Exercise Bank — Coalitions, Organisations, and Institutions

The printed Chapter 13 keeps Exercises 1–6; the bank continues from Exercise 7.

Exercise 7. Simon’s claim that organisations are prosthetics for bounded minds becomes, for language-model agents, an exercise in arithmetic, because the bound has a number. Take a team in which every worker posts 8 status updates of 300 tokens per sprint, a supervisor’s digest costs 500 tokens, and no member can attend to more than W = 200{,}000 tokens of inbound traffic per sprint; count only what a member must read. (a) In the flat congregation — every update visible to every member — compute the per-member load at n = 100 workers, and find the largest team the window admits. (b) In the single-supervisor hierarchy, each worker reads one digest and the supervisor reads everything: compute both loads at n = 100, find the largest pool one supervisor can attend to, and state what the hierarchy did to the overload — the pathology Section 13.3 names. (c) Add a middle tier of k coordinators, each digesting for n/k workers and reading one digest from the top: show that k = 2 makes n = 100 feasible, derive the general branching bound b, compute the worker capacity of hierarchies two and three tiers deep, and conclude with the growth law that says why attention scales with depth. (d) The digest is not free: name its price in the chapter’s terms, then specify the middle coordinator’s position as the three-clause role bundle of Section 13.3 — what it reads and forwards, what it must be empowered to settle without escalating (and what becomes of the saving if it may settle nothing), and what it answers for when its digest omits the fact that mattered.

Exercise 8. Foundry is a four-agent harness assembled by the book’s least favourite method: the system prompts announce a “Chief Executive Officer”, a “Chief Technology Officer” (“ultimately responsible for architecture”), a “Senior Staff Engineer”, and a “Head of Quality”; every agent receives the identical full transcript every turn; every agent holds the identical toolset, including git.push to the default branch; the run terminates when any message contains “ship it”, whoever says it; and no record survives of who approved what. (a) Dismantle it with Section 13.3’s three-clause test: for each title, say what its holder sees, may do, and must answer for, and conclude what the four titles are in the chapter’s vocabulary. (b) Redesign it minimally: for each of the four roles specify the three clauses concretely — the context filter (what it reads), the authority (the one or two tool permissions or decisions it alone holds), and the accountability (the ledger entry that attributes its consequential acts); then write the redesign’s three load-bearing constitutive rules in Searle’s “X counts as Y in context C” form, each machine-checkable in the manner of Section 13.4’s electronic institutions. (c) Map the three MAST failure families the chapter re-reads as missing organisation — specification, inter-agent misalignment, verification-and-termination — each to the clause whose absence invites it in Foundry as shipped, and to the redesign element that forecloses it. (d) Choose exactly one rule of your redesign to regiment and one to enforce, justifying each by the chapter’s decision rule — and note, for the regimented one, what the wall costs on the night the emergency arrives.

Exercise 9 (lab). Section 13.1‘s boldest claim is that for agent teams the characteristic function is an empirical object; measure one. Fix a pipeline of three live-model stages — coder, tester, reviewer, in that order, later stages reading earlier stages’ output — over a suite of ten small, independent programming tasks with hidden unit tests, one fixed prompt per role, one fixed per-run token budget. For each of the seven non-empty subsets S of the three roles, run the pipeline with only S’s stages present (missing stages are simply skipped) and record v(S) as the number of tasks whose hidden tests pass, averaging at least two repetitions per subset; set v(\emptyset) = 0. Then (a) test superadditivity on every disjoint pair of non-empty coalitions and report any violations, with a sentence on what they say about this team’s shape; (b) compute the exact Shapley division of v(N) with the repository’s foundations/algorithms/shapley.py; (c) compute the leave-one-out audit from the same table and report whether it ranks the three roles in the same order; (d) test whether the equal three-way split of v(N) lies in the core using in_core, and if it does not, name a seceding coalition. Record the model identifier and the date beside the table: the scores will not survive the year, and the durable finding is the method — and whether the reviewer’s marginal value survives being measured rather than assumed.

Exercise 10 (lab). The organisational paradigms of Section 13.3 make different promises; buy one of each and audit them. Same four live-model agents, same twelve small independent repository tasks, same total token budget per condition, three wirings: a hierarchy (an orchestrator decomposes, assigns, integrates, and alone declares termination); a congregation (one shared channel, no assigned authority, any agent may claim any task); and a market (each task auctioned to the workers by announce–bid–award, with the repository’s foundations/algorithms/contract_net.py supplying the protocol). Journal every run in the manner of frontier/rig.py, and count per condition four MAST-style failure events, each defined as something legible in the journal — detectors in the manner of frontier/patterns/signatures.py, the census discipline of frontier/scaling_lab/sweep.py: duplicated work (two agents complete the same task), orphaned task (no agent ever claims it), contradictory artefact (two agents’ outputs conflict at integration), and non-termination (the run ends by budget exhaustion rather than by a declared finish). Tabulate the four failure counts beside quality, tokens, and latency for each wiring; then write the finding as Horling and Lesser would — one sentence per topology naming the failure family it invites and the one it forecloses — and check it against the paradigm trade-offs the chapter maps onto modern topologies. Record the model identifier and the date: the counts are perishable; the assignment of failure family to topology is the durable pattern, and the chapter’s claim that these trade-offs were measured decades before today’s frameworks is what your table either confirms or complicates.