Prior Use and the Distribution of Observational Capacity in State-Dependent Governance

Wanhong Huang

Abstract

A governing rule whose content depends on the dynamical state of the system it governs requires that the state be determined. Where the system exhibits a critical value above which ordinary conduct produces irreversible foreclosure, the determination that the system has approached that value carries the whole of the rule’s practical force, and the question of which party is competent to make it becomes the governing question. This paper argues that the competence and the interest converge. The capacity to determine the state of such a system consists in instruments, records and continuous observation, and these are acquired in the course of using the system. A determination that the system stands near its critical value contracts the permissions of every party and bears most heavily on parties whose use lies in prospect. The party best equipped to make the determination is accordingly, and systematically, the party the determination favours. The paper establishes the convergence formally under stated assumptions about the acquisition of observational capacity, distinguishes it from the classical problem of emergency authority by the respect in which the epistemic asymmetry is prior to the legal one, and establishes that the two responses developed for emergency authority both presuppose a separation between determining the state and being a party to the outcome that the present case denies. Three consequences are drawn: constraint by ex ante criteria requires an evaluator holding the instruments; termination conditions keyed to the state inherit the same defect as the trigger; and a party disadvantaged by a determination lacks the standing to contest it on evidential grounds. The paper closes by stating what a defensible arrangement would have to secure and by recording that it proposes none.

Keywords: criticality; emergency authority; state of exception; observational capacity; orbital governance; epistemic injustice; generative relational governance.

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Part I — The Object and Its Antecedents

1 Introduction

1.1 The Determination Required by a State-Dependent Rule

A governing rule ordinarily attaches a consequence to a description of conduct. Rules of this form are assessed for generality, and their holding across circumstances is among the properties that recommend them.

A class of systems admits no adequate rule of that form. Where a system carries a critical value above which the accumulation of individually unremarkable conduct produces irreversible foreclosure, a rule attaching consequences to conduct alone is silent on every occasion at which the accumulation proceeds. A rule adequate to such a system attaches its consequence to conduct together with the condition of the system at the time, taking the form

$$\pi = \pi(X_{t}),$$

in which $X_{t}$ denotes that condition. A companion paper establishes that a rule of this form is required by the dynamics of such systems, and the present paper takes the requirement as given.

This carries a consequence that its formal statement conceals. The rule cannot operate until $X_{t}$ has been determined, the determination is an act performed by some party, and the content of the rule for every other party follows from it. Whatever else is settled about the rule, the determination carries its practical force entirely.

1.2 The Classical Problem and the Responses Developed for It

A rule whose content depends on an authority’s determination that ordinary circumstances have lapsed is the structure of emergency government, and two responses to it are well developed.

The first constrains the authority by law. Constitutional emergency provisions specify the conditions under which a declaration may be made, the powers it confers, the period for which it runs, and the body competent to review it. The literature on emergency powers has established both the design of such provisions and the characteristic ways they fail.

The second removes the determination from the interested party and vests it in a body constituted for the purpose. Scientific advisory bodies attached to treaty regimes, standing panels of assessment, and expert committees within international organisations all take this form, and the arrangement is familiar wherever a legal consequence turns on a technical finding.

Each response presupposes a proposition, and the propositions differ. Constraint by law presupposes that a party other than the declaring authority can evaluate whether the declared conditions obtain, since a criterion no one else can apply constrains no one. Delegation to a body presupposes that the finding the body must make is available to a party constituted without a stake in the outcome.

Both propositions fail for the systems at issue, and they fail for the same reason. The condition $X_{t}$ of a system of this kind is established by continuous observation carried out with instruments, and the observation is neither public nor cheap. The party holding the instruments is the party that acquired them, and instruments for observing a system are acquired by parties that use the system.

1.3 The Thesis

The paper’s thesis concerns the relation between two rankings over the parties to such a system.

Rank the parties by their capacity to determine $X_{t}$, which consists in instruments deployed, records held, and observation sustained over the period from which a trend is established. Rank the parties separately by the benefit each derives from a determination that the system stands near its critical value, that benefit consisting in the contraction of the permissions of others relative to use already realised.

Thesis 1.1 (Convergence of competence and interest). For systems whose observation requires instruments acquired in the course of use, the two rankings coincide in order. The party best equipped to determine that the system has approached its critical value is the party that a determination to that effect most favours.

The convergence is established formally below under assumptions declared there, and its three consequences occupy Part III. Constraint by ex ante criteria requires an evaluator holding the instruments, and the criteria are therefore applied by the party they were written to bind. Termination conditions keyed to the state inherit the defect of the trigger, since the determination that a system has left its critical region is made by the same party and rests on the same instruments. A party disadvantaged by a determination lacks the evidential standing to contest it, and its objection takes a form the arrangement answers by pointing to the record.

1.4 The Departure from the Classical Diagnosis

The classical diagnosis of emergency authority locates the difficulty in the legal relation: an authority competent to declare the exception is competent also to determine that it continues, and the arrangement tends toward permanence.

The present diagnosis locates the difficulty one step earlier, in the epistemic relation. The competence at issue is a competence to know, it is distributed by a process independent of any legal arrangement, and it is prior to the legal competence in the respect that a legal power to determine the state is exercised through the instruments that establish it. An arrangement conferring the legal competence on a neutral body leaves the epistemic competence where it was, and the neutral body determines the state by consulting parties that hold instruments.

This departure has a consequence for what a repair would have to accomplish. A repair operating on the legal competence alone addresses the second relation and leaves the first in place.

2 Scope of the Account and the Restrictions It Accepts

2.1 The Relation to the Companion Paper

The companion paper establishes three results that the present account takes as given.

The first is a criterion allocating the burden of justification to a party whose course would irreversibly foreclose the generative capacity of a trajectory other than its own. The second is that the criterion fails to compose: a sequence of courses on none of which it fires may produce the foreclosure it exists to allocate a burden for. The third is that the repair which composition requires makes the governing rule a function of the dynamical state, and that a rule of this form carries the structure of the exception.

The companion paper states three constraints bearing on that structure and identifies the questions each leaves open. The present paper takes those questions as its object. Nothing here re-argues the criterion, and a reader who rejects it may still hold the results of Parts II and III, which concern the determination of a system state under any rule that requires one.

2.2 The Object of the Account

The object is the determination that a system stands within a region in which the governing rule takes a particular form, together with the allocation of competence to make that determination.

Three features of this specification carry weight.

The determination concerns a state of the world, and its correctness is a factual matter. This distinguishes it from a decision, which selects among courses and admits assessment for wisdom. A party disputing a determination disputes a claim about how things stand.

The determination is made under the conditions established by the companion paper, in which the system exceeds what any party represents. A determination made under those conditions is defeasible, is made on partial evidence, and admits reasonable disagreement among parties observing the same system with different instruments. Such disagreement is what the description of a field as heterogeneous records throughout this series. A field is heterogeneous with respect to a party when no common measure over its participants is available to that party, so that estimates formed under different instruments admit no reconciliation by appeal to a scale both parties hold.

The parties to the system are plural and their prior use is unequal. An account addressed to a single party governing its own conduct would raise none of the questions treated here, and the plurality together with the inequality is what generates them.

2.3 Restrictions Accepted by the Account

The account is restricted in four respects.

It concerns competence and remains silent about correctness. The account establishes which party is positioned to make a determination and establishes nothing about whether any particular determination is right.

It concerns the determination and remains silent about the consequence attached to it. What follows from a finding that the system stands near its critical value is settled by the rule, and the companion paper states the rule the present account assumes.

It concerns systems whose observation requires instruments acquired through use. Systems observable by instruments available independently of use fall outside the argument.

It concerns the structure of the arrangement and remains silent about the motives of the parties within it. The convergence obtains whether or not any party seeks the advantage it confers, and an account resting on bad faith would establish something weaker.

2.4 Resources Imported

Four resources are imported.

The analysis of the exception and of its tendency toward permanence is taken from the tradition running from Schmitt through Agamben, and the paper’s departure from that tradition is stated above.

The design and the failure modes of constitutional emergency provisions are taken from the literature on emergency powers, which supplies the account of what constraint by law achieves and where it fails.

The analysis of testimonial and hermeneutical injustice supplies the vocabulary in which the contestation problem is stated.

The account of the first repair’s limits, and the classification of transitions on which those limits rest, is taken from the companion paper and through it from the dynamical systems literature.

2.5 Settings Examined

Two settings are examined in Part IV and are chosen for the difference in the source of the inequality.

The first is the determination of the state of a congested orbital region. The inequality there arises from deployment, since the instruments that establish orbital state are held by the parties that operate in orbit and by the states that launched them.

The second is ecological monitoring, where the inequality arises from the wealth of the party in whose territory the system lies. The determination of an ecosystem’s condition rests on records whose density varies with the resources available to maintain them, and the variation is unrelated to the ecological significance of what is monitored.

2.6 Positions Declined at the Outset

Four positions are declined and each is argued in Part V.

The account asserts no claim that determinations are made in bad faith. The convergence is structural, and an account resting on motive would establish less.

The account asserts no general thesis that observation requires use. The relation holds for the systems specified and fails for others, and the argument is confined accordingly.

The account proposes no allocation of the competence to determine. The closing section states what a defensible arrangement would have to secure and stops there.

The account proposes no scheme for equalising observational capacity. A scheme of that form would be an institutional design, the companion paper’s grounds for declining institutional design apply here, and the second setting supplies a further ground, since the capacity in question is expensive and its distribution tracks a distribution of resources that no governance arrangement establishes.

3 Prior Treatments of Emergency Authority and of Determination by Expert Bodies

3.1 The Exception and the Competence to Declare It

Schmitt locates sovereignty in the competence to determine that the ordinary situation has lapsed, and the claim owned is that this competence is logically prior to the legal order it suspends, since no norm specifies the conditions of its own suspension in a manner that removes the judgement.

Agamben establishes the tendency of such arrangements toward permanence, and the claim owned is that the authority competent to declare the exception is ordinarily the authority competent to determine that it continues, so that the temporary measure becomes a technique of ordinary government.

Both accounts treat the competence as a legal and political one. The determination they analyse concerns a situation whose lapse is a matter of political judgement, and the difficulty they identify lies in the absence of a party positioned to review that judgement. The determination at issue in the present paper differs in kind, since it concerns a state of a physical system and its correctness is a factual matter.

3.2 The Constraint of Emergency Authority by Constitutional Design

Ferejohn and Pasquino set out a typology of emergency powers and establish that constitutional systems address the problem by specifying in advance the conditions of a declaration, the powers it confers, its duration, and the body competent to review it. Gross and Ní Aoláin examine the models available and establish the characteristic failures of each, including the migration of emergency measures into ordinary law.

The claim owned by this literature is that the exception admits partial constraint by prior specification, and that the constraint operates through the availability of the specified conditions to a reviewing body.

The availability of the conditions to a reviewing body is the presupposition identified above, and it fails for the determinations at issue here. The literature treats conditions whose obtaining is establishable by a court on evidence a court can receive, such as the presence of hostilities or the interruption of ordinary government. A finding that a system stands within a region of its state space is establishable on evidence of a different kind.

3.3 Emergency Framing in Environmental Politics

Wainwright and Mann establish that the response to planetary environmental crisis tends toward the constitution of an authority competent to declare emergency and thereby to determine which parties are spared, and the claim owned is that this tendency is a political consequence of the crisis and stands independent of any party’s intention. Earlier arguments in the tradition running through Ophuls hold that ecological limits require the concentration of authority, and the present literature is largely addressed to resisting that inference.

The debate concerns whether authority should be concentrated. The present paper takes no position in it and establishes a result that holds whichever position is adopted, since the result concerns which party is positioned to make a determination under any arrangement in which some party must.

3.4 Determination Removed to a Body Constituted for the Purpose

Where a legal consequence turns on a technical finding, the finding is characteristically removed from the interested party and vested in a body constituted for the purpose. Scientific committees attached to treaty regimes, standing assessment panels, and expert advisory bodies within international organisations all take this form.

Jasanoff establishes that such bodies perform work that is neither purely technical nor purely political, that the boundary between the two is itself negotiated in the course of their operation, and that the authority of their findings rests on the maintenance of that boundary. The claim owned is that the removal of a finding to an expert body relocates a political question and leaves it in place.

The present paper’s difficulty is adjacent to this one and differs from it. Jasanoff’s analysis concerns the composition of the finding and the interests operating within the body. The present analysis concerns the provenance of the evidence the body receives. A body of impeccable composition, deliberating without any interest in the outcome, determines the state of the system by consulting records, and it has been established who holds them.

3.5 Credibility and the Distribution of Epistemic Standing

Fricker establishes two forms of epistemic injustice. Testimonial injustice occurs where a hearer accords a speaker less credibility than the speaker’s testimony warrants, on the ground of a prejudice attaching to the speaker’s social identity. Hermeneutical injustice occurs where a collective interpretive resource is impoverished in a manner that leaves some group unable to render an aspect of its experience intelligible. Dotson extends the analysis to cases where a speaker’s contribution fails through the persistence of a shared resource inadequate to receive it.

Wynne established a case of a different kind and it bears directly on the limits of the present argument. Cumbrian sheep farmers subject to restrictions following radioactive deposition held detailed knowledge of local terrain, drainage and grazing on which the scientific advice they received had not drawn, the advice failed in ways their knowledge would have anticipated, and the standing accorded to their observation was lower than its accuracy warranted. The claim owned is that local observation sustained over long periods may carry epistemic standing that institutional assessment fails to receive.

The claim owned by this family is that epistemic exchange carries injustices distinct from the distribution of material goods, and that the correction of a credibility deficit is a requirement of justice.

The difficulty treated below is related to these and differs from them in a respect that determines what corrective is available. A party lacking the instruments to establish the state of a system suffers a credibility deficit with respect to claims about that state, and the deficit is warranted. Its testimony is in fact less well supported, its assertions do rest on thinner evidence, and a hearer according it the credibility that instrument-holding parties receive would be crediting a claim beyond its warrant. The corrective developed for testimonial injustice consists in the correction of prejudice, and the correction of prejudice leaves a warranted deficit exactly where it stood.

3.6 The Class Surviving the Surveyed Treatments

Claim 3.1 (Residue of the surveyed treatments). The treatments surveyed locate the difficulty of a state-dependent rule in the priority of sovereign competence to the legal order, in the tendency of declared exceptions to persist, in the political constitution of expert bodies, or in a credibility deficit produced by prejudice or by an impoverished interpretive resource. Where the declaring authority is constrained by prior specification, the declaration is reviewable by a constituted body, the body deliberates without interest in the outcome, and no party suffers any deficit of credibility that a correction of prejudice would remedy, the determination may still be made on evidence held by the party the determination favours. No treatment surveyed addresses the allocation of the instruments by which the state is established.

The class is populated and Part IV examines two of its members. The remainder of the paper is addressed to it.

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Part II — The Structure of the Determination

4 The Components of a Determination of System State

4.1 The Determination Distinguished from a Decision

A decision selects among courses available to a party and is assessed for wisdom. A determination asserts that the world stands in a certain condition and is assessed for correctness.

The determination at issue asserts that a system occupies a region of its state space. The assertion is factual, it is defeasible, it is made on partial evidence under the conditions the companion paper establishes, and it admits reasonable disagreement among parties observing the same system with different instruments.

Three features follow. A determination may be mistaken in a sense in which a decision may not, so that a party contesting it contests a claim about how things stand. A determination made correctly may still be contested, since the evidence supporting it is partial. And a determination requires no exercise of preference, so that a party holding no interest in the outcome may make one, which is the presupposition on which the delegation arrangements rest.

4.2 The Components

The determination decomposes into five components, performed in order and separable in principle.

Observation produces measurements of the system at intervals. The component consists in instruments, their placement, their calibration, and their operation over the period during which measurement continues.

Compilation produces a record from the measurements. The component consists in the retention of measurements, their assembly into a series, and the maintenance of the series against loss and against changes in instrumentation that would render its parts incomparable.

Estimation produces a claim about the present state of the system from the record. The component requires a model of the system sufficient to relate what the instruments measure to the quantity the rule refers to, since instruments measure positions, concentrations and populations while the rule refers to a condition of the system as a whole.

Classification produces a claim about the relation between the estimated state and the boundary of the region in which the rule takes its restricted form. The component requires a specification of the boundary, and the specification is a further matter on which the record bears.

Declaration produces the legal or institutional act by which the rule takes its restricted form for the parties governed. The component consists in an authority stating that the preceding components have been performed and that their result places the system in the region.

4.3 The Components the Instruments Govern

The possession of instruments governs the first two components entirely and the third substantially.

Observation and compilation are constituted by the instruments and their operation. A party lacking instruments performs neither, and a party whose instruments were deployed recently holds a record whose brevity is a defect no present expenditure repairs, since the missing measurements concern past states of the system.

Estimation depends on the record in two ways. The estimate is computed from the record, and the model relating measurement to system state is ordinarily fitted to a record. A party holding a longer record accordingly holds both the input and the instrument of inference.

Classification depends on the record in one way and on a further matter in another. The boundary of the region is specified by a claim about the system’s dynamics, and such claims are established from records of the system’s past behaviour under varying conditions. A party holding the longest record is best positioned to assert where the boundary lies, and a party holding no record is positioned to assert nothing about it.

Declaration depends on the instruments in no way. The component is an institutional act, it may be performed by any party the arrangement designates, and its performance requires only that the designated party be presented with the result of the preceding components.

4.4 The Component the Constraint Machinery Reaches

The constitutional arrangements operate on declaration. Emergency provisions specify who may declare, on what conditions, for how long, and subject to what review, and the review examines whether the declared conditions obtained.

The examination requires that the reviewing body evaluate the preceding four components, and all four rest on a record. A reviewing body holding no independent record evaluates the determination by examining the record presented to it, together with such account of the estimation and classification as the presenting party supplies. Its review is accordingly an audit of an account rendered by the party under review.

This is the precise form the difficulty takes, and it survives every improvement to the specification of declaration. A provision requiring that the declaring authority be independent of the parties governed, that its declaration be reasoned, that it lapse after a fixed period, and that it be reviewable by a court, constrains declaration completely and leaves observation, compilation, estimation and classification where they were.

4.5 Exclusions from the Decomposition

The decomposition asserts no temporal separation in practice. The components are separable in principle and are ordinarily performed by one party in a single continuous operation, and their separability is what permits the argument to identify where the difficulty lies.

The decomposition asserts nothing about the correctness of any determination. A party holding the instruments may determine the state correctly, and the account is restricted to competence.

The decomposition treats the specification of the boundary as a matter on which the record bears and does not treat it as settled by the record alone. Where the boundary is specified by a rule, a treaty or a standard, its specification is an institutional act, and the record bears on whether the specified value has been approached.

5 The Relation between Observational Capacity and Prior Use

5.1 The Constituents of Observational Capacity

Observational capacity with respect to a system consists in three things, and the third is distinguished from the first two by the manner of its acquisition.

Instruments are the devices by which measurements are taken, together with their placement and their maintenance. Instruments are acquired by expenditure and their acquisition is available to any party willing to bear the cost.

Access is the standing by which instruments are placed where measurement is possible. Access to some systems is available from a distance and access to others requires proximity, presence, or the consent of a party controlling the site.

Duration is the period over which measurement has continued without interruption and without a change of instrumentation that renders the series incomparable. Duration is distinguished from the first two in that it cannot be acquired by present expenditure. A party deciding today to observe a system holds a record of zero length today, and no expenditure produces the measurements it did not take.

The third constituent carries the argument. Estimation and classification rest on a record, and a record’s value for both purposes increases with its length, since a trend is established from a series and the specification of a boundary rests on observed behaviour under varying conditions.

5.2 The Acquisition of Capacity in the Course of Use

For the systems specified, the three constituents are acquired in the course of using the system, and the acquisition is a by-product of operation in place of a separate undertaking.

A party operating within a system requires measurements of it for operational reasons. An operator of orbital assets tracks objects in order to avoid them, an extractive operation surveys the resource it draws on, a party discharging effluent monitors the receiving water under the terms of its permit. The instruments are deployed to serve the operation and the measurements accumulate as a consequence.

Access follows from operation in the same way. A party present within a system is positioned to measure it, and presence is what operation consists in. Where access requires the consent of a controlling party, the operating party ordinarily holds that consent already, since its operation required it.

Duration follows from the date at which operation began. A party that has operated within a system for a long period holds a record covering that period, and the record was accumulated at no cost beyond the operation itself. A party proposing to begin operation holds no record and cannot construct one retrospectively.

The relation is therefore of a particular form. Observational capacity is nondecreasing in the duration of prior use, and its most valuable constituent is a strictly increasing function of that duration.

5.3 The Benefit Conferred by a Determination of Approach

A determination that the system stands near its critical value contracts the permissions of every party, since it extends the burden of justification to courses that previously carried none. The contraction bears on parties according to the position of their use in time.

A party whose use is already realised retains what it holds. The contraction reaches courses the party has yet to adopt, and where its principal deployment is complete those courses are marginal to it.

A party whose use lies in prospect loses the whole of that prospect for the duration of the determination. The contraction reaches every course by which the party would enter, and the courses it reaches are the party’s entire participation.

The benefit derived from a determination of approach is accordingly increasing in the share of a party’s use already realised, taking its greatest value for a party whose deployment is complete and its least for a party that has yet to begin.

5.4 The Statement of the Relation

Claim 5.1 (Common ordering by prior use). For a system whose observation requires instruments deployed within it, whose access follows from operation within it, and whose state estimation rests on a record, both observational capacity and the benefit conferred by a determination of approach are increasing in the duration and extent of a party’s prior use of the system. The two are accordingly ordered alike over the parties.

Claim 5.1 is a conditional. Its antecedent states three properties of a system, the convergence section draws the consequence formally, and Part IV examines whether the antecedent holds for two settings.

5.5 The Cases in Which the Relation Fails

The relation fails in three classes of case, and the failures are neither rare nor marginal.

Where observation is performed from outside the system by instruments requiring no presence within it, access does not follow from operation. Satellite remote sensing of terrestrial systems is the standing instance, and a party holding no operational presence in a watershed may observe its condition from orbit.

Where a record is compiled and published by a party constituted for that purpose and made available without charge, duration does not follow from a party’s own operation. Long civil observation programmes maintained as public undertakings supply records of great length to parties that contributed nothing to their accumulation.

Where observation is performed by parties with no operational interest, capacity is distributed by a process unrelated to use. Academic observatories, amateur networks and non-governmental monitoring all take this form, and their records are in some domains the principal ones available.

Each failure is a condition under which the convergence does not obtain, and their existence establishes the shape of what a remedy would consist in. The three classes share a feature: in each, the observation is supported by a party that bears the cost without operating within the system. Such support is an achievement maintained by expenditure and by policy, it is withdrawn when either lapses, and its maintenance is the condition on which a defensible arrangement rests.

6 The Distribution of Observational Capacity among the Parties

6.1 The Sources of the Distribution

Three sources produce the distribution of observational capacity across the parties to a system.

Expenditure produces instruments and their maintenance, and its effect is available to any party at any time. A party entering a system today acquires instruments of the current generation, and those instruments may exceed in quality the instruments an earlier party deployed.

Presence produces access, and its effect follows the geography of operation. A party present at a site measures conditions there, and a party absent from it measures them at a distance or through the consent of a party present.

Timing produces duration, and its effect follows the date at which operation began. A party that entered early holds a record covering the period since, and this constituent stands outside the reach of present expenditure.

6.2 The Permanence of the Inequality in Duration

The inequality produced by the third source has a property the other two lack.

Let two parties enter a system at times $t_{1} < t_{2}$ and operate continuously thereafter. At any later time $T$ their records have lengths $T - t_{1}$ and $T - t_{2}$, and the difference between them equals $t_{2} - t_{1}$ at every value of $T$. The gap is therefore fixed at the moment of the second party’s entry and persists unchanged for as long as both parties operate.

Two consequences follow.

The inequality in duration admits no closure by the diligence of the later party. A party observing continuously from its entry accumulates record at the same rate as the party ahead of it, and equal rates leave a constant difference. The later party may exceed the earlier in instruments, in coverage and in the quality of each measurement, and it will hold the shorter series for as long as the comparison is made.

The relative inequality declines while the absolute inequality persists. As $T$ grows, the ratio of the two record lengths approaches unity, so a system observed for a very long time by both parties yields records whose lengths are comparable in proportion. Whether the absolute gap or the ratio governs depends on what the record is used for.

6.3 The Conversion of Capacity into Standing

Observational capacity converts into standing within the determination through the components identified above.

The conversion operates through the estimate. A party presenting an estimate presents the record supporting it, and a party contesting the estimate contests it with a record of its own. Where the contesting party’s record is shorter, its contest is assessed by a body comparing two series, and the shorter series supports fewer inferences about trend and none at all about the behaviour of the system before it began.

The conversion operates more strongly through the boundary. A claim about where the critical value lies rests on observed behaviour under varying conditions, and the range of conditions a record covers is a function of its length. A party holding a record covering one regime of the system asserts nothing about the value at which the system leaves that regime, and this party may be the one holding the better instruments.

The absolute gap accordingly governs where the question concerns behaviour in a period covered by one record and absent from the other, which is the question a boundary claim raises. The ratio governs where the question concerns the precision of an estimate of a present quantity.

6.4 The Distribution Distinguished from Adjacent Distributions

Three descriptions of the distribution are declined.

The distribution is not a distribution of wealth, though it correlates with one. A wealthy party entering a system today acquires instruments and acquires no duration, and the second deficiency persists. The ecological setting examines a case in which the correlation with wealth is nevertheless strong, and identifies the mechanism as the maintenance of programmes over time in place of expenditure at any moment.

The distribution is not produced by any party’s design. It follows from the order in which parties entered a system together with the by-product character of operational measurement.

The distribution is not a distribution of credibility in the sense treated above. The parties holding shorter records receive less credence on questions about the system’s past, and the lesser credence is warranted. What the distribution produces is a warranted asymmetry.

6.5 Exclusions from the Account of the Distribution

The section establishes properties of a distribution and supplies no measurement of any actual one. Part IV examines two settings and characterises the distribution in each qualitatively, and no quantity stated here is estimated from data.

The section treats continuous operation and treats interruption only implicitly. A party whose observation lapses holds a record with a gap, the gap bears on inferences spanning it, and a full treatment would state how a gapped record compares with a shorter continuous one. The comparison is left open.

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Part III — The Consequences of the Distribution

7 The Convergence of Determining Competence with the Interest Served

7.1 The Construction

Let $N$ parties operate within a system opened at time zero and observed to the present time $T$. Party $i$ entered at $t_{i}$ and has since operated and observed continuously.

Write $D_{i} = T - t_{i}$ for the duration of party $i$’s use and of its record. Write $X_{i}$ for its expenditure on instruments, drawn independently of $t_{i}$, so that a late entrant may hold the better instruments. Write $H$ for the period a party requires to complete its intended deployment, and

$$s_{i} = \min!\left(1, \frac{D_{i}}{H}\right)$$

for the share of that deployment already realised.

Observational capacity combines a term expenditure purchases and a term it cannot:

$$C_{i} = (1-w),\frac{D_{i}^{\mathrm{eff}}}{D_{\max}} + w,\frac{X_{i}}{X_{\max}},$$

where $w \in [0,1]$ weights purchasable instrument quality and $D_{i}^{\mathrm{eff}}$ denotes the effective record length available to party $i$.

The benefit conferred on party $i$ by a determination that the system stands near its critical value is $B_{i} = s_{i}$, since the contraction reaches courses a party has yet to adopt and reaches nothing it has already realised.

A public record of length $L$, compiled by a party bearing the cost without operating within the system, gives every party a record of at least that length, so that $D_{i}^{\mathrm{eff}} = \max(D_{i}, L)$.

7.2 The Convergence and Its Robustness

Proposition 7.1 (Concordance of capacity with benefit). With $L = 0$ and $w = 0$, the ordering of the parties by $C_{i}$ and the ordering by $B_{i}$ are perfectly concordant: no pair of parties is ranked oppositely by the two measures. For $w > 0$ the fraction of pairs so ranked rises slowly, remaining below one tenth for $w \leq 0.3$.

The verification draws $N = 40$ parties with entry times uniform on $[0,T]$ for $T = 60$, expenditure uniform and independent of entry, and $H = 25$, over four hundred draws. The discordant fraction at $w = 0$ is zero in every draw. At $w = 0.1$, $0.2$ and $0.3$ it takes mean values $0.023$, $0.051$ and $0.089$, and at $w = 0.5$ it reaches $0.203$.

Two features of the result deserve record.

The concordance at $w = 0$ is exact and follows from the construction, since both measures are nondecreasing functions of $D_{i}$. The formal content of the proposition lies in the second clause, which establishes that the concordance degrades slowly under the one form of remedy a party may purchase. A late entrant outspending every incumbent on instruments displaces itself a short distance in the ordering, because expenditure enters $C_{i}$ through one term and duration enters through the other.

The rank correlation between the two measures stands at $0.891$ at $w = 0$, below unity, and the shortfall is produced by ties in $B_{i}$. Parties whose deployment is complete are tied at the maximum benefit, and the tie is a feature of the situation in place of an artefact: a determination of approach is equally favourable to every party that has finished deploying, however long each has been present.

7.3 The Condition Defeating the Convergence

Proposition 7.2 (Public-record threshold). The rank correlation between capacity and benefit falls monotonically in the length $L$ of a public record available to every party, and reaches a floor of approximately zero once $L$ attains $D_{\max}$. At that point every party holds an equally long record, capacity is governed by expenditure alone, and expenditure is independent of the position of a party’s use in time.

The verification computes the correlation over the same draws. At $w = 0.2$ it takes the values $0.864$, $0.823$, $0.565$, $0.220$ and $-0.009$ for $L$ equal to $0$, $15$, $30$, $45$ and $60$. At $w = 0.4$ it takes the values $0.740$, $0.662$, $0.378$, $0.103$ and $-0.009$. (A figure in the embedded PDF displays these curves, showing the correlation reaching its floor once the public record attains the length of the longest private one.)

Two readings of the proposition are available and both are intended.

Read as a diagnosis, it establishes that the convergence is a property of the observational regime in place of a property of the parties. Where observation is left to those who operate, the party best equipped to determine the state is the party the determination favours. Where observation is maintained as a public undertaking of sufficient duration, the relation dissolves.

Read as a requirement, it fixes what an arrangement must secure, and the quantity is stated in years. A public record shorter than the longest private one leaves the convergence in place to a degree that falls with its length. The requirement is exacting: the record must be as long as the longest record any operating party holds, and length is the constituent no expenditure supplies at the moment it is wanted.

7.4 The Consequence for the Timing of Provision

Proposition 7.2 carries a consequence about when a public observational programme must be established, and the consequence is unwelcome.

A programme established at the moment a governance arrangement is adopted supplies a record of zero length at that moment. Its record attains the length of the longest private record only after a period equal to the age of that record, and during the whole of that period the convergence obtains to a degree that declines slowly.

An arrangement adopting a state-dependent rule therefore operates under the convergence for a period fixed by the history of the system’s use before the arrangement existed. The period is longest exactly where use began earliest, which is where the state-dependent rule is most likely to be needed.

7.5 Exclusions from the Result

The construction is an existence argument concerning the structure of the two orderings. It establishes that the concordance follows from the stated properties and supports no estimate of $w$, of $L$, or of the discordant fraction in any actual system.

The result concerns competence and concerns correctness in no respect. A party favoured by a determination it is best equipped to make may make it correctly, and the result establishes that the arrangement supplies no party positioned to check.

The result treats the public record as available to every party equally. A record published under conditions restricting its use, or in a form requiring expertise concentrated among the same parties, supplies less than the construction assumes.

8 Termination and the Evidential Origin of Persistence

8.1 The Condition Required for Termination

A state-dependent rule relaxes when the system leaves the region in which the rule takes its restricted form. The condition for relaxation is stated in the same terms as the condition for extension, and the companion paper offers this symmetry as a constraint distinguishing the arrangement from the classical exception.

The symmetry holds at the level of the statement. Both conditions concern the position of $X_{t}$ relative to a boundary, both are factual, and both are established by the components decomposed above. A party asserting that the system has left the region asserts a claim of the same form as the party that asserted it had entered.

The symmetry fails at the level of the evidence, and the failure is the subject of this section.

8.2 The Record Required near a Threshold

A system fluctuating about a stable state returns toward that state at a rate that falls toward zero as the system approaches a threshold at which the state loses stability. The consequence for observation is that successive measurements decorrelate slowly, so that a record of given length contains fewer independent observations of a slow system than of a fast one.

Model the fluctuation by

$$dx = -\lambda,(x - \mu),dt + \sigma,dW,$$

in which $\lambda$ is the restoring rate. A determination distinguishing one value of $\mu$ from another rests on the sample mean of a record of length $T$.

Proposition 8.1 (Record length required near a threshold). For this process, the variance of the sample mean over a record of length $T$ scales as $T^{-1}$ at fixed $\lambda$ and as $\lambda^{-2}$ at fixed $T$. The record length required to attain a fixed precision accordingly scales as $\lambda^{-2}$, so that a system whose restoring rate has halved requires a record four times as long to support a determination of equal confidence.

The verification simulates the process over four record lengths at fixed $\lambda$ and over four restoring rates at fixed $T$. The fitted exponent in $T$ is $-1.004$ against an expected $-1$, and the fitted exponent in $\lambda$ is $-1.943$ against an expected $-2$. The third clause is checked directly: at restoring rates $0.8$, $0.4$, $0.2$ and $0.1$, records of length $200$, $800$, $3200$ and $12800$ attain the same precision, with achieved variances within four per cent of the target in each case.

8.3 The Asymmetry between Approach and Departure

Proposition 8.1 bears asymmetrically on the two determinations, and the asymmetry follows from where each is made.

A determination of approach is made while the system is still leaving the ordinary regime. The restoring rate has fallen and has not yet reached its smallest value, and the record supporting the determination was accumulated over a period during which the rate was higher than it is at the moment of determination.

A determination of departure is made from within the critical region. The restoring rate is at its smallest there, the record supporting the determination must be accumulated under that condition, and Proposition 8.1 fixes the multiple by which it must exceed the record that supported the approach.

The consequence is that the evidential burden for terminating a determination exceeds the burden for making one, and the excess grows as the system’s condition becomes more severe. An arrangement whose termination condition is stated in the same terms as its trigger therefore imposes a heavier requirement for relaxation than for extension, and it does so without any provision to that effect.

8.4 Persistence Explained without Appeal to Interest

The classical account explains the persistence of exceptional arrangements by the alignment of the declaring authority’s interest with their continuation, and Agamben’s analysis rests on the identity between the authority competent to declare and the authority competent to determine that the declaration continues.

Proposition 8.1 supplies an explanation of persistence that stands independent of interest. A determination binding a system in its critical region persists because the evidence sufficient to end it is harder to produce than the evidence that began it, and the difficulty is fixed by the system’s dynamics. An authority holding no interest whatever in the continuation of a determination, applying a termination condition in good faith and with every diligence, will terminate late.

Two consequences follow.

The first bears on the constraint proposed in the companion paper. That constraint held that a condition keyed to a state variable supplies an internal termination condition that the classical exception lacks. Proposition 8.1 establishes that the internal condition is systematically harder to satisfy than the condition that triggered the arrangement, so the constraint operates more weakly than its statement suggests.

The second bears on diagnosis. Where an arrangement of this kind persists, the persistence is evidence of the system’s dynamics before it is evidence of anyone’s interest, and an inference from persistence to capture is unavailable without further argument.

8.5 The Compounding of the Two Results

The convergence and the termination results compound, and the compounding is the paper’s central claim about the position a late-entering party occupies.

A party whose use lies in prospect is disadvantaged by a determination of approach, holds the shortest record among the parties, and is accordingly least equipped to contest that determination. The same party is most advantaged by a determination of departure, and Proposition 8.1 establishes that such a determination requires the longest record of any determination the arrangement admits. The party with the greatest interest in establishing departure is therefore the party least able to establish it, and the excess it must overcome grows with the severity of the condition the arrangement was adopted to address.

8.6 Exclusions from the Result

The proposition concerns a single scalar fluctuating about a stable state and supplies no treatment of systems whose state is multidimensional or whose approach proceeds by a mechanism other than the loss of stability of an equilibrium. The companion paper establishes that transitions of two further kinds occur, and neither is treated here.

The proposition concerns the precision of an estimate and supplies no account of how a boundary is specified. Where the boundary is fixed by a standard in place of by inference from a record, the determination of departure requires an estimate of position relative to a stated value, and the proposition governs the precision of that estimate alone.

The proposition establishes a scaling and supplies no estimate of $\lambda$ for any actual system.

9 Contestation by a Party Disadvantaged by the Determination

9.1 The Forms Available to an Objecting Party

A party disadvantaged by a determination that the system stands near its critical value may object in three forms.

An evidential objection asserts that the determination is mistaken: the system does not occupy the region claimed, or the boundary does not lie where the determining party places it.

A procedural objection asserts that the determination was made irregularly: the components were performed by a party the arrangement does not authorise, or without the disclosure the arrangement requires, or without an opportunity for the objecting party to be heard.

A consequential objection asserts that the determination is correct and that what the arrangement attaches to it is wrong: the contraction of permissions falls unequally, or falls on parties for reasons unconnected with their contribution to the condition determined.

9.2 The Failure of the Evidential Objection

An evidential objection contests a claim about the state of the system, and a claim about the state of the system is supported by a record.

A party contesting on this ground must produce a record supporting a different estimate, or must show that the record produced supports no estimate of the confidence claimed. The first requires a record of its own, and Part II establishes that the objecting party holds the shorter one. The second requires expertise in the analysis of series and access to the series analysed, and it succeeds where the determining party has overreached its evidence and fails where the determining party has not.

The position of a late-entering party is accordingly this. Its objection, where the determining party has proceeded carefully, has no evidential foundation available to it, and the absence follows from the timing of its entry in place of from any defect in its diligence. The deficiency persists for as long as both parties operate.

A body receiving such an objection compares the record supporting the determination with the record supporting the objection, and reaches the conclusion the comparison warrants. The proceeding is regular, the body is impartial, and the outcome is fixed before the proceeding begins.

9.3 The Reception of the Procedural Objection

A procedural objection contests the manner in which the determination was made and requires no counter-record. The objection is accordingly available to a party of any observational capacity, and it is the form the constitutional arrangements are designed to receive.

Its reception is limited. Where the arrangement authorises the determining party to perform the components, requires disclosure of the record, and provides a hearing, an objection asserting that these requirements were unmet fails whenever they were met. The requirements are satisfiable, they are ordinarily satisfied, and their satisfaction leaves the determination standing on a record the objecting party has no means to controvert.

The procedural objection therefore succeeds against irregularity and leaves regular determinations untouched, which is what a procedural objection is for. The difficulty is that the paper’s result concerns regular determinations.

9.4 The Warranted Deficit and the Corrective It Excludes

A party contesting a determination with a shorter record receives less credence, and the lesser credence is warranted. Its estimate does rest on thinner evidence, its claim about the boundary does rest on observation of a narrower range of conditions, and a body according its assertions the weight accorded to assertions supported by the longer record would be crediting claims beyond their warrant.

The corrective developed for testimonial injustice consists in the identification and correction of a prejudice operating in the hearer. Where a hearer discounts a speaker on the ground of the speaker’s social identity, correcting the prejudice restores the credence the testimony warranted throughout. Where a hearer discounts a party on the ground that its record is shorter, there is no prejudice to identify, and a correction would introduce an error in place of removing one.

The claim requires a bound, and Wynne’s case supplies it. A party may hold observation sustained over long periods which the institutional record has failed to receive, and the standing accorded to such observation may be lower than its accuracy warrants. The deficit is then unwarranted, no argument of this section applies to it, and the corrective developed for testimonial injustice is available in the ordinary way. What this section establishes concerns a party that genuinely holds the shorter record, and it establishes nothing about a party whose record is held and unreceived.

The difficulty treated here is accordingly distributive in its origin and epistemic only in its appearance. It arises from the allocation of instruments and records, it presents as a difference in the standing of assertions, and a remedy addressed to the presentation leaves the origin untouched. Proposition 7.2 establishes what a remedy addressed to the origin would consist in and states the quantity in years.

9.5 The Objections the Asymmetry Leaves Available

Three forms of objection survive the asymmetry, and a disadvantaged party’s position is determined by which of them the arrangement admits.

A difficulty of the same form arises in the companion papers by other routes, since the product of a course satisfying their criterion is an absence and a withheld possibility presents the configuration a possibility no scheme addressed also presents. In each the object at issue cannot be verified from the field by the party that would need to verify it.

An objection to the specification of the boundary survives where the boundary is fixed by a standard, a treaty or an administrative act. A specification of that kind is an institutional decision, its adoption is contestable on the grounds on which institutional decisions are contestable, and a party holding no record whatever may contest it. Where the boundary is inferred from a record, the objection reverts to the evidential form and fails.

An objection demanding disclosure of the record survives in every case, since it asserts a claim about access in place of a claim about the system. This is the one form of objection the asymmetry leaves wholly intact, and its availability is the reason disclosure is stated as a condition of a defensible arrangement.

A consequential objection survives entirely, since it concedes the determination and contests what the arrangement attaches to it. The evidential asymmetry operates on claims about the state of the system and operates on nothing else, so a party unable to contest the state may contest the allocation of the contraction with its full standing.

The third form indicates where a disadvantaged party’s argument is to be made. The contest that party can win concerns the consequence and never the trigger, and the companion paper’s separation of those two is what makes the position available. An arrangement collapsing the two, by attaching a single non-derogable consequence to the determination, forecloses the only contest the party is equipped to conduct.

9.6 Exclusions from the Account of Contestation

The section treats a party contesting in good faith and treats obstruction in no respect. A party contesting a determination in order to delay a contraction it accepts as warranted raises a further question the account does not reach.

The section treats objections raised within an arrangement and treats refusal to participate in no respect. A party rejecting the arrangement altogether stands outside the analysis.

The section assumes that the record supporting a determination is disclosed. Where it is withheld, the evidential objection fails for a second and independent reason.

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Part IV — Two Settings

10 The Determination of Orbital State

10.1 The System and the Boundary

A congested orbital shell carries objects whose collisions generate fragments, and Kessler and Cour-Palais established that above a population density determined by the collision rate and the rate of natural decay the generation of fragments becomes self-sustaining. The shell then carries a critical value in the sense the companion paper requires, and the determination that the shell has approached it is the determination this paper treats.

Two features of the setting bear on what a determination involves.

Natural decay operates on a timescale set by altitude, and at the altitudes carrying the densest traffic the timescale runs to centuries. A determination of approach accordingly concerns a condition from which recovery is unavailable within any period the parties can act over.

The boundary is specified in part by inference and in part by institutional act. Mitigation guidelines adopted through the Committee on the Peaceful Uses of Outer Space state practices in place of a critical density, so a party contesting a determination of approach contests an inference from a record, and the objection to the boundary specification is available only where a stated value exists to contest.

10.2 The Parties Holding the Constituents

Observational capacity in this setting is held with marked concentration.

The most extensive catalogue is maintained by the United States through its surveillance network, which tracks a population reported in the tens of thousands of objects, and the second most extensive is maintained by Russia. Other parties maintain networks of smaller extent, including a European tracking arrangement and observation systems developed within Asian cooperative programmes, and commercial providers have entered the field.

Reported assessments of European capability indicate that for operationally significant determinations European parties rely on the more detailed data held by the United States military, and analyses of ground-based tracking note that the geographic distribution of sensors leaves coverage gaps. Both features bear on the argument: the first establishes that even parties holding substantial instruments occupy a dependent position on the determinations that matter, and the second establishes that the record is partial in a manner varying by region.

10.3 The Antecedent Tested against the Setting

Claim 5.1 states an antecedent in three parts, and the orbital setting satisfies two of them and requires a refinement of the third.

The duration clause is satisfied strongly. Tracking of orbital objects began with the opening of the system, the parties that launched first began observing first, and the resulting gap persists. A party beginning to track today begins a record covering none of the period over which the population accumulated.

The estimation clause is satisfied. A determination of approach rests on a population estimate and on a model relating the tracked catalogue to the untracked population of smaller fragments, and both rest on a record.

The access clause requires refinement, and the refinement is the finding of this section. Orbital tracking is performed principally from the ground, so access to the system does not follow from operating within it. A party holding no orbital assets may in principle build radars and telescopes and observe the shell.

The convergence nevertheless obtains, through a mechanism the refined statement identifies. The capacity to build and sustain a tracking network and the capacity to place assets in orbit are produced by the same national programme and are acquired together, and the date at which each began is the same date. Observational capacity and prior use are accordingly correlated through a common cause in place of through the direct relation Claim 5.1 states, and the ordering the convergence requires is produced either way.

10.4 The Consequence for a Late-Entering Party

A state beginning orbital operations now occupies the position described above.

A determination that a shell has approached its critical value contracts its prospective deployment and leaves the deployments of established operators in place. The party holds the shortest record of the shell and the fewest sensors, so an evidential objection is unavailable to it. The determination of departure that would restore its prospect requires the longest record of any determination the arrangement admits, and Proposition 8.1 establishes the multiple.

The forms of objection preserved are correspondingly narrow here. The boundary is stated as practice in place of as a value, so the institutional objection has a limited object. A demand for disclosure of tracking data is available and is the strongest instrument the party holds. The consequential objection is available in full, and it is the objection the equitable-access arguments raised within the allocation of orbital and spectrum resources have historically taken.

10.5 Exclusions from the Treatment of the Setting

The section characterises a distribution qualitatively from reported assessments and estimates no quantity. Figures for catalogue size and for capability are drawn from secondary and institutional sources of varying independence, they change rapidly, and no conclusion here rests on the value of any of them.

The section treats observational capacity and treats the legal regime governing orbital activity only where the two intersect. The provisions of the Outer Space Treaty concerning jurisdiction over registered objects bear on what may be done about debris and bear on the present argument only through the disclosure question.

The section treats states and treats commercial operators as holders of instruments without examining the arrangements by which their data enter a determination.

11 The Determination of Ecological State and the Density of Monitoring

11.1 The Determination Required and the Records Supporting It

A determination that an ecological system has approached a condition from which its present configuration is unrecoverable rests on a record of population, composition, extent, or a related quantity, observed over a period long enough for a trend to be established against natural variability.

The requirement is demanding in a specific respect. Ecological variability operates over periods of years and decades, so a record establishing a trend against that variability must run for a comparable period, and such length cannot be acquired at the moment it is wanted.

11.2 The Characterisation of the Distribution

The distribution of ecological records is uneven in a manner that has been documented for several decades and that persists.

Studies of the principal aggregating repositories report that occurrence records are concentrated in a small number of countries, that the concentration has been marked since such repositories were first assessed, and that observation density per unit area is several times higher in high-income countries than in others. Assessments of coverage report that only a small fraction of the terrestrial surface has been surveyed at a density adequate for the purposes such records are put to.

Two qualifications belong with these figures. The concentration has declined over the past two decades as data mobilisation programmes have operated, and analyses of national trajectories report increasing coverage in regions that began from low values. And coverage has been found to be stronger for species over which a nation holds greater stewardship, which operates against the concentration in the cases where it holds.

11.3 The Antecedent Tested against the Setting

Claim 5.1 states that observational capacity follows from use of the system, and the ecological setting satisfies the antecedent weakly and satisfies a related condition strongly.

Use of an ecological system does generate records where a permit requires monitoring, and an operator discharging effluent or extracting a resource ordinarily holds a record of the receiving system. The relation therefore holds within a single site.

Across sites the relation is dominated by another. The records supporting a determination about an ecosystem are ordinarily produced by research institutions, government agencies and long-running survey programmes, and their existence follows from the sustained expenditure of the party in whose territory the system lies, or from the sustained expenditure of a party funding observation elsewhere. The constituent that governs is duration, and duration in this setting follows from the maintenance of a programme over decades in place of from any party’s operational presence.

The distribution therefore correlates with wealth, and the description of the distribution as a distribution of wealth was declined. The description remains declined and the mechanism is now statable: what wealth purchases here is the maintenance of a programme over time, and a party acquiring wealth today acquires the programme and acquires none of the record it would have produced.

11.4 The Inversion of the Convergence

The convergence takes an inverted form in this setting, and the inversion is the finding that distinguishes the two settings of Part IV.

In the orbital setting, the party holding the longest record is a party operating within the system, and the party disadvantaged by a determination is a party seeking to enter.

In the ecological setting, the party holding the longest record is frequently a party external to the system: a research programme, an international body, or a state funding observation beyond its own territory. The party in whose territory the system lies may hold a shorter record than the external party, and it is the party whose prospective use a determination of approach contracts.

The consequence is that the disadvantaged party is the host. A determination that an ecosystem within a state’s territory has approached a critical condition contracts that state’s prospective development, and the state may hold no record adequate to contest the determination on evidential grounds. The forms of objection preserved are accordingly the ones raised in this setting: contestation of the boundary where a threshold is stated by an international instrument, demands for disclosure and for participation in monitoring, and consequential objections concerning who bears the cost of a contraction.

The inversion establishes that the convergence is not a claim about incumbency in operation. It is a claim about the relation between the holder of a record and the bearer of a contraction, and the two settings instantiate that relation with different parties in each position.

11.5 Exclusions from the Treatment of the Setting

The section reports figures from published assessments and from secondary summaries of them. The figures are used to characterise a distribution qualitatively, they are contested in detail, and no conclusion here depends on the value of any of them.

The section treats records held by institutions and treats knowledge held by resident populations in no respect. Observation sustained over long periods by parties resident within a system exists in many of the settings at issue, its relation to the records that enter a determination is a substantial question, and the analysis of credibility bears on it directly. The question is left open.

The section treats the distribution as it stands and treats the programmes addressing it only in passing. Data mobilisation and capacity-building programmes operate on exactly the quantity Proposition 7.2 identifies, and an assessment of their effect against that proposition would require the empirical work the paper does not undertake.

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Part V — Declinations and Limits

12 Positions Declined and the Arguments for Declining Them

12.1 The Declination of an Account Resting on Bad Faith

The position declined holds that determinations of criticality are made by parties seeking the advantage such determinations confer, and that the difficulty is accordingly one of capture.

The ground for declining it is derived from Proposition 7.1. The concordance of the two orderings follows from the structure of the distribution and holds over every draw of the construction, with no term representing any party’s intention. A determination made by a party indifferent to its own advantage, on the best evidence available, with every diligence, is made by the party the determination favours, and the favouring is a property of who holds the record.

An account resting on bad faith would establish something weaker in two respects. It would fail where parties act well, which is the case the paper is addressed to, and it would license the inference that an arrangement staffed by disinterested parties is thereby repaired. The convergence establishes that it is not.

The cost is that the account supplies no ground for objecting to any particular determination.

12.2 The Declination of a General Relation between Observation and Use

The position declined holds that observation of a system generally requires participation in it, so that the difficulty identified here attends governance of every system whose state must be determined.

The ground for declining it is derived from the three classes of case in which the relation fails, and from the orbital finding, which establishes that the relation fails in its direct form even in the setting the argument was built around. The orbital case satisfies the convergence through a common cause in place of through the direct relation, and a thesis asserting the direct relation generally would be refuted by the very setting Part IV examines first.

The cost is that the argument’s scope is fixed by an antecedent requiring examination in each case. Claim 5.1 is a conditional, its antecedent holds in some settings and fails in others, and the paper establishes nothing about how large the first class is.

12.3 The Declination of a Proposed Allocation of Competence

The position declined holds that a paper identifying a defect in the allocation of a competence should propose an allocation that lacks the defect.

The ground for declining it is derived from Proposition 7.2 together with the timing consequence. The convergence is defeated by a public record of sufficient duration and by nothing else the paper has identified, and duration is the constituent that no allocation of competence supplies. An arrangement conferring the competence on any party whatever leaves that party determining the state from the records available, and a body holding no independent record audits an account rendered by the party under review.

A proposal would therefore relocate the competence and leave the difficulty in place, and its adoption would furnish an appearance of repair. The paper states conditions in place of a proposal, and the difference is that a condition is assessable against an arrangement while a proposal invites adoption.

The cost is that a party designing an arrangement receives from this paper a set of conditions and no design.

12.4 The Declination of a Scheme for Equalising Observational Capacity

The position declined holds that the paper, having identified the public record as the quantity that defeats the convergence, should propose the programme that would supply it.

The ground for declining it has two parts. The first is that such a programme is an institutional design, and the companion paper’s argument against specifying machinery applies here: a specification supplies the party administering it with a determinate account of what compliance consists in, and the predictable result is a programme complete in every specified feature whose records are unsuited to the determinations at issue. The second is that the capacity in question is expensive, its distribution follows the maintenance of programmes over decades, and no governance arrangement establishes the distribution of resources on which such maintenance rests.

The cost is stated plainly. The paper identifies a quantity, establishes that securing it dissolves the difficulty, establishes that it must be secured long before the arrangement requiring it is adopted, and proposes no means of securing it.

13 The Limits of the Account and the Conditions a Defensible Arrangement Would Secure

13.1 Limits Internal to the Argument

Four limits attach to the argument itself.

The construction represents observational capacity by a weighted sum of a duration term and an expenditure term, and the representation is a simplification of a relation that is unlikely to be additive. A capacity requiring both a long record and current instruments would be represented better by a form penalising the absence of either, and the concordance would be stronger under such a form than under the one used.

Proposition 8.1 treats a single scalar fluctuating about a stable state, and the companion paper establishes that transitions occur by two further mechanisms for which no equilibrium loses stability. The scaling established here governs the first mechanism and governs neither of the others.

The argument treats the record as the object whose distribution matters and treats the capacity to analyse a record as available to any party holding one. Where the analysis requires expertise concentrated among the same parties that hold the records, the difficulty is aggravated and the argument understates it.

The argument treats parties as unitary. A state, an operator and a regulator within one jurisdiction hold different records and different interests, and an account resolving parties into their components would establish something more precise and possibly something different.

13.2 Limits of the Two Settings

Both settings are characterised qualitatively from published assessments and from secondary summaries.

The orbital figures concern catalogue sizes and capability comparisons drawn from institutional and secondary sources of varying independence, they change rapidly, and no conclusion rests on any of them. The ecological figures concern the concentration of records in aggregating repositories, the concentration is documented over several decades and is contested in detail, and the trend over the past two decades runs against it.

Neither setting is used to test Claim 5.1 empirically. Each is used to establish that the antecedent is satisfiable and to identify the mechanism by which it is satisfied, and the mechanisms differ.

13.3 The Conditions a Defensible Arrangement Would Secure

Five conditions follow from the results established, and each is stated with the result it follows from.

Disclosure of the record supporting a determination follows from the surviving forms of objection. A demand for disclosure asserts a claim about access in place of a claim about the system, and it is the one objection the evidential asymmetry leaves wholly intact. An arrangement withholding the record removes the only instrument a record-poor party holds without qualification.

A public record whose duration approaches that of the longest record held by any operating party follows from Proposition 7.2, which establishes that the concordance falls monotonically in that duration and reaches its floor at parity.

Establishment of such a record in advance of the arrangement requiring it follows from the timing consequence. A programme begun when the arrangement is adopted supplies a record of zero length at that moment and attains parity only after a period equal to the age of the longest private record. The condition is therefore temporal before it is institutional: the observation must begin long before the rule that will need it.

Specification of the boundary as a stated value by institutional act, in place of by inference from a record, follows from the surviving objections together with the orbital finding. Where the boundary is stated, a party holding no record may contest its adoption on the grounds on which institutional decisions are contestable. Where it is inferred, the contest reverts to the evidential form and the record-poor party has no standing in it.

Termination provisions operating on a fixed period, in addition to any condition keyed to the state, follow from Proposition 8.1 and the approach-departure asymmetry. A determination whose relaxation requires establishing departure from a region imposes an evidential burden exceeding the one that produced it, and the excess grows with the severity of the condition. A provision requiring re-determination after a stated period places the burden of establishing continuation on the party asserting it, which is the reverse of the allocation the evidential structure produces unaided.

The five conditions are assessable against an existing arrangement.

13.4 Objections the Account Leaves Unanswered

Three objections bear on the account and none is answered.

The first concerns observation sustained by resident populations. Such observation exists in many of the settings at issue, it may run far longer than any institutional record, and its exclusion from the records that enter a determination is a difficulty of a different kind from the one this paper treats. Wynne establishes a case of the kind, and the bound it imposes on the argument is stated above. The analysis of credibility bears on it directly and in the opposite direction, since a credibility deficit attaching to such observation may be unwarranted and therefore may admit exactly the corrective that is unavailable here. The question is substantial and is left open.

The second concerns the relation between the conditions and the incentive to comply with them. Each condition imposes a cost on the party best placed to resist it, and the paper establishes that this party holds the strongest position within the arrangement. An account of why such conditions would be adopted requires an argument the paper does not supply.

The third concerns the possibility that the convergence is benign. A party holding the longest record may determine the state more accurately than any other party would, and an arrangement vesting the determination elsewhere may produce worse determinations. The paper establishes that no party is positioned to check, and it establishes nothing about whether checking would improve the result.

13.5 The Relation to the Remaining Papers of the Series

The companion paper establishes the criterion, establishes its failure to compose, and establishes that the repair requires a state-dependent rule. The present paper establishes who is positioned to operate such a rule and what an arrangement adopting it would have to secure.

Two matters raised here belong to papers not yet written. The relation between the records that enter a determination and the observation held by parties whose knowledge takes another form is the first. The unifying treatment of the governance operations under which restraint, prevention and deliberate non-occupation are placed within a single vocabulary is the second, and the position of the present results within that treatment is fixed by the inversion finding: the convergence concerns the relation between the holder of a record and the bearer of a contraction, and the parties occupying those positions differ by setting.

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References

Agamben, Giorgio. State of Exception. Translated by Kevin Attell. Chicago: University of Chicago Press, 2005.

Collen, Ben, Mala Ram, Tara Zamin, and Louise McRae. “The Tropical Biodiversity Data Gap: Addressing Disparity in Global Monitoring.” Tropical Conservation Science 1, no. 2 (2008): 75–88.

Dotson, Kristie. “A Cautionary Tale: On Limiting Epistemic Oppression.” Frontiers: A Journal of Women Studies 33, no. 1 (2012): 24–47.

Ferejohn, John, and Pasquale Pasquino. “The Law of the Exception: A Typology of Emergency Powers.” International Journal of Constitutional Law 2, no. 2 (2004): 210–239.

Fricker, Miranda. Epistemic Injustice: Power and the Ethics of Knowing. Oxford: Oxford University Press, 2007.

Gross, Oren, and Fionnuala Ní Aoláin. Law in Times of Crisis: Emergency Powers in Theory and Practice. Cambridge: Cambridge University Press, 2006.

Jasanoff, Sheila. The Fifth Branch: Science Advisers as Policymakers. Cambridge, MA: Harvard University Press, 1990.

Kessler, Donald J., and Burton G. Cour-Palais. “Collision Frequency of Artificial Satellites: The Creation of a Debris Belt.” Journal of Geophysical Research 83, no. A6 (1978): 2637–2646.

Oliveira, Ulisses, et al. “Global and National Trends, Gaps, and Opportunities in Documenting and Monitoring Species Distributions.” PLOS Biology 19, no. 8 (2021): e3001336.

Ophuls, William. Ecology and the Politics of Scarcity. San Francisco: W. H. Freeman, 1977.

Scheffer, Marten, et al. “Early-Warning Signals for Critical Transitions.” Nature 461 (2009): 53–59.

Schmitt, Carl. Political Theology: Four Chapters on the Concept of Sovereignty. Chicago: University of Chicago Press, 2005. Originally published 1922.

Treaty on Principles Governing the Activities of States in the Exploration and Use of Outer Space, including the Moon and Other Celestial Bodies, 610 UNTS 205, opened for signature 27 January 1967.

United Nations Committee on the Peaceful Uses of Outer Space. Guidelines for the Long-term Sustainability of Outer Space Activities. Adopted 2019.

Wainwright, Joel, and Geoff Mann. Climate Leviathan: A Political Theory of Our Planetary Future. London: Verso, 2018.

Wynne, Brian. “Misunderstood Misunderstanding: Social Identities and Public Uptake of Science.” Public Understanding of Science 1, no. 3 (1992): 281–304.