralised an organisation should be. There is only a list of functions, and each function has its own answer. "Should we centralise?" is not a hard question; it is a malformed one, and the reason the argument never resolves is that the two sides are almost always holding different functions in mind while using the same word.

What to do instead. Write the list. Twenty to sixty lines for most organisations, one line per thing the federation actually performs: purchasing, brand, pricing, hiring, safety standards, compliance, product specification, customer data, treasury, training. Then answer each line separately.

Worked example. A group argues for a year about "centralising operations." Written as a list, it turns out that purchasing was already agreed by both sides, safety standards were agreed by both sides, and the whole disagreement was about two rows: local hiring and menu design. The argument was never about centralisation. It was about two functions, and both were settled in a morning once they were named.

Why it matters. Every federation that has done this well — Switzerland, the German cooperative banks, the European Union's own treaty structure — got there by placing functions one at a time. None of them decided once, at the top, how centralised to be. That decision does not exist.

You already know this because you have sat in a meeting where two people agreed completely and argued for an hour, and you could feel that they were talking about different things without being able to say which.

BRIEF 2 — Oates's Decentralisation Theorem

The idea. Wallace Oates, in Fiscal Federalism (1972): in the absence of cost savings from central provision and in the absence of spillovers across jurisdictions, welfare is at least as high — and usually higher — when each jurisdiction provides the level its own residents want than when one uniform level is imposed on everybody.

The three assumptions, which are the whole of the theorem.

No spillovers. The benefit stops at the border.
No economies of scale in central provision.
The centre cannot differentiate — it is stuck with one answer for all.

Worked example. Twelve branches would each choose a different opening hour. Head office must pick one. The loss is the average of how far each branch is from its own best answer. If the branches barely differ, that loss is tiny and uniformity is free. If they differ a great deal, uniformity is expensive, and the theorem says leave the decision with the branch.

The modern correction. Besley and Coate (2003) showed that when the centre can vary its answer by region, assumption 3 fails and the uniformity cost largely disappears. Software has made differentiation nearly free for most firms. So the theorem is not a licence to devolve; it is a price tag on uniformity, and the price is lower than it was in 1972.

You already know this because you have watched a national policy land perfectly in one office and absurdly in another, and known that nobody was at fault — the policy simply had to be one thing.

BRIEF 3 — Fiscal Equivalence

The idea. Mancur Olson (1969), in six pages: the boundary of the jurisdiction should match the boundary of the benefit. Where the two agree, the people who decide are the people who pay and the people who gain, and the decision is made with the right information. Where they diverge, everything downstream goes wrong in a predictable direction.

Worked example. A town upstream decides how much to spend on waste-water treatment. Most of the benefit is enjoyed downstream, in a different town, which does not vote in the first town's elections and does not pay its rates. The upstream town is not being selfish; it is deciding correctly on the information its boundary gives it. The boundary is wrong, so the decision is wrong.

The move. Fiscal equivalence says: redraw the boundary, or move the decision. Frey and Eichenberger (1999) pushed this to its conclusion with functional, overlapping, competing jurisdictions — let a boundary form around a single function rather than forcing every function through one boundary. Two sites sharing a back office, and nothing else, is that idea in miniature.

Why it matters. It converts a moral argument ("they should care about their neighbours") into a structural one ("the decision is in the wrong place"), and structural arguments can be fixed.

You already know this because you have seen a department hit its own target by doing something that cost another department more than it saved, and known that nobody in it was acting in bad faith.

BRIEF 4 — Tiebout Sorting, and What It Needs

The idea. Charles Tiebout (1956): if people can move freely, they sort into the jurisdiction whose bundle of services and taxes suits them. Preferences get revealed by feet rather than by ballots, and local provision becomes efficient without anybody having to ask.

The conditions. Seven of them. Full mobility; full knowledge; many communities to choose from; income independent of where you live; no spillovers; an optimal community size; and communities that actively seek it.

What the numbers say. In the United States Census mobility series, 7.8 percent of the population moved in 2023–24, and about 64 percent of movers stayed inside the same county. So the share crossing a jurisdiction is 7.8 percent times 36.0 percent = 2.808 percent a year. At that rate the half-life of a mis-sorted population is 24.3 years. In 1948, at 20.2 percent movers, it was 9.2 years — the mechanism is 2.65 times slower than it was.

Income independent of location? The mean one-way commute is 26.8 minutes, or 223.3 hours a year. Many communities? There are 90,837 US local governments and 19,479 municipalities across 3,031 counties — 6.4 municipal choices per county.

Why it matters. Tiebout sorting is real and it is slow. It cannot correct a mis-assignment inside a budget cycle, so you cannot lean on it while deciding. Rhode and Strumpf (2003) found American jurisdictions became less unlike each other as mobility rose, which is the opposite of what pure sorting predicts.

You already know this because you have watched somebody stay in a place they complained about for a decade, for reasons that had nothing to do with the services.

BRIEF 5 — The Spillover Fraction, s

The idea. s is the fraction of a function's benefit that lands outside the unit that decides it. It is the single most useful number in governance design and almost nobody estimates it.

Three ways to get it in ten minutes.

The leakage question. If this unit does this well, what share of the benefit is enjoyed by somebody who did not pay for it?
The migration route. For anything invested in people, s is roughly the fraction who leave. Payroll answers this in an hour.
The complaint route. Of the people who complain when this is done badly, what share are outside the unit?

Worked example. About 57 percent of Americans live in the state they were born in. So roughly 0.43 of the benefit of educating a child lands in a different state from the one that paid for the schooling. That is s = 0.43 for education, computed from a published table, and it is why every federation on earth has moved education finance upward.

What it does to behaviour. A unit internalising only (1 − s) of the benefit stops short of the efficient level. The shortfall, as a fraction of what should have been provided, is s/(1 − s) at the neutral calibration. At s = 0.35 that is 0.5385 — a local decider provides barely half of what the whole system needs.

You already know this because you have watched a training budget get cut in a business unit with high turnover, and understood exactly why the manager did it.

BRIEF 6 — Preference Heterogeneity, h

The idea. h is the coefficient of variation of the level each unit would choose if it chose alone: the standard deviation of their ideal answers divided by the mean. It is the price of making everybody do the same thing.

Two ways to get it. Ask five units what level they would choose and compute the coefficient of variation directly. Or, where the function is already local, measure the actual variation in current provision — that is h revealed rather than stated, and it is better.

Worked example. Six branches would choose weekly cleaning frequencies of 2, 3, 3, 4, 5 and 7. The mean is 4.00 a week; the sample standard deviation is 1.79; h is 0.45, and one uniform frequency for all six costs 0.2000 of the function's value. That is a high-heterogeneity function, and uniformity will cost real money.

The loss. With quadratic welfare loss, forcing one level on everybody costs h² of the function's value. At h = 0.28 that is 0.0784 — just under eight percent. At h = 0.50 it is 0.250, a quarter of the function's value, which is the point at which uniformity stops being a tidiness preference and becomes a material expense.

The bound worth holding. h cannot grow without limit — preferences cannot differ by more than everything. s/(1 − s) can, and does, as s approaches one. That asymmetry is the whole reason the assignment threshold sits low.

You already know this because you have seen a company-wide standard that fitted the biggest site perfectly and nobody else at all, and could have named the three sites it hurt before it was announced.

BRIEF 7 — The Assignment Rule

The idea. Two losses, both measured as a fraction of the same thing — the annual value at stake in getting this function right. The value cancels, so the rule needs no money in it to be used.

  assign UP   costs   h²
  assign DOWN costs   ( s / (1 − s) )²        at the neutral calibration

  equal when          s* = h / (1 + h)

Read the threshold table and notice where it sits.

  h      s*
  0.10   9.1%
  0.20   16.7%
  0.30   23.1%
  0.40   28.6%
  0.50   33.3%

Worked example. A function with s = 0.35 and h = 0.28. Shortfall is 0.5385, so assigning down costs 0.2899 of the function's value. Assigning up costs 0.28² = 0.0784. The threshold is 0.28 / 1.28 = 0.2188, and s is well past it. The function goes up, and it goes up by a factor of 3.70 — a ratio you can put in a board paper.

The cut. Intuition says keep it local unless it obviously spills. The arithmetic says the crossover is far lower than that: for units that differ by half, the threshold is still only 33.3 percent leakage. Subsidiarity's own arithmetic is more centralising than subsidiarity's rhetoric, because the spillover term is convex and the heterogeneity term is bounded.

You already know this because you have seen a decision left local out of principle, and watched everyone under-invest in exactly the way the model predicts, and nobody could name the cost because it never appeared as a line.

BRIEF 8 — Subsidiarity as Actually Applied

The idea. The European Union is the one place that turned subsidiarity from a principle into a procedure with a vote count and a clock. Article 5(3) of the Treaty on European Union; Protocol No. 2; every proposal goes to every national parliament; each parliament holds two votes; eight weeks to object. A third of the votes is a yellow card; a simple majority is an orange card.

The record, December 2009 to December 2025 — sixteen years.

card	year	states	votes	cast	needed	margin
Monti II	2012	27	54	19	18	+1
European Public Prosecutor	2013	28	56	18	14	+4
Posting of Workers	2016	28	56	22	19	+3

Three cards. Mean margin 2.67 votes, and a unicameral parliament casts two — so every yellow card in the history of the procedure passed by less than two parliaments. One card every 5.33 years. Orange cards: zero; the threshold is 29 votes in an EU of twenty-eight and the highest vote ever cast, twenty-two, is 75.9 percent of it. One of the three proposals was withdrawn — 33.3 percent. EU acts annulled by the Court for breach of subsidiarity: zero.

Why it matters. The procedure is genuinely valuable: it forces every proposal to justify its level in writing, and hundreds of reasoned opinions have been produced. But as an instrument the reading is exact: a principle with a procedure and no arithmetic behind it fires once every five years and changes one proposal in three. Brief 7 is what the procedure is missing.

You already know this because you have worked somewhere with a policy everybody cited and nobody could apply to a specific case.

BRIEF 9 — The Capability Gap

The idea. Subsidiarity assigns a function to the lowest level capable of performing it. Capability is largely income. So strict subsidiarity, applied without correction, systematically advantages the localities that were already rich — and the effect is measurable.

Worked example, from a real federation. Switzerland publishes a resource index rebased to a national mean of 100. The strongest canton runs above 250; the weakest sits near 67 — a raw spread of 3.73 to one in the capacity to fund a function from own resources. A unit that can fund 0.67 of the efficient level loses (1 − 0.67)² of the function's value: 10.89 percent, in the canton that could least afford it.

And the direction it points. Capability moves. Rabobank's local member banks fell from 174 in 2010 to 106 in 2015 — 39.1 percent in five years — and in 2016 the remaining banks merged into a single legal entity, because supervision and capital rules had raised the cost of being capable. The German cooperative banks went from about 7,100 around 1970 to 672 at the end of 2024: a fall of 90.5 percent over 54 years, at a compound 4.27 percent a year.

Why it matters. Subsidiarity is not a settlement. It is a moving answer to a moving question, and the thing that moves fastest is what the lowest level can actually do. A register written once and never reviewed will be wrong within a decade, in a direction that quietly hurts the weakest member first.

You already know this because you have watched a small supplier lose a contract not for price or quality but because the compliance paperwork had grown past what a small supplier could carry.

BRIEF 10 — The Capability Floor

The idea. The correction for Brief 9 is not full equalisation. It is a floor, and the floor has a computable height.

      F*  =  100 x ( 1 − C / 2W* )

  C   annual cost of providing the function efficiently, per member
  W*  annual surplus at stake in providing it, per member

Raise the floor while the last index point of top-up removes more expected loss than it costs. Marginal loss removed per index point is 2W(1 − i/100)/100; marginal cost is C/100; they cross at F.

Worked example. Forty member societies, indices from 62 to 145, W of 225,000 pounds a member and C of 120,000. Then C / 2W = 0.2667 and F* = 73.33 — much lower than instinct. At that floor the facility costs 32,000 pounds a year, removes 36,865 of expected loss, nets 4,865, and returns 1.15 pounds per pound. Full levelling to 100 costs 385,200, removes 176,692, and returns 0.46 pounds per pound — it destroys 208,508 a year while looking like the generous answer.

Why a floor beats levelling, in one line. The loss is quadratic, so it is concentrated at the bottom. In Switzerland, lifting the weakest canton from 67 to the legal floor of 86.5 is 19.5 index points and removes 9.07 percentage points of loss — 0.4650 per point. Lifting it further, from 86.5 to 99.0, is 12.5 points and removes only 1.813 — 0.1450 per point. The first stretch is worth 3.21 times the second.

You already know this because you have seen how much difference the first small amount of help makes to someone who has none, and how little the same amount adds to someone who is nearly fine.