When Coordination Is Avoidable: A Monotonicity Analysis of Organizational Tasks

Abstract: Organizations devote substantial resources to coordination, yet which tasks actually require it for correctness remains unclear. The problem is acute in multi-agent AI systems, where coordination overhead is directly measurable and routinely exceeds the cost of the work itself. However, distributed systems theory provides a precise answer: coordination is necessary if and only if a task is non-monotonic, meaning new information can invalidate prior conclusions. Here we show that a classic taxonomy of organizational interdependence maps onto the monotonicity criterion, yielding a decision rule and a measure of avoidable overhead (the Coordination Tax). Multi-agent simulations confirm both predictions. We classify 65 enterprise workflows and find that 48 (74%) are monotonic, then replicate on 13,417 occupational tasks from the O*NET database (42% monotonic). These classification rates imply that 24-57% of coordination spending is unnecessary for correctness.

• The paper proves a Bridge Theorem connecting Thompson’s interdependence taxonomy to CALM, showing that pooled and sequential tasks can avoid coordination while reciprocal tasks require it.
• Empirical analysis finds 48 of 65 enterprise workflows and 41.5% of 13,417 occupational tasks are monotonic, implying that 24–57% of coordination spending may be unnecessary for correctness.
• Simulation results show uncoordinated monotonic tasks retain 70–100% validity, whereas all tested non-monotonic tasks fail, supporting tiered architectures based on task structure.

Overview and motivation

This paper addresses a question that organizational theory has left formally unanswered: which tasks actually require coordination for correctness, as opposed to merely benefiting from it? The author, Harang Ju, imports a precise criterion from distributed systems theory—the CALM theorem (Consistency As Logical Monotonicity), which states that a computation can execute without coordination if and only if it is monotonic (2602.18673)—and proves that Thompson's classic interdependence taxonomy maps onto this criterion. The result is both a decision rule for classifying tasks and an estimable quantity, the "Coordination Tax," measuring how much coordination spending is structurally unnecessary. The empirical stakes are sharpened by multi-agent AI systems, where coordination overhead is directly countable in tokens and reportedly consumes 40–60% of total compute in agentic software engineering.

The Thompson–CALM Bridge Theorem

The paper's central theoretical contribution establishes a correspondence between two traditions that developed independently. Under assumptions of deterministic task evaluation, reliable message delivery, and eventual consistency, the Bridge Theorem states:

• Pooled interdependence implies a monotone specification, executable coordination-free via merge over a join-semilattice.
• Sequential interdependence implies a monotone specification under causal ordering (Lamport's happened-before relation), since composition of non-retractive functions remains non-retractive.
• Reciprocal interdependence implies a non-monotone specification requiring coordination; the paper's counterexample involves shared budget allocation, where one agent's proposal invalidates another's.

A companion result, the Feedback Boundary proposition, resolves an ambiguity Thompson's taxonomy leaves open: feedback from downstream to upstream agents preserves monotonicity only when it is additive; retractive feedback (revision or replacement of prior output) renders the task non-monotone. This formalizes Argyris and Schön's distinction between single-loop refinement and double-loop revision in coordination-theoretic terms.

The Coordination Tax follows directly. For a portfolio with non-monotonic fraction $f$ and overhead multiplier $c > 1$, the avoidable fraction of coordination spending under uniform coordination is:

$T(f, c) = \frac{(1-f)(c-1)}{c}$

This is explicitly an upper bound, valid under the idealization that all tasks receive uniform coordination regardless of structural necessity.

Empirical classification of two corpora

The first corpus is an exhaustive census of 65 enterprise workflows at APQC Levels 2–3, spanning all 13 categories of the Process Classification Framework. The headline finding is bold: 48 of 65 workflows (73.8%) are monotonic, meaning they can execute correctly without any coordination mechanism—39 fully coordination-free and 9 requiring only causal ordering. Prevalence varies systematically across categories, from 100% monotonic in Risk & Compliance down to 57% in Financial Resources, where shared budget allocation concentrates non-monotonicity. Notably, nearly all 17 non-monotonic tasks involve allocating shared finite resources, echoing Thompson's observation that reciprocal interdependence clusters at critical integration points while explaining it mechanistically through negation. The finding is robust to borderline reclassification (60–74% monotonic under worst-case coding).

The second corpus scales the analysis to 13,417 core task statements from O*NET 29.1 across 22 SOC major groups, classified by an LLM classifier validated against the author-coded APQC corpus ($\kappa \geq 0.88$, $\geq$95% accuracy, with misclassifications biased safely toward non-monotonic). Here 41.5% of tasks are monotonic (95% CI [40.6, 42.3]), with every SOC group exceeding 30%. The lower rate relative to APQC reflects the unit of analysis—individual work activities rather than team-level workflows—but extends the scope of coordination avoidance to the broader occupational landscape.

Combining corpora with measured overhead ratios yields the paper's central quantitative claim: 24–57% of coordination spending is unnecessary for correctness (APQC-derived tax of 42–57%, O*NET-derived tax of 24–32%, at simulated $c = 2.3$–$4.4\times$). Using published multi-agent framework overheads of 4–10× pushes the APQC range to 56–67%.

Simulation validation

Ten tasks spanning the monotonicity spectrum were run under coordinated (orchestrator-mediated) and uncoordinated (concatenated outputs) conditions across three model families—GPT-4.1 mini, Claude Haiku 4.5, and Claude Sonnet 4.5—with LLM-as-judge validity evaluation at temperature 0. The results are strikingly binary:

Task type	Uncoordinated validity
Monotonic	70–100% (model-dependent)
Sequential (ordering-only)	50–100% (model-dependent)
Non-monotonic	0% across all models and all four tasks

Every non-monotonic task fails completely without coordination on every model, while monotonic tasks largely preserve validity; residual variance on monotonic tasks reflects model capability rather than CALM violations. Coordinated runs consume 2.3–4.4× more tokens. These simulations validate the Bridge Theorem as a practical design tool, not merely a classification scheme.

Theoretical significance

The Bridge Theorem converts Thompson's descriptive taxonomy into a prescriptive decision rule with computability guarantees, advancing Malone and Crowston's program of characterizing dependencies by answering the prior question: given a dependency type, is coordination necessary at all? The Coordination Tax also isolates a category of transaction cost that neither Coase nor Williamson identified—overhead that is structurally unnecessary rather than merely excessive—and unlike most transaction costs, it is computable ex ante from two observable quantities. The practical prescription is a tiered architecture in which task topology, rather than inherited authority structure, determines coordination intensity: roughly 60% of enterprise work needs only fire-and-forget execution with merge, 14% needs causal delivery, and only 26% requires full mutual adjustment. Because CALM guarantees consistency under partition, monotonic tasks additionally tolerate asynchronous and distributed execution without correctness loss—a property with direct relevance to remote-work organizations and geographically distributed agent fleets.

Limitations and open questions

The paper is explicit about several boundary conditions. CALM guarantees correctness, not quality: independently produced outputs may be valid yet stylistically inconsistent, so coordination for coherence may remain worthwhile even where it is unnecessary for correctness. Misclassification risk is asymmetric—a false monotonic label endangers correctness—motivating a default-to-coordination rule under uncertainty. The 74% prevalence holds specifically at APQC Levels 2–3; coarser decomposition pushes toward non-monotonic classification. The classification is static, leaving runtime reclassification of tasks that shift mid-execution as future work. Stochastic LLM agents may not faithfully implement monotone specifications, so output validation remains essential alongside classification. Finally, the simulation's binary VALID/INVALID criterion is an idealization; real coordination failures often produce gradual quality degradation or rework rather than clean failure, so field validation outside the experimental sandbox remains untested.

Conclusion

This paper demonstrates that whether a task requires coordination is a computable property of its dependency structure, formalized through a proven correspondence between Thompson's interdependence taxonomy and the CALM monotonicity criterion. Across 65 enterprise workflows and 13,417 occupational tasks, 42–74% of tasks are monotonic and provably need no coordination for correctness, implying that 24–57% of coordination spending is structurally unnecessary. Multi-agent simulations confirm the predicted boundary with a clean binary failure pattern. The results prescribe tiered architectures—for human organizations and AI systems alike—in which coordination intensity follows task topology rather than organizational convention.