La Bourse / Volume VI / Nº VI.08 / Quiz, reflection, essays

A team seated around a white table in a meeting, one woman standing to speak, a board of sketches behind them. — Plate VI.08 · Quiz, reflection, essaysThe 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.

ASSESSMENT · Chapter VI.08 — Federation and Subsidiarity

Three instruments: a ten-point quiz, eight reflection questions, five essay prompts. The quiz checks comprehension rather than recall. The reflections are private and first-person. The essays are arguable from more than one side.

THE QUIZ — ten points

Four on recall.

1. State Oates's decentralisation theorem and name its three assumptions.

In the absence of cost savings from central provision and in the absence of inter-jurisdictional spillovers, welfare is at least as high — and generally higher — if each jurisdiction provides the efficient level for its own residents than if one uniform level is imposed everywhere. The assumptions: no spillovers; no economies of scale in central provision; and the centre cannot differentiate its answer across regions. One mark for the statement, one for all three assumptions. The third is the one that has moved: Besley and Coate (2003) showed the theorem loses most of its force where the centre can vary its answer, which today it usually can.

2. Write the assignment rule and define each term.

Assigning up costs h²; assigning down costs (ρ·s/(1 − s))²; they are equal at s = h / (ρ + h), which at the neutral calibration ρ = 1 is s = h / (1 + h). s is the fraction of the benefit landing outside the deciding unit; h is the coefficient of variation of the level each unit would choose alone. Note that the value at stake cancels — the rule can be applied to a function nobody has costed.

3. How many yellow cards has the EU's early warning system produced, over how long, and what happened to the proposals?

Three, between December 2009 and December 2025 — sixteen years, one card every 5.33 years. One proposal was withdrawn, which is 33.3 percent. Orange cards: zero. EU acts annulled by the Court for breach of subsidiarity: zero.

4. What is Switzerland's guaranteed minimum resource index, and what does it replace?

86.5, in force since 2020. It replaces nothing — it is a floor, not a levelling. The weakest canton's raw index sits near 67 against a national mean of 100, so the floor lifts it 19.5 index points and leaves the rest of the spread in place on purpose.

Four on application.

5. A colleague argues that a function should stay local "on the principle of subsidiarity." What two questions do you ask, and what do you do with the answers?

What fraction of the benefit lands outside the unit (s), and how unlike would the units' own answers be (h). Compute s = h/(1 + h); if s exceeds it, the principle of subsidiarity is itself arguing for the higher level. The stronger answer notes that both estimates can be rough — the threshold is a factor-of-two decision — and that a row where s exceeds s by less than a third should be marked contested and left alone.

6. Your firm's training budget is set at site level. Annual staff turnover out of each site is about 43 percent over the horizon the training pays back over, and sites would differ in their chosen spend by a coefficient of variation of about 0.30. Diagnose it.

s = 0.43, h = 0.30, so s = 0.231. The spillover is nearly double the threshold: the shortfall is 0.754 and assigning down costs 0.569 of the function's value against 0.090 for assigning up. Training belongs at the level at which the leavers are still inside the boundary. Full marks note the structural echo: this is exactly the calculation that put schooling at the state level in every federation on earth, and about 57 percent of Americans living in their birth state is where the 0.43 comes from.*

7. A federation proposes to equalise every member's capability index all the way to 100, "so that nobody is disadvantaged." What is wrong with that, in the federation's own financial terms?

The loss from a capability shortfall is quadratic, so it is concentrated at the bottom; the cost of topping up is linear. Past the point where the last pound of top-up removes less than a pound of loss, levelling destroys value. In the worked federation, full levelling costs 385,200 pounds a year to remove 176,692 — a return of 0.46 pounds per pound, and a net destruction of 208,508 a year, which is money that could have gone into the function itself.

8. Somebody says Tiebout sorting will fix a mis-assignment over time. Under what conditions is that true, and what is the operative timescale?

True if people are mobile, informed, have many jurisdictions to choose from, and their income does not depend on where they live. Measured: 7.8 percent of Americans move in a year, about 64 percent of movers stay in the same county, so 2.808 percent cross a jurisdiction — a half-life of 24.3 years. Sorting is real. It clears at about one human generation and cannot be leaned on inside a budget cycle. Rhode and Strumpf (2003) found jurisdictions grew less unlike each other as mobility rose.

Two that cannot be answered without doing the arithmetic.

9. A federation of forty member societies is deciding where to place its compliance function. It estimates that 0.35 of the benefit of good compliance accrues to members other than the one performing it — through the shared brand and shared regulatory standing — and that members' own preferred spending levels have a coefficient of variation of 0.28. Compute the threshold, both losses, and the ratio between them. State the decision and the sentence you would put in the paper.

Threshold: s* = 0.28 / 1.28 = 0.2188. Shortfall from assigning down: 0.35 / 0.65 = 0.5385. Loss of assigning down: 0.5385² = 0.2899. Loss of assigning up: 0.28² = 0.0784. Ratio: 3.70.
s of 0.35 comfortably exceeds s of 0.2188, so compliance goes up. The sentence for the paper: leaving this function with the member costs the federation 3.70 times what standardising it costs, and the difference is under-provision nobody currently reports. One mark for the threshold and one for the ratio. An answer that stops at "it goes up" has not produced the number that makes the paper survive a challenge.*

10. The same federation has capability indices running from 62 to 145. The function's annual surplus at stake is 225,000 pounds per member and it costs 120,000 a year per member to provide efficiently. Compute the optimal floor, the annual cost of the facility at that floor, and what one pound of top-up returns. Then say what changes if the function's surplus at stake were only 70,000 pounds.

F = 100 × (1 − C / 2W). With C / 2W = 120,000 / 450,000 = 0.2667, F = 73.33. 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 of top-up.
If W were 70,000, then C / 2W = 120,000 / 140,000 = 0.857, so F = 14.3 — below every member's index, which means the correct floor is no floor at all. That is the mark worth two: the formula does not only set a height, it tells you when the facility should not exist. A function that costs nearly as much to provide as it is worth should not be subsidised into existence at the weak members; it should be reconsidered, shared, or dropped.*

REFLECTION — eight questions, private and first-person

These are for one person and a pen. Nobody marks them.

Think of a decision you make that affects people who have no say in it. What fraction of its consequence lands on them, honestly estimated?

Where in your own life have you accepted a uniform answer that did not fit you, and what did the misfit cost — in money, in hours, in willingness?

When have you been the capable unit, given something to do because you could do it, while somebody less capable was quietly left out? What would a floor have looked like there?

What is something you would do better if it were decided closer to you — and what would you have to be able to do, that you currently cannot, for that to be true?

Recall a time you argued for local control on principle. If you had estimated s that day, what would you have found?

Which of your commitments has outgrown the level you hold it at? Capability moves in both directions — where has yours grown past the container?

Who has topped you up, quietly, without making you ask? What did that cost them, and what did it save you?

If somebody drew the boundary of every consequence you produce, what shape would it be, and how far would it reach past the edge of what you are accountable for?

ESSAY PROMPTS — five

Each is arguable from more than one side. Each requires a source the chapter cites and one it does not.

1. "Subsidiarity's own arithmetic is more centralising than subsidiarity's rhetoric." Defend or dismantle this claim, using the threshold s* = h/(1 + h) and at least one historical case where a function was devolved on principle and the under-provision was later measured. Engage with Oates (1972) and with at least one source on the empirical record of decentralisation the chapter does not cite.

2. The European Union's early warning system has fired three times in sixteen years and has never produced an orange card or an annulment. Argue either that this is evidence the procedure works — proposals are drafted subsidiarity-compliant in the first place — or that it is evidence the procedure is decorative. Use the vote margins (mean 2.67) and at least one study of national parliaments' reasoned opinions beyond Cooper (2006).

3. Switzerland guarantees its weakest canton 86.5 on the resource index; Germany levels its weakest Land to about 99.0. Compare the two designs on cost, on incentive, and on what each implies about what a federation owes its weakest member. Bring in a third federation the chapter does not treat — Canada, Australia, Spain or India — and say which of the two designs it more closely resembles and why.

4. Ostrom's eighth design principle is nested enterprises, which is subsidiarity stated for commons rather than for states. Argue whether the assignment rule in this chapter is compatible with Ostrom's account of polycentric governance or in tension with it. Use Governing the Commons (1990) and at least one empirical commons study Ostrom did not write.

5. Rabobank's local member banks fell from 174 to 106 in five years and then merged into one legal entity; the German cooperative banks fell 90.5 percent over 54 years while the functions assigned to their federation did not move. Argue whether the lowest capable level rises inevitably under modern regulation, or whether that rise is a policy choice that could be reversed. Use a primary source on prudential regulation the chapter does not cite, and at least one cooperative federation that has resisted the trend.