Watching the Baltic seabed

Six statements about the model; the mapping to the Baltic is a reconstruction R.

• Prices coordinate, and they prove. Without coordination every unit goes to the zone that is best for it — the same zone for all five — and the alliance's detection value is $8$. Bidding through prices, with no member revealing its values, reaches $33$ in eight bids, and the final prices with each member's own profit prove that no plan does better: the duality gap is $\frac{2}{3}$, below the integer step (Proposition 8.11 (p. 338)(a), Table 8.2 (p. 324)). A coordinator who could never collect the values can still verify the plan D [Proposition 8.11 (p. 338)(a)].

• The increment is a policy choice. With an increment of $2$ or more the auction settles one unit short of the optimum, at $32$; the a priori guarantee $\mathrm{OPT}-n\epsilon$ falls much faster than the value actually reached (Table 8.2 (p. 324)b). Faster bidding buys speed with a guarantee, and the price is written in advance D [Proposition 8.11 (p. 338)(a)].

• A withheld unit has an exact price, and the plan bounds it in advance. Withholding costs $6$, $7$, $4$, $6$ and $5$ for the frigate, aircraft, cutter, drone group and minehunter. The interval between the unit's profit less the gap and its own value in its zone contains each cost, and both ends come from the auction's output alone, with no re-planning (Proposition 8.11 (p. 338)(b)). The cutter holds the most valuable zone but is the cheapest to lose, because the others can reshuffle to cover it: how much a unit is worth depends on the whole assignment, not on the zone it holds D [Proposition 8.11 (p. 338)(b)].

• An agreed assessment is a weighted average, and the weights are politics. From the same five assessments, equal weights give the pooled view $\frac{1}{2}$ and the lead-nation weights give $\frac{37}{65}$, because the lead nation controls $\frac{5}{13}$ of the result instead of $\frac{1}{5}$ (Proposition 8.11 (p. 338)(c), Figure 8.4 (p. 325)). Against the threshold $\frac{11}{20}$ the first protocol does not act and the second does. Under the lead-nation weights the pooled view sits $\frac{1}{52}$ above the threshold, so the lead nation reverses the decision by lowering its own assessment by any amount more than $\frac{1}{20}$ (exactly $\frac{1}{20}$ leaves the view on the threshold, where the alliance still acts), and any other member needs more than $\frac{1}{8}$. Under equal weights a member must raise its own assessment by $\frac{1}{4}$ to bring the view up to the threshold, which every member except M1, already at $\frac{4}{5}$, can do. The sentence “the alliance assessed the vessel as a threat” therefore describes the pooling rule as much as the evidence D [Proposition 8.11 (p. 338)(c)].

• One member that never updates outweighs a lead nation. If M5 holds its assessment fixed, every member converges to $\frac{1}{5}$, under equal weights and under the lead-nation weights alike: the stubborn member's share is all of it (Proposition 8.11 (p. 338)(c)). A member that never revises its view, for good legal reasons or bad ones, does not hold one vote among five; it holds the outcome D [Proposition 8.11 (p. 338)(c)].

• Two fixed views split the alliance. With M1 and M5 both fixed there is no agreement: the others settle at mixtures of the two fixed views set by their place in the network, and only one of them ends above the threshold (Proposition 8.11 (p. 338)(d)). A shared picture fed by members who will not move still converges, but not to one view; it hardens into positions D [Proposition 8.11 (p. 338)(d)].

The members are not a team. Each has its own waters, laws and priorities, and its units have national tasks first; the auction assumes members bid their true values for a common objective, and nothing here shows that a member gains by doing so (Model A1's certificate is a verifier's object, not an incentive property). Jurisdiction is part of the problem, not a parameter: the record shows two Finnish courts disagreeing over whether Finnish criminal law applies to damage done from a foreign-flagged ship, and a member's legal tools may decide whether a “unit” can do anything in a “zone” at all. Detection values are not additive: two units in one zone detect more than one, coverage overlaps across zone boundaries, and units move, refuel and rotate, which turns a static assignment into scheduling over time. Pooling assessments by averaging is a protocol, not inference: members whose reports rest on the same data (the same ship-tracking feed, the same radar picture) are counted twice by an average, and a Bayesian fusion would weight evidence, not members (Chapter 1). And the variable being assessed is itself contested: in the record, one incident first treated as suspicious was later found by prosecutors to be an accident, and others remain unresolved; a “stubborn” member may simply be applying a higher evidential standard before boarding a ship. The model says what each rule computes; it does not say which rule is right.