FIGHTING TRAINED RAIDERS: THE ARITHMETIC OF COMMUNITY DEFENCE

When institutional protection thins out, the question that gets asked is what people should acquire. It is the wrong question, and it is wrong in a way that can be demonstrated rather than asserted. An organised raiding group does not select targets by how well defended they are in principle. It selects by expected value, and expected value is dominated by one term: the probability that the encounter stops being one against many before the work is finished.

That probability is a function of information latency, not of force. It is set by whether a household’s neighbours know within seconds and have agreed in advance what happens next. Nothing acquired individually moves it much, and the gap between the two approaches is roughly eight to one.

This note prices that gap. Every figure below is a stated model parameter, and the arithmetic is shown so that anyone who disputes the inputs can substitute their own.

The target selection function

Model an organised group that requires 12 minutes on a target and expects to extract 4,000 units of value from a single household. Model the cost of a contested encounter to that group, meaning injury, capture, identification, or the loss of a member, at 50,000 units.

The group’s expected cost is the probability of a contested encounter multiplied by the cost of one. Call that probability p. The group proceeds while expected take exceeds expected cost.

At a ratio of 1.00 the settlement is break-even and will be worked repeatedly, because a group that repeats a break-even operation profits from the variance. At 0.12 it is a losing proposition on the eighth attempt as reliably as on the first, and organised groups do not persist with losing propositions. They relocate.

Now hold p at the dispersed value of 0.08 and ask what the cost of a contested encounter would have to become to produce the same deterrence:

0.08 x C = 32,500, therefore C = 406,250 units

That is 406,250 / 50,000 = 8.125 times the modelled cost of an encounter. To match by force alone, every household would have to become roughly eight times more dangerous to meet, individually, while remaining alone. There is no acquisition that does that. Coordination reaches the same number by changing the other term, and the other term was free.

Why latency decides it

The reason p differs so sharply is geometric, and it can be computed from settlement density rather than assumed.

Model 400 households across 12 square kilometres. Density is 400 / 12 = 33.3 households per square kilometre. For a randomly distributed population, the expected distance to the k-th nearest neighbour is approximately the square root of k divided by twice the square root of the density.

• Nearest neighbour: 1 / (2 x 5.774) = 0.087 km, or 87 metres
• Sixth nearest neighbour: 2.449 / (2 x 5.774) = 0.212 km, or 212 metres

At an unhurried 1.5 metres per second, 212 metres takes 212 / 1.5 = 141 seconds, or 2.4 minutes. Six households can be present inside a 12 minute window with nine minutes to spare, and they were always that close. The distance was never the constraint.

Now the institutional alternative. Model a district response centre 22 kilometres away, moving at an average 60 km/h, with 8 minutes from first call to vehicles moving.

22 / 60 = 0.367 hours = 22.0 minutes of travel, plus 8 minutes of dispatch, gives 30.0 minutes.

The ordering is 2.4 < 12 < 30, and everything else in this analysis is a consequence of that line. Institutional protection was never the thing preventing the encounter. It was the thing that arrived afterwards and wrote it down, and its withdrawal changes the paperwork rather than the physics. What changes the physics is whether the 2.4 minute responders know, and whether they know what they agreed to do.

What each approach costs

Model a household hardening programme at 1,200 units per household: 400 x 1,200 = 480,000 units for the settlement. Model a shared alerting arrangement at 40 units per household: 400 x 40 = 16,000 units.

The ratio is 480,000 / 16,000 = 30 to 1, and the cheaper option is the one that moves p. The expensive option raises the cost of one encounter for one household and leaves the probability of a contested encounter almost where it was, because a raiding group facing a single hardened household simply visits a different one 87 metres away.

This is the actual finding, and it is unwelcome to both of the usual positions. It says that individual preparation is close to irrelevant at settlement scale, and it also says that the effective substitute is not a public institution but an agreement between neighbours, which no institution can supply and no purchase can replace.

The strongest counter-argument

Three objections are serious, and the third is fatal to part of the model.

The first is that coordination is not an intervention, it is a precondition. A settlement capable of agreeing and rehearsing a convergence protocol already possesses the social capital that the protocol is supposed to demonstrate. Where that capital is absent, prescribing coordination is not advice; it is a restatement of the deficit. The dispersed posture is frequently not a philosophy anybody chose but the residue left when nobody knows their neighbours’ names, and the residue cannot be argued away by showing it a table.

The second is that the coordinated posture carries a failure mode the dispersed one does not. The same p of 0.65 that deters a rational group also produces contested encounters with people who are not raiders: a lost driver, a delivery at an odd hour, a neighbour’s relative. The model prices the cost of contact to the raiding group and never prices the cost of a false positive, which falls entirely on someone innocent and is not recoverable. A settlement that raises p without raising identification quality has bought deterrence and sold accuracy, and the second transaction is the one it will remember.

The third objection voids the analysis in a specific case. The entire model assumes a group that is economically rational, can observe p, and is free to relocate. A group acting under coercion, under orders, or on ideological grounds does none of those things. Against such a group the expected value calculation predicts nothing at all, because the operation was not selected on expected value in the first place. Everything above applies to predation. None of it applies to policy.

That boundary matters more than the numbers, because the two situations look identical from inside a house at three in the morning and require completely different assessments.

Consequence

Three things follow.

The decisive variable in a thinning security environment is the time between an event being observed and being known to more than one household. That interval is measured in seconds, it costs almost nothing to shorten, and no individual acquisition shortens it.

The comparison that gets argued about, individual preparedness against institutional protection, is a comparison between two options that both arrive too late for different reasons: one arrives instantly with a force ratio of one, the other arrives with adequate force at 2.5 times the window. The option that is neither is the one nobody costs.

And the number to watch, in any settlement or any assessment of one, is not how much has been acquired. It is how many households can be reached in under three minutes by someone who has already agreed what to do, because that figure is p, and p is the only term in the raider’s arithmetic that anyone on the receiving end controls.

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