Coalitions · attribution · assumptions
Three different questions. Coalition worth and the Shapley allocation describe contribution to an invented game. A separate consent index sketches reactions to a package. Neither is a consent decision, a payment agreement, or evidence that a real project can proceed.
Start by switching guideline clarity off and on. Inspect the paired inspection effect, then open Scenario lab to see every party’s signed contribution and any coalition objection. Change the selected gate parties under Parties. All scenario coefficients export with the versioned calculation rules.
An exact allocation in an invented game
Grand coalition worth: model units.
| Party | Signed Shapley φ | φ / grand worth | Consent index, round 1 | Utility |
|---|
Negative contributions stay negative. Ratios can exceed 100% or be negative in nonmonotone games; no ratio is shown when total worth is near zero. These are allocations of mathematical worth, not charges or agreed shares.
Shortfall = v(S) − Σ φᵢ for i in S. The gate filter below affects only the ranked explorer; attribution and this diagnostic always use the full game.
| Party | Role | Gate | Threshold | Concession cost | Risk | Schedule | Cost | Public |
|---|
o(S) = clip₀¹(b + sequence + Σ active owned levers + Σ included pair effects)
Four coordinates: risk control, schedule confidence, cost certainty, public confidence. Base b = (0.46, 0.42, 0.43, 0.45). Pair effects apply only when both levers and their owners are present.
H(o) = ∏ₖ max(0.005, oₖ − 0.20)
v(S) = max(0, H(o(S)) − H(o(∅)))
The floor and clipping are original modelling choices. v(∅) = 0. Negative worth is clipped in this scenario, but a party’s marginal contribution can still be negative. Concession costs and gate flags do not change v.
φᵢ = Σₛ |S|!(n−|S|−1)! / n! × [v(S∪{i}) − v(S)]
Sum over coalitions excluding i. Seven parties give 128 coalitions. This exact weighted-subset calculation equals averaging all 5,040 arrival orders. Efficiency, symmetry and the dummy property concern this specified game.
Σᵢ φᵢ = v(N)
Σᵢ∈ₛ φᵢ ≥ v(S) for every S
These are the core conditions tested here with numerical tolerance 10⁻¹⁰. Failure means the Shapley vector is outside the core; it does not prove that no other allocation lies in the core.
Utility is normalised weighted outcomes minus active costs: each active lever charges its owner’s concession cost plus the lever’s listed costs. A logistic response combines α × (utility − threshold), β × (reputation − base reputation), and the influence-weighted deviations of other indices from 0.5.
Indices start at 0.52 and update 34 times using 0.62 × old + 0.38 × logistic response. There is no convergence guarantee or probability calibration. With gates enabled, the project index is the product of selected gate indices times 1 − product(1 − optional index). Without gates it is 1 − product(1 − every index). No optional parties means optional factor 1; no mandatory parties means mandatory factor 1.
Each round: reputation target = clip(base reputation + 0.30 if utility ≥ threshold, otherwise −0.12, minus 0.55 × total surprise). Next reputation = 0.84 × current + 0.16 × target. Total surprise is the selected preset plus the slider. The timeline shows 12 rounds with no time units.
Working-split utility = party utility + platform effect × (group mean utility − 0.5). The group averages remain fixed during the comparison. All gains, including negative gains, are recorded before testing ε.
Clause priority is active linked-lever count + 2 if linked to the top pressure + 1 if owned by the largest attributed contributor. A score of at least 2 highlights a clause. The full pressure formulas, coefficients and narrative inputs are preserved in model.js and data.js ; all numerical scenario inputs and coefficients export with each scenario. The calculation rules remain in this versioned model file.
The original Shapley memorandum (1951) supplies the mathematical attribution idea. The outcome coefficients, influence matrix, trust rules and clause-selection heuristics here are invented demonstration inputs, not results from that paper.
ONR’s licensing account describes statutory nuclear site licensing. The Environment Agency’s nuclear-site permit guidance applies to England. Those processes are distinct from the voluntary coalition game and its scores. Changing an in-app gate or agreeing a commercial package cannot grant a licence or permit.
Primary sources checked 3 October 2026. The original UK-wide framing is narrowed to a hypothetical England setting because EA is the named environmental regulator. NDA, councils, operator, contractor and insurer roles here are broad scenario shorthand.
Preservation inventory, provenance and verification. This bounded example belongs with Decisions & trade-offs: how contribution, coalition objections and an agreement differ. It does not establish a new research result.
Attribution asks: across every arrival order, what is each party’s average marginal contribution? Signed contributions sum to the grand coalition worth; they do not determine payment or bargaining power.
ONR and EA start as selected gate parties in this fictional example. The product of their indices is multiplied by “at least one optional party” under an independence-shaped formula. These are coupled scores, so that expression is not a calibrated project probability.
The toy rule moves reputation toward a target depending on whether utility meets a threshold, minus a surprise penalty. This is an assumption to inspect, not a measured account of trust.
The retained heuristic compares fixed assurance and delivery group averages. Stable means max positive gain ≤ ε/2; At risk means ε/2 < gain ≤ ε; Unstable means gain > ε. It does not model a move or the ensuing group response.
The largest illustrative pressure score chooses the first discussion prompt. Question the score, omitted constraints and any proposed clause before using the prompt.
The numbers are demonstration coefficients. Use them to rehearse judgment, not to decide statutory, engineering, or legal questions.