The Price of Publicity: Loudness, Deterrence, and What a Revealed Rate Cannot Rank

An administered liability shelter can be operated loudly or quietly, and publicity is not free to the people it shelters: every unit of it lowers the threshold below which they are safe, while the deterrence it buys accrues to nobody inside the shelter. An administrator choosing a loudness is therefore trading a protection it owes against a deterrence it wants, in different units. This paper does not say what that exchange rate ought to be. It observes that the administrator’s choice states one, and that the statement is legible. Dividing protection lost by deterrence gained yields a price — the protected floor burnt per unit of deterrence bought — which is a property of the technology rather than of anyone’s preferences. Three quantities a companion paper presents separately are that price read at three points: its marginal cost is the numerator, its first-order condition says that a chosen loudness states the chooser’s own rate, and its backfire threshold is the price at a fixed loudness. Because the revealed rate and the threshold are the same price, their ratio is a pure number and the comparison needs no social welfare function. The same construction shows that the companion’s regularity condition is exactly the statement that the price never falls with loudness — the companion’s own reading of that condition, restated as a property of the price. The deterrence technology enters through a single number, its slope at the backfire loudness, because the threshold’s other ingredients contain none of it; any two admissible forms agreeing there agree everywhere. Over a population of monitors, under a declared map from tasks to shelter terms, the administrator’s revealed rate fails to clear the threshold on about one covered task in six. The reading has a measured domain: a silent administrator yields a bound rather than a rate, and where the regularity condition fails the identity survives while identification does not. What the reading does not support is stated as a result rather than a caveat. The conventional threshold is not the loudness at which protection ends, and counting harm instead of crossings gives a smaller share and reverses the ranking of deterrence forms. One welfare conclusion survives without any weight: any harbour that speaks at all, up to the conventional threshold, leaves the sheltered weakly better protected than no harbour and delivers strictly positive deterrence. Choosing among louder harbours does not, because every interior loudness is Pareto-efficient, so a strict ranking requires a weight, a constraint, or a priority — and a decision criterion under ambiguity cannot supply one, since the metric that made the comparison weight-free has only one direction.