The Declared Regard and the Two Seats

A designer who allows an administrator to charge for something buys deterrence and imposes a loss on monitors who were sheltered before the charge existed. The classical way to price such a bargain is a bucket that leaks: so much reaches the intended end, so much is lost on the way, and the loss is a number that characterises the transfer. Neither the metaphor’s author nor the first careful measurement of it treated that number as single — the one named two acceptable leakages for two transfers, the other drew a frontier along which the marginal cost rises — so a leakage that varies is not offered here as a discovery. This paper takes a substrate in which the bargain is fully specified, and asks what a schedule of leakages does to a weight a designer has declared in advance. A companion paper has already answered a neighbouring question, and answered it exactly. It establishes the weight at which a designer who cares enough about the sheltered monitor declines to charge at all — an existence margin, in closed form, with the deterrence family entering only through its slope at the origin. That result is inherited here and not re-derived. But the question that was posed in print, by the paper whose objective could pose it and which disclaimed the answer in the same sentence, is about how far the administrator goes once he has crossed a threshold. It was posed at one margin and has to be answered at another, and at the margin where it was answered the leakage reading is empty: it returns the designer’s declared regard divided by a constant somebody else has published, and carries nothing about the model at all. At the other margin it is not a number. What the sheltered monitor loses per unit of deterrence bought varies along the charge path, so what such an instrument asks a designer to accept is a leakage schedule and not a leakage. A designer handed a single figure has been handed one point of that schedule, and which point depends on how deep the charge goes — which is the very thing the designer is choosing. The variation is not small and it is not an artefact of how the derivative was taken: it is reported on two stencils that agree to seven orders below it. Against a declared regard the schedule marks out a band of deterrence weights on which the instrument is shut. The band has one free end, because its other end is a boundary the designer does not choose; its width is exactly the declared regard times a ratio in which the least stable quantity in the problem does not appear, so the width is far more robust than the position. And the position moves in opposite directions on the two seats the companion supplies: greater prudence makes the instrument harder to defend where the monitor cannot be destroyed and easier where he can — for every regard on a ladder fixed in advance, and on cells the prediction was not formed from. A single sentence about prudence and defensibility is therefore false as soon as there are two seats, and neither seat is an invention of this paper. The paper prices what a designer is asked to accept and does not say what a designer should accept; no welfare direction is claimed anywhere in it. A reversal that a companion has located lies at regards several times the highest this paper declared, and is reported as out of reach rather than reached for — the ladder was fixed before the distance was known, which is what makes the distance worth reporting. Whether the schedule’s variation has a shape, rather than merely a size, is left where an unregistered pattern belongs.