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REVIEW 3 major objections 3 minor 1 cited by

Multi-agent LLMs coordinating private calendars leave avoidable costs and fairness shortfalls that completion metrics miss.

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T0 review · grok-4.3

2026-06-30 22:18 UTC pith:ASXOA3TJ

load-bearing objection CalBench gives a new controlled benchmark for multi-agent LLM calendar scheduling under privacy, but the headline findings rest on whether the CP-SAT oracles truly face identical information partitions. the 3 major comments →

arxiv 2605.09823 v3 pith:ASXOA3TJ submitted 2026-05-10 cs.MA cs.AI

CalBench: Evaluating Coordination-Privacy Trade-offs in Multi-Agent LLMs

Chelsea Zou , Yiheng Yao , Selena She , Noah Goodman , Robert D. Hawkins This is my paper
classification cs.MA cs.AI
keywords multi-agent LLMscalendar schedulingprivacy trade-offscoordination benchmarksinformation constraintstask metrics
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents CalBench as a testbed for multi-agent LLMs acting as calendar assistants that must coordinate meetings without accessing each other's private schedules. It demonstrates that across several model families, simply succeeding at the scheduling task does not capture the full picture of performance. Models often incur higher costs than necessary, their amount of communication does not reliably lead to better results, and attempts to protect privacy by staying silent can result in uneven sharing of meeting burdens. This matters because personal AI delegates are emerging, and the benchmark highlights coordination failures that could affect users in practice. The evaluation uses known optimal solutions from an oracle to quantify these issues under controlled privacy conditions.

Core claim

CalBench creates matched scenarios where multiple agents with private calendars schedule a stream of meetings to minimize disruption costs, using language for coordination since direct inspection is impossible. Evaluation across seven model families shows that task completion alone fails to reveal cases where agents leave avoidable costs, where communication volume does not predict lower regret, and where privacy-preserving silence deprives the group of information needed for fair burden allocation.

What carries the argument

CalBench benchmark, which generates solvable calendar scheduling tasks with CP-SAT oracle solutions and decentralized reference protocols to measure success, excess cost, communication efficiency, burden fairness, and privacy leakage under information constraints.

Load-bearing premise

That the generated solvable scenarios with CP-SAT oracle solutions and decentralized non-LLM reference protocols provide a representative and matched information-constraint testbed for real multi-agent coordination under private calendars.

What would settle it

Observing that LLM agents in CalBench achieve zero excess cost and perfect fairness matching the oracle solutions across all tested scenarios would falsify the finding that completion metrics miss important failures.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • Task completion metrics are insufficient for evaluating multi-agent LLM coordination.
  • Communication volume does not reliably correlate with reduced regret or better performance.
  • Privacy-preserving behaviors can lead to unfair allocation of costs among agents.
  • Language-mediated coordination under private information requires new evaluation approaches beyond standard benchmarks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Future systems might benefit from protocols that allow selective sharing of cost information without full calendar disclosure.
  • The benchmark could be adapted to other multi-agent tasks involving private data, such as resource allocation or negotiation.
  • Real deployments may need to incorporate optimization tools alongside LLMs to approach oracle-level performance.
  • Testing with actual user calendars could reveal whether the generated scenarios capture key real-world dynamics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. The manuscript introduces CalBench, a benchmark for multi-agent LLM coordination in private-information calendar scheduling. Tasks involve N agents managing separate private calendars to schedule M meetings while minimizing disruption costs; success requires language-mediated coordination. Scenarios are generated as solvable instances with CP-SAT oracle solutions and decentralized non-LLM reference protocols. Evaluation across seven model families measures task success, excess cost, communication efficiency, burden fairness, and privacy leakage under matched information constraints. Central claims are that completion alone misses failures: agents leave avoidable cost on the table, communication volume does not predict lower regret, and privacy-preserving silence can deprive teammates of information needed for fair burden allocation.

Significance. If the matched-constraint claim holds, CalBench supplies a reproducible, oracle-grounded testbed for coordination-privacy trade-offs, directly relevant to deployed personal AI assistants. The inclusion of both centralized oracles and decentralized non-LLM baselines, plus multi-dimensional metrics beyond binary success, strengthens the contribution over purely qualitative case studies.

major comments (3)
  1. [§3 (scenario generation and oracle)] The load-bearing claim of 'matched information constraints' (abstract and §3) between CP-SAT oracle solutions and LLM agents requires explicit verification. The manuscript must show that oracle optima are computed under identical decentralized private-calendar partitions rather than centralized full information; otherwise the reported excess costs and fairness shortfalls cannot be attributed to LLM limitations versus the information structure.
  2. [Results (communication-regret analysis)] The claim that communication volume does not predict lower regret (results section) needs quantitative support: report Pearson or Spearman correlations, p-values, and controls for task difficulty or model family. Qualitative observation across seven families is insufficient to support the headline finding that volume is uninformative.
  3. [Results (burden fairness)] The burden-fairness metric and the causal link from privacy-preserving silence to unfair allocation (results) require precise definitions: how fairness is quantified (e.g., cost variance, max-min ratio), and evidence that information deprivation is the operative mechanism rather than a correlate of task type or model behavior.
minor comments (3)
  1. [Abstract] Abstract lists 'seven model families' without naming them; add the list (e.g., GPT-4o, Claude-3, Llama-3, …) for immediate clarity.
  2. [§2] Ensure first use of CP-SAT is accompanied by its expansion (Constraint Programming - SAT solver).
  3. [Figures] Figure captions should explicitly state whether plotted regret values are normalized or absolute and whether error bars represent standard error or deviation across runs.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments, which help strengthen the clarity and rigor of the manuscript. We address each major point below and will incorporate revisions as noted.

read point-by-point responses

  1. Referee: [§3 (scenario generation and oracle)] The load-bearing claim of 'matched information constraints' (abstract and §3) between CP-SAT oracle solutions and LLM agents requires explicit verification. The manuscript must show that oracle optima are computed under identical decentralized private-calendar partitions rather than centralized full information; otherwise the reported excess costs and fairness shortfalls cannot be attributed to LLM limitations versus the information structure.

    Authors: We agree that explicit verification is required to support the matched-constraints claim. The current manuscript computes CP-SAT solutions with full information to establish an absolute performance ceiling, while agents and non-LLM baselines operate under private partitions. In revision we will add to §3 (and an appendix) a precise description of the oracle generation procedure, including verification that each reported optimum respects the same per-agent private-calendar constraints used by the LLM agents. Where full-information optima differ from private-information optima, we will report both and adjust the excess-cost interpretation accordingly. revision: yes

  2. Referee: [Results (communication-regret analysis)] The claim that communication volume does not predict lower regret (results section) needs quantitative support: report Pearson or Spearman correlations, p-values, and controls for task difficulty or model family. Qualitative observation across seven families is insufficient to support the headline finding that volume is uninformative.

    Authors: We accept that the current presentation relies on qualitative patterns. In the revised results section we will add Pearson and Spearman rank correlations between total communication tokens (or messages) and regret, together with p-values. We will also include regression controls for task difficulty (number of agents, meetings, and calendar density) and model family fixed effects. These statistics will be reported both pooled and stratified by family. revision: yes

  3. Referee: [Results (burden fairness)] The burden-fairness metric and the causal link from privacy-preserving silence to unfair allocation (results) require precise definitions: how fairness is quantified (e.g., cost variance, max-min ratio), and evidence that information deprivation is the operative mechanism rather than a correlate of task type or model behavior.

    Authors: We will add an explicit definition of the burden-fairness metric in the methods section (e.g., variance of per-agent disruption costs normalized by total cost, or max-min cost ratio). To address the causal mechanism, the revision will include (i) an ablation that isolates episodes in which agents remain silent on cost-relevant information and (ii) controls for task type and model family when comparing fairness outcomes. We will report whether the observed unfairness persists after these controls. revision: yes

Circularity Check

0 steps flagged

Empirical benchmark evaluation with no derivation chain

full rationale

The paper presents CalBench as an empirical testbed for multi-agent LLM coordination under private calendars, generating scenarios solved by CP-SAT oracle and non-LLM reference protocols. No mathematical derivations, first-principles predictions, fitted parameters renamed as outputs, or self-citation load-bearing steps appear in the abstract or described structure. All reported findings (excess cost, communication-regret correlation, fairness impacts) are direct experimental measurements against external oracles under stated information constraints. This is a standard self-contained benchmark study; the central claims rest on observable task performance rather than any reduction to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the central claim rests on the assumption that the benchmark scenarios are valid proxies for the target problem.

pith-pipeline@v0.9.1-grok · 5734 in / 1007 out tokens · 25176 ms · 2026-06-30T22:18:39.906187+00:00 · methodology

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Cite this review

Pith. "Pith review of CalBench: Evaluating Coordination-Privacy Trade-offs in Multi-Agent LLMs." pith.science (2026). https://pith.science/paper/ASXOA3TJ

@misc{pith2026260509823,
  author       = {Pith},
  title        = {Pith review of: CalBench: Evaluating Coordination-Privacy Trade-offs in Multi-Agent LLMs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ASXOA3TJ}},
  note         = {Machine review of arXiv:2605.09823}
}
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read the original abstract

Personal AI assistants are beginning to act as delegates with access to calendars, inboxes, and user preferences. Calendar scheduling makes the trust problem concrete: an assistant must coordinate with other assistants while deciding what to reveal about the person it represents. We introduce CalBench, a controlled benchmark for multi-agent calendar scheduling under private information. In each task, $N$ agents manage separate private calendars and schedule a stream of $M$ incoming meetings while minimizing disruption costs. Because no agent can inspect another agent's calendar, success requires language-mediated coordination rather than centralized planning. CalBench generates solvable scenarios with CP-SAT oracle solutions and decentralized non-LLM reference protocols, enabling evaluation of task success, excess cost, communication efficiency, burden fairness, and privacy leakage under matched information constraints. Across seven model families, we find that completion alone misses important failures: agents leave avoidable cost on the table, communication volume does not predict lower regret, and privacy-preserving silence can deprive teammates of cost information needed for fair burden allocation. CalBench provides a reproducible testbed for studying whether autonomous assistants can coordinate on behalf of users before deployment at scale.

Figures

Figures reproduced from arXiv: 2605.09823 by Chelsea Zou, Noah Goodman, Robert D. Hawkins, Selena She, Yiheng Yao.

Figure 1
Figure 1. Figure 1: Overview of the CalBench environment. (A) Environment setup: Each of N agents maintains a private calendar with T discrete time slots containing free times, errands with private semantic contexts, and scheduled meetings. Meetings must be placed at the same slot across all participants’ calendars. Calendars are initialized by reserving a hidden feasible solution and filling remaining slots to a target densi… view at source ↗
Figure 1
Figure 1. Figure 1: Overview of the CalBench environment. (A) Environment setup: Each of N agents maintains a private calendar with T discrete time slots containing free times, errands with private semantic contexts, and scheduled meetings. Meetings must be placed at the same slot across all participants’ calendars. Calendars are initialized by reserving a hidden feasible solution and filling remaining slots to a global or pe… view at source ↗
Figure 2
Figure 2. Figure 2: Privacy–efficiency plane: uniform VPS leakage (mean per game; §3.2) against excess cost [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 2
Figure 2. Figure 2: Privacy–efficiency plane for the canonical CalBench games, with uniform-cost games on the left and [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Communication efficiency for model runs only. Each point is a single game’s messages [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Average direct messages by meeting index for uniform and varied tasks. The metric is [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 4
Figure 4. Figure 4: Fairness cost by model and cost setting. Lower [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Average direct messages by speaker position. We measure speaker-position effects because [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 5
Figure 5. Figure 5: Meeting-level scheduling failure modes in [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Mean number of prior meetings rescheduled per game. Values are averaged across [PITH_FULL_IMAGE:figures/full_fig_p028_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Average cheap-talk messages sent by selected [PITH_FULL_IMAGE:figures/full_fig_p022_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Average cheap-talk messages sent by selected [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Mean number of prior meetings rescheduled [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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Reference graph

Works this paper leans on

31 extracted references · 31 canonical work pages · cited by 1 Pith paper

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    This hidden solution achieves a known cost

    Awitness slot wc is drawn uniformly at random for each meeting c from slots not already used by any of its participants. This hidden solution achieves a known cost. 10 Table 2: Scenario generation parameters. Parameter Type Description seedint RNG seed; fixes all randomness num_agentsint Number of agentsN num_slotsint Calendar lengthS(default 16) densityf...

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    Witness slots are deliberately seeded with errands (when force_witness_errand is true) to create dis- placement pressure

    For each agent i, errand items are placed in ⌊S·ρ i⌋ slots drawn randomly, where ρi is ei- ther the shared density value or the agent- specific entry in a density vector. Witness slots are deliberately seeded with errands (when force_witness_errand is true) to create dis- placement pressure

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    This preserves the invariant that the wit- ness solution is feasible under any sequence of moves needed to clear the witness slots

    A small set ofabsorbing slots— one per er- rand occupying a witness slot — is kept free so displaced errands always have a valid landing pad. This preserves the invariant that the wit- ness solution is feasible under any sequence of moves needed to clear the witness slots

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    Each errand is assigned a displacement cost drawn from Uniform[1,errand_cost_level]

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    Intake ses- sion at the Willow Tree Eating Disorder Clinic

    The optimal cost, greedy cost, and CP-SAT feasible-assignment fraction are computed and stored in the scenario dict. The feasible- assignment fraction counts distinct injective meeting-slot assignments that satisfy the CP- SAT constraints and divides byS!/(S−C)!. Calendar data model.Each agent’s calendar is a fixed-length list ofslots. A slot is either nu...

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    RULES— hard constraints: no double-booking, same-slot consistency for all participants, same- slot constraint for rescheduled meetings

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    IMPORTANTCONSTRAINTS— information constraints: own-only visibility, prohibition on sharing errand/meeting details with non- participants, prohibition on sharing cost func- tions

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    NEGOTIATIONSTRATEGY— six negotiation guidelines instructing the agent to prefer free slots, push back on costly proposals, and use only qualitative language about difficulty

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    CALENDARSLOTTYPES— definitions of the four slot types ( free, blocked, errand, meeting)

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    TOOLS— the JSON tool-call schema for dm, participant groupchat, all-agent groupchat, schedule, and reschedule, with phase- specific validity rules

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    PHASES— descriptions of the four phases each agent participates in (CHEAP_TALK, VOL- UNTARY , DECISION, RESOLUTION)

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    thinking

    RESPONSEFORMAT— the required {"thinking": ..., "actions": [...]} envelope with a worked example

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    IDENTITY— the agent’s own ID and the full agent list

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    ENVIRONMENTPARAMETERS— slot count, retry budget, multi-round structure. Adversarial variant injection.Agents config- ured with theNOSY-HIGHPRESSUREorREDTEAM variants receive one additional section appended verbatim after the base prompt (see §A.2 and §A.2). No other section changes; the injection is self- contained. DSPy variant injection.Agents configure...

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    A=== ROUND N START ===header

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    The meeting to schedule: ID, participant list, duration in slots, and the private meeting label (visible only to participants)

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    The agent’s own calendar as a rendered slot list

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    The agent’s cumulative penalty incurred in pre- vious rounds

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    CHEAP_TALK turn budget: turn 1 of N.kturn(s) remain after this one

    The active phase ( CHEAP_TALK) and, when max_turns_per_round is set, a turn-budget line of the form “CHEAP_TALK turn budget: turn 1 of N.kturn(s) remain after this one.” 12 Table 3: User-message sequence per round. Each row is one message appended to an agent’s conversation thread. Phase / condition Message builder Delivered to CHEAP_TALK, turn 0build_rou...

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    Turn message.Produced by build_turn_message(messages, turn_index, max_turns_per_round)

    A reminder that DECISION follows CHEAP_TALK and that agents should negotiate for a low-displacement slot. Turn message.Produced by build_turn_message(messages, turn_index, max_turns_per_round). Delivered for every subsequent CHEAP_TALK turn to agents in the current speaker order. When the agent has new messages, the body lists each incoming private or gro...

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    No new messages in your inbox

    From Agent 2 (meeting 3): <content> When the inbox is empty, the body reads “No new messages in your inbox.” On the final allowed turn ( turn_index + 1 == max_turns_per_round), an additional sentence in- structs the agent not to ask open-ended questions and to return[]if coordination is complete. Voluntary-reschedule message.Produced by build_voluntary_re...

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    Slot bounds.All slot, from_slot, and to_slotvalues must be integers in[0, S)

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    Item identity.Each reschedule action’s item_id must match the errand_id or meeting_id of the item actually present at from_slot

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    No blocked moves.Items with blocked: truemay not be moved

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    No destination conflicts.No two actions in the batch may target the sameto_slot

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    Freeness after batch.Each to_slot must be free on the calendarorbe freed by another reschedulein the same batch

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    (The VOLUNTARY phase usesrequire_schedule=FALSE.)

    Exactly one schedule.In the DECISION phase, the batch must contain exactly one schedule action. (The VOLUNTARY phase usesrequire_schedule=FALSE.)

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    bump iff the existing meeting has strictly fewer other participants than the new meeting

    Schedule slot free.The schedule slot must be free after all reschedule operations are ap- plied. Validation is transactional: nothing is applied until the entire batch passes. On failure the harness emits aBATCH_REJECTEDevent with the exact conflict string and delivers a RETRYmessage to the agent. Up to decision_retries retries are attempted; if all fail,...

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