Delegation Gap (DG): Divergence in Delegated Authority

• Delegation Gap (DG) is defined as the divergence between a principal's intended mandate and the realized execution across various domains.
• DG manifests in multiple forms—behavioral, calibration, representational, and infrastructural—impacting AI agents, human–AI teams, and liquid democracy.
• Recent research highlights the need for process-level measurement and improved provenance to verify delegated authority and mitigate these gaps.

Searching arXiv for the cited papers and closely related work on delegation-related gaps, agentic delegation, and delegation in governance. Delegation Gap (DG) is a broad term for divergences between a delegated mandate and the behavior, outcome, or representation that results once authority, judgment, or execution is transferred to another actor or system. Across recent work, DG is not a single standardized construct but a family of closely related problems: in open-world AI agents, it appears as a path-level divergence between intended authorization and realized execution; in human–AI collaboration, as a mismatch between when humans should rely on AI and when they actually do; in voting and liquid democracy, as a difference between outcomes under direct participation and delegated voting; and in digital identity or observability systems, as a failure to represent, verify, or reconstruct delegated authority itself (Wu et al., 10 May 2026). A unifying interpretation is that DG concerns the integrity of delegation under partial information, incomplete specification, dynamic execution, or biased social routing. This suggests that DG is best treated not as a single metric but as a cross-domain analytical lens for studying how delegated authority, judgment, or influence is transformed, distorted, or lost.

1. Conceptual scope and cross-domain meaning

The most explicit recent foundation for a general DG framework comes from work on open-world agents, even though that paper uses the term “Authorization-Execution Gap” rather than Delegation Gap. It defines the Authorization-Execution Gap (AEG) as “the divergence between what a principal intends to authorize and what an open-world agent ultimately executes,” and insists that this divergence must be analyzed “over the full path from intended task and intended authorization scope to realized execution, rather than through any single visible failure at the end of the workflow” (Wu et al., 10 May 2026). This provides a strong processual model for DG: delegation is not a one-time transfer of intent, but a sequence of transformations under partial observability and execution pressure.

That same paper also supplies a vocabulary useful beyond agent safety. A principal is “the party that delegates a bounded task or role.” The agent is “the system acting on the principal’s behalf.” Delegation is “the act by which the principal attempts to convey a bounded mandate to the agent.” Delegated context is “the concrete signal through which the principal’s delegation is conveyed to the agent,” and, crucially, “the only operationally accessible representation of the principal’s intent” (Wu et al., 10 May 2026). In DG terms, this means that delegation is always mediated by an imperfect operational proxy rather than a transparent transfer of intent.

Other domains instantiate the same family of problems with different objects. In human–AI question answering, the paper on cooperative reliance distinguishes delegation choice—“deciding when to let AI act autonomously without knowing its output”—from adoption choice—deciding whether to use AI advice after seeing its answer, confidence, and explanation (Gor et al., 27 May 2026). In governance and voting, DG can refer to the difference in representational or epistemic outcomes between direct participation and delegated voting rights (Gersbach et al., 2021, Gersbach et al., 2021, Strnad, 7 May 2025, Li et al., 2 Jul 2026, Mooers et al., 2022). In digital identity systems, DG can also mean Delegation Grant, a cryptographic authorization artifact, while the broader problem is described as the absence of a common interoperable delegation layer (Saavedra, 21 Jan 2026). In agent observability, DG becomes a structural non-identifiability problem: “delegation-scoped execution is not identifiable from standard observables” (Mishra et al., 8 Jun 2026).

A useful synthesis is that DG has at least four recurring meanings in current literature: a behavioral gap between delegated intent and execution, a calibration gap in reliance decisions, a representational gap in delegated collective choice, and an infrastructural gap in the ability to encode or reconstruct delegated authority.

2. Structural model of delegation failure in agentic systems

The most developed process model comes from the AEG framework for open-world agents (Wu et al., 10 May 2026). It represents delegation as an authorization-execution path made of nodes and edges, with structural sources of failure attached to edges rather than terminal outcomes. The path consists of five stages:

Edge	Input	Output
Delegation	intended task and intended authorization scope	delegated context
Interpretation	delegated context	interpreted task and interpreted authorization scope
Execution	interpreted task and scope	execution state
Handoff	execution state	downstream interpreted task and scope
Termination	execution state	realized execution

This model matters for DG because it makes delegation failure processual rather than static. The interpreted task and interpreted authorization scope are not directly given by the principal; they arise through agent interpretation of delegated context, including “default assumptions about acceptable actions, inferred stopping rules, and background constraints that later execution requires” (Wu et al., 10 May 2026). A plausible implication is that DG in agentic settings often opens not at the final outcome but at earlier interpretive or compositional transitions.

The paper identifies three structural sources of AEG, each of which maps naturally onto a broader DG concept:

1. Delegation-level incompleteness on Edge 1.
2. Channel-level corruption on Edge 3.
3. Composition-level fragmentation on Edge 4.

The first is the narrowest and most direct form of delegation gap. It exists “whenever safe execution depends on qualifications, exceptions, escalation conditions, or stopping rules that are not fully expressed” in delegated context (Wu et al., 10 May 2026). Its canonical manifestations are task misinterpretation and scope underspecification.

The second source, channel-level corruption, arises when environmental content—tool outputs, web content, stored state, upstream-agent outputs—is treated as if it carried delegated authority. Its canonical forms are authority hijacking and authority promotion (Wu et al., 10 May 2026). This is broader than prompt injection, which the paper treats as one manifestation of a deeper structural source.

The third source, composition-level fragmentation, arises in multi-agent handoff. “The authorization relation does not automatically transfer.” Each downstream agent receives only a partial view, so “locally acceptable steps can compose into an outcome that falls outside the overall intended authorization scope” (Wu et al., 10 May 2026). Its canonical manifestations are recomposition violation and scope accumulation.

This structural account is complemented by observability work arguing that, even if individual actions are logged, delegation-scoped attribution is generally non-identifiable from standard telemetry. That paper defines observed events $E$, an execution graph $G_{\mathrm{exec}}$, and a latent authorization relation $R_{\mathrm{auth}} \subseteq D \times E$, then proves that distinct authorization relations can induce identical observables (Mishra et al., 8 Jun 2026). In DG terms, this means a system may suffer not only from delegation failure but from an inability to determine, after the fact, which delegation generated which actions.

The result is a layered picture of DG in agentic AI: incomplete mandate encoding, runtime contamination of authority boundaries, fragmentation across handoffs, and limited observability of delegation lineage.

3. Reliance calibration as a delegation gap in human–AI collaboration

A distinct but closely related usage appears in human–AI cooperation research, where DG is the mismatch between optimal and actual reliance decisions. The strongest recent evidence comes from a live quizbowl-style study of expert humans and AI teammates in which humans made both ex ante delegation decisions and ex post adoption decisions (Gor et al., 27 May 2026).

The study separates two reliance regimes. In tossups, humans decide whether an AI remains active or is muted for future autonomous buzzing. This is delegation choice because the decision is made without seeing the AI’s future output. In bonus questions, humans first commit to an initial answer, then inspect AI guesses, confidence scores, and explanations before deciding whether to switch. This is adoption choice (Gor et al., 27 May 2026). The distinction is central because the paper shows the two gaps differ materially.

For adoption, the paper gives explicit formal definitions. Let $hc \in \{0,1\}$ indicate whether the humans’ initial answer is correct; let $agc \in \{0,0.5,1\}$ denote AI guess correctness; let $arc \in \{0,0.5,1\}$ denote whether the correct answer appears in AI output; let $s \in \{0,1\}$ indicate whether the team switched; and let $fc \in \{0,1\}$ denote final correctness. Then:

$$\text{Under-reliance} = P(s = 0 \mid hc = 0,\ arc > 0)$$

$$\text{Over-reliance} = P(s = 1 \mid hc = 1,\ agc < 1)$$

Empirically, under-reliance was 3.9% and over-reliance was 1.7% (Gor et al., 27 May 2026). This means the dominant adoption gap was failure to use correct AI help rather than blind trust in bad AI.

For delegation in tossups, the paper uses an oracle muting policy that maximizes total tossup points. Human teams captured 79% of the oracle’s maximum possible gain, but only 9% of muting decisions were made at the optimal time, 73% occurred later than optimal, and average muting occurred 3.4 questions earlier than optimal overall, with early muting sometimes 9.8 questions earlier than optimal (Gor et al., 27 May 2026). This is a distinctly ex ante delegation gap: humans often knew enough to mute eventually but not when.

The mechanisms behind this gap are also spelled out. AI-AI disagreement increases caution: when both AIs gave the same correct answer, teams switched 82% of the time; when AIs disagreed, switching dropped to 45% even when one AI was correct (Gor et al., 27 May 2026). Confidence scores were weak decision aids: confidence guided only 2.2% of decisions overall, and “reported model confidence is near chance when humans and AI disagree” (Gor et al., 27 May 2026). Confirmation bias was especially strong: when humans were wrong and one AI agreed with that wrong answer while another AI provided the correct answer, under-reliance rose to 64.5% (Gor et al., 27 May 2026).

This literature frames DG as a trust-calibration problem rather than an execution-integrity problem. A plausible implication is that delegation gaps in human–AI systems can emerge even when the delegated system itself is competent; the failure lies in the human’s selection or adoption policy.

4. Delegation gap in collective choice, voting, and liquid democracy

A separate body of work studies DG as a difference in representational or epistemic outcomes between direct participation and delegated voting. Here the basic objects are voting rights, collective outcomes, and information aggregation rather than tasks or tool actions.

The paper “Vote Delegation with Unknown Preferences” analyzes binary choice with delegators who abstain under conventional voting or delegate uniformly at random among active voters when preferences are private (Gersbach et al., 2021). Let $G_{\mathrm{exec}}$0 be the probability that the ex ante majority alternative wins under conventional voting, and $G_{\mathrm{exec}}$1 under free delegation with $G_{\mathrm{exec}}$2 delegators. The main theorem states:

$G_{\mathrm{exec}}$3

Thus delegation strictly lowers the winning probability of the ex ante majority and raises the probability that the ex ante minority wins (Gersbach et al., 2021). The same result holds for capped delegation when the cap $G_{\mathrm{exec}}$4. The mechanism is concentration of voting weight: delegation preserves expected shares but increases dispersion, reducing the effective number of independent observations.

The closely related paper “Vote Delegation and Misbehavior” studies costly voting with well-behaving and misbehaving agents under a Poisson game model (Gersbach et al., 2021). Its central comparative result is regime-dependent. If the number of misbehaving voters $G_{\mathrm{exec}}$5 is high, both delegation and conventional voting fail. If $G_{\mathrm{exec}}$6 is intermediate, conventional voting yields a positive probability of the desirable outcome while delegation fails with probability one. If $G_{\mathrm{exec}}$7 is low, delegation can outperform conventional voting (Gersbach et al., 2021). This is a sharp example of a non-monotone delegation gap: delegation can help or harm depending on the adversarial environment.

Experimental evidence on liquid democracy points in a similar direction. “Liquid Democracy. Two Experiments on Delegation in Voting” finds that delegation underperforms both universal majority voting and abstention (Mooers et al., 2022). In a controlled setting with mathematically explicit precisions, only non-experts with precision below 0.53 should delegate, yet observed delegation was two to three times the interior-equilibrium rate. In one treatment, the average observed delegation threshold was 0.604 versus an optimal 0.543; in another, 0.614 versus 0.532 (Mooers et al., 2022). The paper attributes this to overdelegation, overestimation of expert precision, and neglect of the fact that delegation reduces the number of independent signals represented in the vote.

A more general epistemic treatment is given in “Delegation and Participation in Decentralized Governance” (Strnad, 7 May 2025). The benchmark weight for voter $G_{\mathrm{exec}}$8 is

$G_{\mathrm{exec}}$9

where $R_{\mathrm{auth}} \subseteq D \times E$0 is competence. The paper argues that partial abstention can often implement the epistemically optimal weighting more robustly than transfer delegation, because abstention reduces one’s own weight without altering others’ relative weights (Strnad, 7 May 2025). By contrast, transfer delegation requires broad knowledge of others’ competencies and current vote allocations, making it fragile. A canonical example shows a near-optimal direct system with correctness about 0.997 collapsing to 0.731 under liquid-democratic overdelegation to a single expert (Strnad, 7 May 2025).

More recent work introduces a related but not identical quantity, the recoverable gap $R_{\mathrm{auth}} \subseteq D \times E$1, defined as

$R_{\mathrm{auth}} \subseteq D \times E$2

in a liquid-democracy setting (Li et al., 2 Jul 2026). The paper argues that delegation helps only when there is substantial abstention-induced representational distortion to recover. In Aarau municipal participatory budgeting, abstention accuracy was 0.729, so $R_{\mathrm{auth}} \subseteq D \times E$3, and delegation improved representational accuracy by +0.061. In contrast, in the CES 2022 setting, abstention accuracy was 0.971, so $R_{\mathrm{auth}} \subseteq D \times E$4, and expert delegation reduced accuracy to 0.917 (Li et al., 2 Jul 2026). This provides a threshold-style view of DG: delegation is beneficial only when the recoverable distortion is sufficiently large.

Across these papers, DG in governance is typically the difference in outcome probabilities, representational fidelity, or truth-tracking performance between direct or abstention-based aggregation and delegated influence. A common mechanism is concentration: delegation often routes many weak but independent signals into a few influential representatives.

5. Infrastructure, provenance, and observability dimensions of delegation gap

A further line of work treats DG as an infrastructural rather than behavioral deficiency: the inability of systems to encode, verify, or observe delegated authority.

In digital identity, “Interoperable Architecture for Digital Identity Delegation for AI Agents with Blockchain Integration” uses DG explicitly to mean Delegation Grant (Saavedra, 21 Jan 2026). A DG is defined as a “first-class authorization artefact” that encodes bounded transfers of authority and enforces scope reduction along delegation chains. The central monotonicity constraint is:

$R_{\mathrm{auth}} \subseteq D \times E$5

The broader problem, however, is described as a missing interoperable delegation layer: existing centralized, federated, and self-sovereign identity systems do not provide a common verifiable way to delegate bounded authority across heterogeneous environments (Saavedra, 21 Jan 2026). In a DG encyclopedia sense, this is a reminder that the term can denote both the problem and a proposed artifact intended to solve it.

In agentic AI, the Human Delegation Provenance protocol addresses a “fundamental accountability gap” in multi-agent delegation: verifying that terminal actions were genuinely authorized by a human principal, through what chain, and under what scope (Dalugoda, 6 Apr 2026). HDP binds a root human authorization to a session and appends signed delegation hops. Its validity conditions include session binding, chain integrity, and optional maximum hop count. A reconstructed succinct validity condition is:

$R_{\mathrm{auth}} \subseteq D \times E$6

when a hop bound is present (Dalugoda, 6 Apr 2026). The paper’s contribution is not semantic alignment but cryptographic provenance: it narrows the delegation gap at the level of authorization traceability.

Observability work goes further by arguing that delegation-scoped execution is structurally non-identifiable from ordinary traces and audit logs (Mishra et al., 8 Jun 2026). The paper defines a delegation-observable system as one in which, for every delegation $R_{\mathrm{auth}} \subseteq D \times E$7, the events executed under $R_{\mathrm{auth}} \subseteq D \times E$8 and its descendants can be reconstructed from telemetry without heuristic correlation. It derives four core requirements: persistent delegation context, authority–causality separation, delegation closure, and cross-system normalization (Mishra et al., 8 Jun 2026). Its proposed mitigation is a gateway plus a Common Information Model that binds delegation_id at execution time.

These infrastructural papers broaden DG beyond outcome mismatch. They show that a system can suffer a delegation gap even if actions are individually authorized and logged, if the semantics needed to attribute them to a delegation context are absent.

6. Measurement, evaluation, and open research directions

Recent work increasingly treats DG as something that must be measured at the process level, not inferred solely from end outcomes. This is clearest in open-world agent safety and agentic benchmark design.

The AEG paper argues that papers on open-world agents should report “not only outcome-level metrics such as task success or attack resistance, but also process-level evidence showing where AEG was detected, constrained, and attributed to a structural source during execution” (Wu et al., 10 May 2026). It proposes five runtime checks: Delegation Completeness Check, Authority Attribution Check, Scope Compliance Check, Provenance Preservation Check, and Recomposition Authorization Check (Wu et al., 10 May 2026). A plausible implication is that DG research should instrument delegation edges rather than evaluate only final outputs.

DecisionBench makes a similar methodological point in long-horizon agentic workflows (Gao et al., 18 May 2026). Mean end-task quality was statistically indistinguishable across four awareness conditions, with $R_{\mathrm{auth}} \subseteq D \times E$9 and $hc \in \{0,1\}$0, yet routing fidelity@1 ranged from 7.5% to 29.5%, and a counterfactual delegation ceiling sat 15–31 percentage points above measured performance on every suite (Gao et al., 18 May 2026). The benchmark therefore motivates at least two DG-like measures: a routing gap $hc \in \{0,1\}$1 and a ceiling gap between actual quality and counterfactual perfect delegation.

SearchSwarm addresses a related “delegation intelligence” gap for long-horizon deep research (Ning et al., 8 Jun 2026). It defines delegation intelligence as the ability to decompose tasks, decide when and what to delegate, and integrate returned results. The system uses a harness to encourage delegation, comprehensive briefing, main-agent retention of core judgment, and citation-grounded reporting, then distills successful trajectories into supervised training data (Ning et al., 8 Jun 2026). This suggests that some forms of DG may be trainable deficits rather than fixed architectural limits.

In DAO governance, the paper on fairness in token delegation provides a measurement pipeline for representational DG using forum-derived interest embeddings, identity linkage, and concentration measures (Messias et al., 7 Oct 2025). It reports that voting-power Ginis exceed 0.94 and reach 0.99 in several protocols, while delegations are “frequently misaligned with token holders’ expressed priorities” (Messias et al., 7 Oct 2025). Although it does not provide a final scalar DG metric, it lays out the ingredients for a token-weighted semantic mismatch measure.

A more normative formalization appears in decision-theoretic delegation under uncertainty. “A Decision-Theoretic Approach for Managing Misalignment” analyzes when a principal should delegate to an imperfectly aligned agent under uncertainty about beliefs, values, and reach (Herrmann et al., 17 Dec 2025). In its score-based framework, one can reconstruct a context-specific delegation gap as the difference between delegated and self-action scores across problem distributions. Its central claim is that universal delegation requires near-perfect trust and alignment, whereas context-specific delegation can be rational even under significant misalignment if epistemic or reach advantages compensate (Herrmann et al., 17 Dec 2025).

Finally, older theory on recursive delegation via quitting games shows that delegation can itself be a multi-step stochastic process, with performance losses arising from onward delegation and failure propagation rather than just the first handoff (Afanador et al., 2018). This suggests that DG in long-horizon systems may depend not only on local delegation decisions but on recursive structures.

Taken together, current research suggests several recurring open problems:

• Standardization: DG is used inconsistently across domains; no single formal definition dominates.
• Attribution: many systems cannot determine where in a delegation path divergence arose (Mishra et al., 8 Jun 2026).
• Calibration: humans and agents both mismanage delegation under uncertainty (Gor et al., 27 May 2026, Mooers et al., 2022).
• Composition: local correctness does not guarantee end-to-end integrity (Wu et al., 10 May 2026).
• Measurement: quality-only metrics often miss the orchestration signal (Gao et al., 18 May 2026).
• Representation vs concentration: delegation may improve participation while worsening epistemic or representational fidelity (Strnad, 7 May 2025, Li et al., 2 Jul 2026, Messias et al., 7 Oct 2025).

A reasonable synthesis is that Delegation Gap is best understood as an umbrella concept for integrity losses in the transfer of bounded authority, judgment, or influence. The specific form it takes depends on the domain: execution divergence in agentic AI, reliance miscalibration in human–AI systems, concentration-driven representational distortion in governance, or missing semantics in identity and observability infrastructure. What unifies these cases is that delegation is not merely transfer; it is transformation, and DG is the name for the structured divergence introduced by that transformation.