La Bourse / Volume VI / Nº VI.01 / Quiz, reflection, essays

Four colleagues walking toward a long table set with dried grasses, the room bright with sun. — Plate VI.01 · Quiz, reflection, essaysThe Table Before the Meeting.A decision rule is furniture. It decides who can be in the room, how long they will be there, and who is not in the room at all — and it does this before anybody has said a word.

ASSESSMENT · Chapter VI.01 — Who Decides

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. Name the two cost curves in Buchanan and Tullock's calculus of consent, say which way each moves as the required majority rises, and state what the optimal majority is.

External cost — the harm to those a decision goes against — falls as k rises and reaches zero at unanimity. Decision cost — the time and bargaining needed to assemble agreement — rises as k rises, and rises steeply near unanimity. The optimal majority is the k that minimises their sum. One mark for the two curves and their directions, one for the sum being a minimum rather than a principle.

2. Write the expression for the minimal blocking coalition under a k-of-n rule, and give the figure for Article V of the United States Constitution.

n − k + 1. Article V needs 38 of 50 states, so 13 states can block — and those thirteen, if they are the least populous, hold 4.41 per cent of the population.

3. What distinguishes a consent rule from unanimity?

Consent keeps the veto and narrows the grammar of objection: an objection must be argued and paramount — a reason the proposal will not work or will harm the aim — and a preference does not qualify. That restriction is what collapses the expected number of rounds.

4. State May's theorem and say what it implies about every supermajority rule.

For a choice between two alternatives, simple majority rule is the only rule that is anonymous, neutral and positively responsive (May, 1952). Neutrality means treating the status quo and the proposal alike; therefore every supermajority rule is a deliberate, priced preference for the status quo.

Four on application.

5. A cooperative of nine adopts unanimity "so that nobody can be overruled." On the chapter's parameters, what have they bought and what have they paid?

They have bought external cost of £0 and paid decision cost of 99.23 rounds per decision — £3,858,025 a year for twelve decisions. The stronger answer notes that this is not stable: bodies in this position stop bringing contested questions to the rule at all, so the real effect is that decisions migrate to whoever can act without asking, which is an unpriced and unaccountable rule.

6. A team says its consent process "means everyone agrees, so nobody loses." Correct it, with a number.

At an admissible-objection rate of 10 per cent in a body of nine, consent behaves like a 6.23-of-9 rule — 69.2 per cent — and carries external cost of £110,918 a year against £0 under true unanimity. The people paying it are those whose objection is a genuine preference they cannot phrase in the required grammar. Full marks require naming the group, not just the number.

7. The Senate's 1975 reform raised the blocking coalition from 34 senators to 41 and filibustering became more common, not less. Explain.

A rule has two parameters: the threshold and the effort. The reform raised the threshold — blocking got harder on paper — and simultaneously removed the requirement to hold the floor, which cut the effort to near zero. Decision cost for the blocker fell, so blocking rose. Changing only the threshold is how an institution reforms itself in the wrong direction.

8. A colleague argues that a 99-member citizens' assembly is "statistically representative of the nation." What is wrong, and what is the better defence of sortition?

At n = 99 the 95 per cent margin of error on a simple proportion is ± 9.8 points, which is not a polling instrument. The better defence is counterfactual: a deliberative body reports what the public concludes when it has the evidence, the time and each other — which no poll of any size produces.

Two that cannot be answered without doing the arithmetic.

9. A board of nine, with p = 0.60, three hours of each member's time per round at £120 an hour, and twelve contested decisions a year, is about to decide a class of question where a member left outside the winning coalition bears £100,000. What threshold should it use, and what does that rule cost a year?

One round costs 9 × 3 × £120 = £3,240. Compute the total at each k and take the minimum. It falls at 7 of 9 — 77.8 per cent — at £434,407 a year. Marks are for the method: the candidate must show the sum being minimised, not assert a threshold. Note that at £30,000 the same board should sit at 6 of 9 and at £300,000 at 8 of 9; the body has not changed, only the stake.

10. An assembly of 1,200 deciding directly costs £10,114,446 a year in decision cost for twelve decisions. Delegated to a board of nine at 6-of-9 the same decisions cost £80,562. The board is expected to diverge from the assembly's majority preference on 25 per cent of decisions. Above what loss-per-divergent- decision should a matter be reserved to the assembly rather than delegated?

The saving is £10,114,446 − £80,562 = £10,033,884. The break-even is saving / (divergence × decisions) = 10,033,884 / (0.25 × 12) = £3,344,628 per divergent decision. Delegate below it, reserve above it. The stronger answer observes that this is the reserved-matters schedule derived from first principles, and that the number is large — which is why delegation is universal and why the exceptions must be written down before anyone knows the question.

REFLECTION — eight questions, for one person and a pen

Think of a decision that went against you under a rule you had agreed to in advance. What did that feel like compared with one that went against you under a rule you found out about afterwards?

Where in your working life do you currently hold a veto? What does it cost the people around you for you to hold it, and what does it prevent?

What is the largest loss-if-wrong you are personally responsible for, and what rule is that decision currently made under? Did anybody choose that rule?

When you object to something, is your objection usually about whether it will work, or about whether you would prefer something else? Be honest about the ratio.

Name a group that pays for a rule you benefit from. What would it take for you to find out what it costs them?

Where have you spent decision cost — hours, meetings, attention — on a question whose stake did not justify it? What would you have done with those hours?

Think of a time you delegated something and it came back wrong. Was the loss above or below the level at which you should have reserved it — and did you know that level at the time?

What is one decision you have been protecting with a high threshold because you are afraid of the outcome rather than because the stake is large?

ESSAY PROMPTS — five

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

1. "A supermajority is a transfer of decision rights to a named minority, and an institution that cannot name that minority has not chosen its rule." Argue this for or against, using Article V and one further constitutional example the chapter does not treat.

2. Buchanan and Tullock price every cost from the status quo, so the status quo costs nothing. Argue whether the calculus of consent survives the addition of a status-quo harm term, and what it implies for the constitutional rules of existing organisations. Draw on May (1952) and on at least one critic of public choice theory.

3. "Sortition's claim is counterfactual, not statistical." Defend or attack this, using the Irish Citizens' Assembly and one deliberative process outside Ireland that the chapter does not cite.

4. Zappos claimed Holacracy would lower both decision cost and external cost at once. Argue what actually happened to each, who paid, and whether a differently designed self-management system could have avoided it. Use Bernstein et al. (2016) and at least one primary account from inside a self-managing organisation.

5. "Every organisation should have three decision rules, not one." Make the case for or against a banded schedule of reserved matters as standard corporate practice, and address the consolidation consequences under IFRS 10. Cite one accounting or legal source beyond those in the chapter.