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Commerce · VI.08 · MMXXVI · daylight

La Bourse  /  Volume VI  /  Nº VI.08  /  Workbook — the student

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

WORKBOOK — THE STUDENT

Chapter VI.08 · Federation and Subsidiarity

For the person studying this alone, or in a seminar, with no federation to govern yet. The assignment problem is not a thing organisations have. It is a thing every group of two or more people has, including the one you live in.

WHY THIS WORKBOOK IS DIFFERENT

The chapter was written for someone with a register to build and a levy to propose. You may have neither. What you do have — and this is the whole of the advantage — is a life that is already full of assignment decisions, all of them being made badly, none of them being measured.

Who decides what the shared flat buys. Who decides the reading for a study group. Who decides the pace of a project with four people on it. Whether your society's branches set their own subscriptions. Whether you make a decision or your family makes it with you. Every one of those is an s and an h, and the fact that nobody has ever written them down is why the same argument keeps coming back.

So you will do exactly what the executive does. You will simply do it on systems you can actually observe from inside, which for the next decade is a considerable advantage: you can measure h by watching, where a director has to ask a committee.

PART ONE — DISCOVERY

Days 1–30: find the assignments already working

Exercise 1.1 — The function list (90 minutes)

Pick one group you belong to: a household, a study group, a society, a team, a family. Write every function it performs. Not roles — functions. Buying food. Choosing where to meet. Setting deadlines. Handling money. Deciding standards. Handling somebody's bad week. Twenty lines is normal; fewer means you are writing roles again.

Beside each, write where the decision currently sits: each person alone, or the group.

Do not evaluate yet. The list is the work.

Exercise 1.2 — Find the three that are right (60 minutes)

Mark the three functions you are confident are at the right level, and beside each write why you know. Not "it feels fine" — what would go wrong if it moved. This is the appreciative move and it is not softness: you are calibrating your judgement on cases where you already have the answer, which is the only way to trust it on the cases where you do not.

Exercise 1.3 — Read a federation from outside (2 hours)

Take one real federation and find its assignment. Recommended, in order of how much material is public: Switzerland, the European Union, the German cooperative banking sector, a national credit union league, your own university's relation to its departments.

Answer three questions in writing.

  1. Name three functions held at the top and three held at the bottom.
  2. For one of the top three, estimate what fraction of its benefit would land outside a single unit if it were devolved.
  3. Find one function that has moved levels in the last twenty years, and find out what changed — the spillover, the heterogeneity, or the capability.

The third question is the valuable one. Switzerland's communes fell from 2,899 in 2000 to 2,131 in 2024 — 768 gone, a fall of 26.5 percent at a mean of 32.0 a year — and every one of those mergers was a capability answer, not a philosophical one.

PART TWO — THE ARITHMETIC

Days 31–45: learn to compute before you argue

Exercise 2.1 — Estimate s six times (2 hours)

Take six functions from your list and estimate s for each: what fraction of the benefit lands on somebody other than the decider. Use the three routes from the chapter — the leakage question, the migration route, the complaint route.

Write the number to one decimal place and write the route beside it. A number without a route is a feeling.

Exercise 2.2 — Measure h rather than asking for it (90 minutes)

For any function currently decided individually, you can measure h by observation. Ask six people what level they would choose, or better, look at what they already do.

Worked, from the briefs: six branches 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 = 0.45. One uniform frequency for all six costs 0.2000 of the function's value — a fifth of the point of doing it at all.

Do this for three of your functions. You will find h is smaller than you expect for practical things and larger than you expect for aesthetic ones, and that discovery alone will change how you argue.

Exercise 2.3 — Run the rule (60 minutes)

For each of your six functions compute s* = h / (1 + h) and compare it to your s. Build the table:

functionshs*verdict

Mark any row where s exceeds s* by less than a third as contested and leave it alone. You are looking for the two or three rows where the answer is not close, because those are the only ones worth moving.

Exercise 2.4 — Sit with the cut (30 minutes, thinking only)

Write, in your own words, why the threshold is so low. At h = 0.50 — units that differ by half — the threshold is still only 33.3 percent leakage. At h = 0.20 it is 16.7 percent.

The answer is that s/(1 − s) is convex and unbounded while h is bounded: preferences cannot differ by more than everything, but leakage can approach all of it. Write that out until you could say it aloud without the page. It is the most portable thing in the chapter.

Exercise 2.5 — The condition that fails (90 minutes)

Tiebout's model says mis-assignment self-corrects because people move. Compute how long that takes where you are.

Find your country's annual residential mobility rate and the share of moves that cross a local authority boundary. For the United States: 7.8 percent moved in 2023–24; about 64 percent of movers stayed in the same county; 7.8 percent times 36.0 percent gives 2.808 percent crossing a jurisdiction in a year, and a half-life of 24.3 years. In 1948, at 20.2 percent movers, it was 9.2 years — the mechanism is 2.65 times slower.

Then ask the question that matters for your own life: how long would you stay somewhere that was assigned wrong? The honest answer is usually several years, and that is the whole reason the rule exists.

PART THREE — DREAM AND DESIGN

Days 46–70: build the register

Exercise 3.1 — Write the register (2 hours)

One page. Every function, its level, s, h, s*, the verdict, the date, and your initials. Initials matter: an estimate with nobody's name on it cannot be corrected, so it hardens into a fact.

Exercise 3.2 — Propose exactly two moves (90 minutes)

Not five. Two — the two clearest rows. For each, write four sentences: what moves, why the arithmetic says so, what the losing side gives up, and what they get instead.

Then take it to the group, and watch what happens to the conversation when two numbers arrive with the proposal. This is the exercise people report back on.

Exercise 3.3 — The capability question (60 minutes)

For each function you propose to keep local, ask whether every unit can actually perform it. Not whether they should — whether they can.

Then compute what it would cost to bring the weakest up. Use the floor formula:

      F*  =  100 x ( 1 − C / 2W* )

If C is close to 2W, F goes to zero and the answer is that no floor should exist — the function costs nearly what it is worth and should be shared or dropped. With C = 120,000 and W = 70,000, C / 2W = 0.857 and F = 14.3, below every member: no floor. With W = 225,000 the same C gives 0.2667 and F* = 73.33, and the floor is worth building.

Exercise 3.4 — Find the boundary that does not exist (2 hours)

Frey and Eichenberger's idea: let a boundary form around a single function rather than forcing every function through one boundary. Find one function in your life that wants its own boundary — a shared subscription, a rota, a purchase, a study group inside a study group — and propose exactly that boundary, for exactly that function, and nothing else.

Most people find this the most immediately useful exercise in the workbook.

PART FOUR — DESTINY AND DELIGHT

Days 71–90: make it hold, and enjoy it

Exercise 4.1 — Set a review date (10 minutes)

One date, in a calendar, for reviewing the register. Anything reviewed by exception is reviewed when somebody is angry, and angry reviews move functions for reasons the rule cannot see.

Exercise 4.2 — Watch capability move (ongoing)

Over the term, note every time a unit becomes capable of something it could not do before, or loses a capability it had. This is the variable that moves fastest. Rabobank's local member banks fell from 174 in 2010 to 106 in 2015 — 39.1 percent in five years — and then merged into one entity, because the cost of being capable rose underneath them. 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, compounding at 4.27 percent a year.

And note the other half, which is the hopeful half: through all that, the functions assigned to the federation did not move. Their joint protection scheme has run since 1934, and in the ninety years to 2024 the number of member failures that cost a depositor money is zero.

Exercise 4.3 — Notice the temperature change (ongoing)

The delight in this chapter is specific and you should look for it. It is the moment in a meeting when somebody asks what fraction of the benefit leaves the unit, and two positions that were about identity become two estimates about a function. Write down when it happens. You are learning what it feels like to dissolve an argument rather than win one.

THE TERM PROJECT

One piece of work, carried the whole way

Build a complete assignment register for one real organisation you can observe, and defend two proposed moves.

Choose something you have genuine access to: a student union, a sports club, a volunteer organisation, a small employer, a church, a co-operative, a hall of residence. Access beats prestige — a register of a twelve-person society you can actually interview is worth more than a speculative one about a government.

The deliverable, four parts.

  1. The register. Every function, level, s, h, s*, verdict, source of each estimate, and the name of whoever gave it.
  2. The two moves. Each with the arithmetic, the ratio between the two losses, and the sentence you would put in front of a committee.
  3. The capability page. One index across the units, the raw spread, the computed F*, and what the facility would cost as a share of turnover or subscriptions.
  4. The honest page. What you could not measure, which estimates are weakest, and what would change the answer. A survey that hides its gaps is an advertisement.

How it is assessed. Not on whether the moves are right. On whether the arithmetic is reproducible by somebody else from your page alone, and whether your honest page names the three things most likely to be wrong.

SELF-ASSESSMENT

Score each honestly, 1 to 5.

Under 24 and the arithmetic has not landed yet. Go back to Exercises 2.3 and 2.4, which are the two that carry the rest.

CARRYING IT FORWARD

Three things from this chapter outlive the term.

The function list. Any argument about control gets shorter the moment somebody writes the list, because most such arguments are two people holding different functions. You will be the person who writes the list, and it will make you useful in rooms you have no seniority in.

The two estimates. s and h, rough, named, in ten minutes. This is a portable skill and there is almost no competition for it: the theory has been settled since 1972 and it is still not applied outside public finance departments.

The floor. Everywhere you go you will meet the argument between "everyone should get the same" and "everyone should stand on their own." You now have the third answer, which is arithmetic: a floor, at a computed height, because the loss is quadratic and concentrated at the bottom. In Switzerland, lifting the weakest canton from 67 to 86.5 removes 9.07 percentage points of loss at 0.4650 per index point; the next stretch to 99.0 removes only 1.813, at 0.1450 per point. The first stretch is worth 3.21 times the second, and that is why the generous-sounding answer is not the good one.

APPRECIATIVE QUESTIONS FOR YOUR SEMINAR

  1. Which function in this group is at exactly the right level, and how do we know?
  2. Where have two of us solved something together without being asked to, and what made that pairing work?
  3. What would we stop arguing about if every function had a level, two numbers and a date?
  4. If our least-resourced member had what our median member has, what would change about what we can attempt?
  5. What could one of us do now that we could not do a year ago — and which decision should move because of it?
  6. When we next disagree about who decides, what will we point at, and who here could point at it without the rest of us?