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The Delegation Blind Spot: Auditing Product Decisions from Agent Choices

Shivam Gupta

arXiv:2609.26642v1cs.AIcs.LG

TL;DR

Successful agent execution need not reveal which future product improvement a customer would value. The paper audits whether a declared observation channel supports a specified product-value contrast, using bounds and compatible populations. In a matched-count follow-up, supplied-preference receipts resolve three of nine comparisons per model, while matched original actions resolve none.

  • Problem

    Successful agent execution can leave indistinguishable transactions from populations that would favor different future product investments, so the question is whether observed activity supports a specified product decision.

    Source: §1 · p. 1

  • Method

    The paper presents a reproducible decision-oriented audit that maps a declared observation channel and product-value contrast to bounds and compatible populations.

    Source: §1 · p. 1, §3 · p. 2

  • Results

    Three of nine primary follow-up conditions per model resolve with receipt channels versus zero of nine with matched original actions, and mean interval width falls from 0.0872 to 0.0436 (50.0%).

    Source: §7.3 · p. 5

  • Takeaways & Limitations

    The conclusion recommends preserving useful structured input and distinguishing structural ambiguity from statistical imprecision before changing an interface or collecting more logs.

    Source: §8 · p. 8, §10 · p. 9

    The experiment uses two model snapshots and one synthetic task family, so it cannot establish a general relationship between agent capability and product-learning value.

    Source: §9 · p. 9

Abstract

from arXiv · show

Successful agent execution need not identify which future product improvement its user would value. We present a decision-specific audit that maps a declared observation channel and product-value contrast to compatible intervals and witness populations. Its foundations are established identification and decision theory; the contribution is an executable measurement workflow and a controlled study of its limits. A frozen experiment makes 4,800 requests to two pinned model snapshots on shared synthetic tasks. All 36 conservative primary intervals remain unresolved despite different execution accuracy. An exploratory 2,400-call follow-up records supplied preferences and resolves three of nine comparisons per model. A deterministic extractor resolves seven of nine without model calls or calibration observations, exposing unnecessary uncertainty introduced by model-generated reports. A further 14,400 controlled multinomial simulations distinguish structural ambiguity from weak identification and finite calibration precision. We propose a source-labeled decision receipt and provide an offline viewer for inspecting the audit. These results motivate preserving decision-relevant structured input and diagnosing why a decision is unresolved before collecting more telemetry. The study contains no human participants or real customer outcomes. Full proofs, raw model provenance, controlled experiments, and reproducible analyses accompany the report.

1 Introduction

Successful agent execution may leave the company unable to distinguish which customer populations would favor different product investments. The paper asks whether a specified stream of delegated activity supports a specified future product decision and presents a reproducible audit for answering that question.

1 Introduction

  • Identical successful transactions can arise from customer populations that would favor different future product investments.The motivating example contrasts investment in soundproofing with transport links.Source: §1 · p. 1
  • The operational question is whether a specified stream of delegated activity supports a specified future product decision.This requires distinguishing execution utility, company-available information, and customer value from a future change.Source: §1 · p. 1
  • The reproducible audit reports bounds and compatible populations, then separates reasons evidence may remain inconclusive.Structural ambiguity may require a different observation, whereas sampling uncertainty may require better calibration or more data.Source: §1 · p. 1
  • The workflow operationalizes existing identification principles, and its evaluation on constructed preferences and utilities does not establish market prevalence, customer adoption, or commercial value.The study combines actual model responses, a deterministic extraction baseline, and controlled channels with analytically known identification properties.Source: §1 · p. 1

2 Related work

The paper situates its audit within established work on decision value, partial monitoring, inverse problems, and measurement error. It distinguishes its calibrated population contrast and coarse logs from prior studies of delegated choice and preference transmission.

2 Related work

  • Blackwell’s comparison of experiments [2], linear partial monitoring [6], and optimal recovery provide conceptual foundations for observability and lower-bound results.The paper presents these as antecedents rather than new principles.Source: §2 · p. 1
  • Label-shift estimation [11] and partial identification under measurement error [5] inform the channel model and linear-programming bounds.A specific contrast may be identifiable even when full prevalence recovery requires an invertible confusion matrix.Source: §2 · p. 1
  • Prior work studies delegated choice, preference transmission, agent responses to stated profiles [3], and human-agent alignment across menus [12].The paper distinguishes those targets and richer menu variation from its calibrated population contrast and coarse logs; unresolved intervals do not refute identification from richer observations.Source: §2 · pp. 1–2

3 A decision-specific observation model

The observation model maps population proportions across declared intent classes through a channel to logged action categories. It evaluates a specified product-value contrast over populations compatible with the observed law.

3 A decision-specific observation model

  • A population p gives proportions across a declared finite intent taxonomy, and a channel A maps those proportions to logged action-category probabilities q = Ap.The fixed agent, interface, and task distribution induce the channel.Source: §3 · p. 2
  • The definition of logged action category is part of the measurement design, so logging product type, type with context, or the full menu defines different experiments.The example contrasts selected product type with type paired with context.Source: §3 · p. 2
  • The target contrast weights each intent class’s independently specified outcome difference between product variants by its population share.In the study, the outcome differences are known means over an independent finite bank of synthetic menus.Source: §3 · p. 2
  • Minimizing and maximizing the contrast over populations compatible with q gives an interval whose endpoints can support one variant or whose straddling can leave opposite decisions compatible.The contrast is not automatically a causal effect or financial return; those interpretations require an appropriate outcome design, and investment decisions also require costs and constraints.Source: §3 · p. 2

4 Identification, ambiguity, and decision loss

The section characterizes when a product-value contrast is identified from a channel and what decision loss remains when compatible populations disagree. Its results distinguish learning one contrast from recovering all population proportions.

4 Identification, ambiguity, and decision loss

  • For known A, the contrast is globally identified for every feasible q exactly when d lies in row(A), and locally identified at fixed q exactly when d is orthogonal to feasible population differences.A rank-deficient channel can still identify a contrast at a boundary observation that isolates one class.Source: §4 · p. 2
  • The worst compatible contrast width W is a global measure of disagreement between populations sharing an observation law, and the interval at an actual q may be narrower.The paper relates this width to a standard inverse-problem quantity specialized to a decision contrast, not a new duality principle.Source: §4 · p. 2
  • With an exactly known observation law and an interval straddling zero, every estimator has worst-case mean absolute error at least (U − L)/2 and mean squared error at least (U − L)^2/4.The minimax randomized decision balances endpoint regrets; outside the straddling case, minimum regret is zero.Source: §4 · p. 2
  • The decision-regret result follows by balancing endpoint regrets, while randomization is a theoretical decision rule rather than a recommendation to randomize a costly business commitment.Deterministic minimax regret in the straddling case is min(−L, U).Source: §4 · p. 2
  • When two intent classes have identical channel columns and d = (−0.3, 0.5), their shared action law permits an interval [−0.3, 0.5] and minimax regret 0.1875.More samples from that channel cannot resolve the ambiguity; direct outcome feedback or a new informative channel can.Source: §4 · p. 3

5 Uncertainty and measurement design

The section bounds a declared value contrast over compatible population and channel models, then separates calibration, sampling, and channel-drift uncertainty. It also shows how recording the measurement condition can preserve information.

5.1 Attainable bounds with uncertain channels

  • The linear program minimizes and maximizes the value contrast over compatible joint masses, yielding sharp bounds for the declared rectangular channel model.The reparameterization is exact for that uncertainty description, not for unspecified correlated constraints.Source: §5.1 · p. 3
  • With uncertain channels and field frequencies, the interval has at least 1 − αA − αq coverage under model correctness and matching iid assumptions; unknown classes and channel drift are not automatically covered.Adding rectangular outcome uncertainty adds its failure probability; separately built coarse- and fine-log boxes need not be nested.Source: §5.1 · p. 3

5.2 A bias-aware linear certificate

  • The bias-aware certificate separates approximation, channel drift, and sampling error, but estimated calibration must be covered by τ or another uncertainty argument.The code minimizes the bound independently of field observations; a point-estimated channel alone does not guarantee coverage.Source: §5.2 · p. 3

5.3 Record the measurement condition

  • A logged probe identifies the contrast when it lies in the joint row span; discarding the probe label can destroy information by pooling distinct channels.The passage’s identity and row-swapped identity example is informative when the probe is recorded and completely pooled when omitted.Source: §5.3 · p. 3

6 Computational experiment

The computational study prospectively freezes model calls on synthetic tasks to examine declared observation logs and product-value contrasts. An exploratory follow-up tests explicit reports of supplied preferences, with stated limits on what those reports establish.

6.1 Frozen design and provenance

  • The frozen run assigns 4,800 requests across two pinned model snapshots and shared synthetic tasks, using four intent classes, three context regimes, and randomized option order.The domain framings share a mathematical generator and are not independent real-world datasets; the objectives are synthetic, not elicited human preferences.Source: §6.1 · pp. 3–4

6.2 Targets, schemas, and baselines

  • The target compares best attainable utility after capacity versus flexibility investment, while the primary analysis uses an exact mean contrast from a finite synthetic outcome bank.The target assumes optimal future selection, and neither the primary nor secondary outcome analysis establishes real customer value.Source: §6.1 · p. 4, §6.2 · p. 4
  • The two declared logs use selected product type, with or without context regime, and omit full continuous menu information; unresolved intervals do not rule out identification from richer features.Baselines include constrained least-squares prevalence estimation and a fixed-channel bootstrap that omits calibration uncertainty and has no claimed finite-sample coverage.Source: §6.2 · p. 4

6.3 Exploratory explicit-preference receipts

  • The exploratory follow-up compares 1,200 supplied-preference receipt requests per model with action-only logging, but does not test private-preference inference or independent validation of supplied weights.It reuses original field draws and actions, and its resolution counts are exploratory rather than a confirmatory significance test.Source: §6.3 · p. 4

6.4 AI-assisted research development and verification

  • OpenAI Codex supported an author-directed workflow spanning formulation, proofs, protocols, code, analysis, visualizations, and manuscript text; internal AI critiques were not external peer review.The stated automated and source-based checks do not certify human-author review; research assistance was distinct from the pinned models evaluated.Source: §6.4 · pp. 4–5

7 Results

The audit leaves the primary decision intervals unresolved despite differences in task execution, while supplied preference attributes and deterministic extraction resolve more comparisons in selected follow-ups. Controlled simulations separate structural ambiguity from weak identification and finite calibration precision.

7.1 Execution competence and decision uncertainty

  • Mini chooses a utility maximizer more often and incurs lower mean synthetic regret, while point estimates select the wrong sign in 2 of 18 Mini and 4 of 18 Nano conditions.The performance comparison is descriptive for the frozen generator; bootstrap target-hit counts omit calibration error and are not calibrated coverage.Source: §7.1 · p. 5
  • All 18 conditions per model remain unresolved—even the optimal-choice control—so zero wrong certified decisions reflects abstention, not demonstrated accuracy.The primary intervals cross zero, with nominal marginal coverage of at least 96% under stated assumptions, not a simultaneous guarantee.Source: §7.1 · p. 5, Figure 2 · p. 7

7.2 Compute and interpretation

  • The study uses synthetic preferences and outcomes; best attainable utility after investment is not realized future behavior of the tested models or real customer value.Operational errors also cluster over time, cautioning against treating each as an independent stationary draw.Source: §7.2 · p. 5

7.3 Explicit preference information at matched counts

  • Each model’s receipt channel resolves 3 of 9 conditions versus 0 of 9 matched action conditions, reducing mean interval width from 0.0872 to 0.0436.All resolved conditions are in the positive cohort; negative and near cohorts remain unresolved, and these selected follow-up results have no post-selection coverage guarantee.Source: §7.3 · p. 5

7.4 A deterministic baseline for supplied preferences

  • Direct extraction of supplied weights resolves 7 of 9 comparisons with no calibration observations or API calls, and produces more decisive intervals in this selected benchmark.The extractor does not validate a supplied profile against a real customer.Source: §7.4 · p. 6

7.5 Structural ambiguity versus finite precision

  • At η = 0, every population has the same action law and the compatible contrast interval is [−.04, .06]; for η > 0, exact-observation width is zero.Thus identification alone does not describe finite-sample difficulty.Source: §7.5 · p. 6
  • At η = .01, even 2,560 calibration tasks per class and 5,120 field observations leave every joint interval unresolved, with median width .10 despite zero structural width.The sufficient Hoeffding sample bound scales with 1/η², and channel estimation adds uncertainty.Source: §7.5 · pp. 6–7
  • Across 14,400 multinomial simulations, field-only coverage ranged from 96% to 100%, while all joint and calibration-only intervals contained the target in these runs.There were 84 infeasible intervals and four incorrect resolutions, all in the field-only ablation; no simultaneous claim across cells is made.Source: §7.5 · p. 7

8 From telemetry to a decision receipt

A decision receipt is proposed as a compact, decision-specific record of measurement conditions and evidence sources. The section also distinguishes what the offline viewer exposes from what the receipt experiment validates.

8 From telemetry to a decision receipt

  • The offline viewer displays precomputed audit intervals and endpoint witness populations, but its prototype has no measured usability or effect on analyst decisions.It neither silently reruns inference nor asks an LLM to recommend an investment.Source: §8 · p. 8
  • A decision receipt records the measurement condition and evidence relevant to a declared future decision, rather than requiring a complete customer profile.It is a proposed interface artifact, not an established standard or a claim of terminology priority.Source: §8 · p. 8
  • The receipt distinguishes observed actions, supplied preferences, agent inferences, and customer-confirmed outcomes, alongside versions, constraints, missing information, and the intended decision.An agent’s confident repetition does not validate a supplied preference.Source: §8 · p. 8
  • The design recommendations are to preserve assigned measurement conditions, test cheaper measurements against the current contrast, and revisit the receipt when the decision changes.Evidence for capacity versus flexibility need not identify willingness to pay, trust, or an unrelated feature; direct, consented outcome measurement may be simpler than recovering a latent taxonomy.Source: §8 · pp. 8–9
  • Figure 4 reports exact identification at every η > 0 alongside wide finite-sample intervals in multinomial simulations, with the positive mixture displayed.Width summaries condition on feasibility, while resolution denominators retain all repetitions; the figure is not based on additional LLM calls.Source: Figure 4 · p. 9

9 Implications and limitations

The implications depend on defining the product decision, outcome, and measurement scope. The paper’s evidence remains computational and does not establish customer-level effects or broad claims about agent capability.

9 Implications and limitations

  • Stable agent activity need not imply stable preference composition, and activity changes after an agent update need not imply changed demand.These are possible confoundings, not findings of widespread market failure; calibration should record agent, interface, prompt distribution, and time window.Source: §9 · p. 9
  • The diagnostic’s witness populations show which different customer mixtures fit the same declared evidence while favoring different product changes.They may motivate targeted, consented feedback, but do not establish that a proposed question is unbiased, cost-effective, or privacy preserving; agent explanations are not ground truth.Source: §9 · p. 9
  • Ordinary A/B testing remains valid for measured outcomes under its assumptions; the concern is using agent activity as a substitute for unmeasured value.Direct measurement of the relevant customer outcome may already resolve this particular gap; retention and support contacts also provide information subject to timing and selection issues.Source: §9 · p. 9
  • The model assumes a declared finite taxonomy, stable within-class behavior, and a meaningful contrast.Missing classes, elicitation errors, selective feedback, correlated calls, or channel drift can invalidate calibration transport; the experiment uses two snapshots and one synthetic task family.Source: §9 · p. 9
  • No human participants were recruited, so empirical claims are restricted to computation rather than customer outcomes.A customer study would require reviewed recruitment and consent, an independently meaningful outcome measure, and actual responses.Source: §9 · p. 9

10 Conclusion

The conclusion distinguishes successful agent execution from evidence about future product value. It calls for preserving decision-relevant structured input and diagnosing unresolved evidence before gathering more telemetry, while limiting empirical claims to the studied computational task.

10 Conclusion

  • Successful execution and evidence for a future product decision are distinct objectives, and a calibrated channel model makes that distinction testable for a declared contrast and logging scheme.Bounds and witness populations expose what observations leave unresolved; uncertainty accounting prevents calibration estimates from becoming unwarranted certainty.Source: §10 · p. 9
  • The deterministic parser and controlled channels support preserving useful structured input and distinguishing structural ambiguity from statistical imprecision before changing interfaces or collecting more logs.The released package includes proofs, actual model traces, controls, and reproducible analysis for this task.Source: §10 · p. 9
  • Extending the conclusions to customers requires customer evidence, and the accompanying repository is identified as a technical preprint rather than peer-reviewed or accepted work.The repository provides code, source, numerical records, and experiment provenance.Source: §10 · pp. 9–10

A Proofs and extensions

The appendix gives identification and decision-theoretic foundations for auditing a population value contrast from a declared observation channel. It also develops finite-sample and channel-uncertainty extensions, with assumptions and boundaries stated for each.

A Proofs and extensions

  • The appendix frames its results as applications of established identification, convex-duality, concentration, and decision-theoretic arguments, not new general mathematical principles.It cites antecedents in partial monitoring [6], measurement-error partial identification [5], optimal recovery, and comparison of experiments.Source: A Proofs and extensions · p. 11
  • For a declared taxonomy, the channel maps population proportions p to logged-action distribution q, while d defines the population contrast; extrema over compatible populations are bounds, not individual preference recovery.The contrast is identified globally when d lies in row(A), and locally when it is orthogonal to pairwise differences among populations compatible with q.Source: A Proofs and extensions · p. 11
  • A rank-deficient channel may still identify a contrast at a boundary observation, so feasible-set analysis is more informative than a rank-only test.The magnitude of globally hidden contrast is defined by the largest contrast difference between populations producing the same observations; its dual is a distance to an observable subspace, not a measured market effect.Source: A Proofs and extensions · p. 11
  • With exact q, any estimator’s worst-case mean absolute and squared error are bounded below by half the interval width and its square divided by four, respectively.When the interval straddles zero, the appendix also derives minimax decision regret; finite-sample uncertainty can add loss, and a probe that changes the channel can break indistinguishability.Source: A Proofs and extensions · pp. 11–12
  • Coarsening an observation channel enlarges compatible populations and cannot narrow the identified interval; logging probe identities can preserve information that pooling probes destroys.The appendix’s identity and row-swapped-identity example is fully informative with probe labels but uninformative when equally weighted and pooled; this does not establish that a more capable agent coarsens another.Source: A Proofs and extensions · pp. 12–13
  • The finite-sample certificate combines a channel-approximation bias term with a concentration term, and channel drift adds a bound proportional to τ rng(v).Choosing v using the same field observations requires a separate argument; estimated-channel uncertainty must be covered rather than treated as known.Source: A Proofs and extensions · p. 12
  • Rectangular channel and frequency confidence sets yield attainable contrast bounds, with coverage at least 1 − αA − αq when the respective boxes cover their true values.An infeasible program is a failure state, not a narrow interval; fixed-sample intervals do not justify optional stopping.Source: A Proofs and extensions · p. 13
  • Calibration on a fixed heterogeneous prompt panel targets its average channel, not an arbitrary deployment channel; transport requires matching prompt composition or an explicit bound.Refusals and errors must remain declared categories or enter a missing-data model, while dependence or adaptive prompt selection is outside the elementary panel argument.Source: A Proofs and extensions · p. 14

B Exploratory audit-estimator pilot

The exploratory pilot evaluates audit-corrected estimators under matched expected audit budgets; the artifact audit records claim boundaries and reproducibility materials.

B Exploratory audit-estimator pilot

  • Across five scenarios, four expected audit budgets, and five sampling policies, 1,000 replicates per setting yielded 100,000 estimator evaluations on fixed synthetic pools of 4,000 records.Expected audit budgets were matched, but independent Bernoulli selection made realized audit counts random; these were recorded.Source: B Exploratory audit-estimator pilot · p. 14
  • The estimator adds an inverse-probability weighted residual correction to proxy predictions, comparing observable-information policies with an oracle that accesses unavailable outcome residuals.Policies included uniform, historical-error active, fixed-mixture, and robust linear-path sampling; the robust-path policy adapts Li et al. [10] and is not presented as a new method.Source: B Exploratory audit-estimator pilot · p. 14
  • At 100 expected audits, robust-path RMSE .0558 and nominal 95% Wald coverage 93.4%, versus uniform .0577 and 93.9%.Historical active sampling had RMSE .0663 and coverage 88.9%; conservative Bernstein intervals covered every recorded run but were often uninformative. In the constructed hidden-shift case, the target contrast changed from .0065 to −.104 while visible records and the proxy contrast .0105 stayed fixed.Source: B Exploratory audit-estimator pilot · p. 15, Figure 5 · p. 15

C Artifact and claim audit

  • The claim audit distinguishes standard mathematics and sampling or drift certificates from named-model behavior and synthetic product-decision uncertainty.The artifact summary lists decision-specific identification theorems, LP witnesses, and independent numerical checks.Source: C Artifact and claim audit · p. 15
  • The empirical claims are limited to computation, with no conclusion about every possible telemetry schema and no completed human study.The offline instrument is an investigator preview; customer validity requires a reviewed protocol and genuine recruitment, among other requirements.Source: C Artifact and claim audit · p. 15
  • The source package includes pinned scientific dependencies, tests, exact preparation and analysis commands, checksums, an MIT license, and a citation file.Offline analysis reproduces figures from recorded responses, but regenerating an API request does not guarantee an identical remote response.Source: C Artifact and claim audit · p. 15
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