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arxiv: 2605.03621 · v1 · submitted 2026-05-05 · 💰 econ.TH · cs.GT

Recognition: 2 theorem links

· Lean Theorem

Going Public: Communication in Collective Decisions

Boli Xu, Yingkai Li, Zhicheng Du

Pith reviewed 2026-05-08 18:19 UTC · model grok-4.3

classification 💰 econ.TH cs.GT
keywords cheap talkpublic messagingprivate messagingcollective decisionsinformation designapproval mechanismsweak dominance
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The pith

Public messaging can implement any outcome achievable with private messaging, and sometimes strictly more, when agents must approve a project.

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

A principal learns about an unknown state by running a test and then uses cheap-talk messages to persuade at least k out of n agents to approve a project whose payoffs depend on that state. The paper establishes that any outcome the principal can achieve by sending different private messages to different agents can also be achieved by sending the same public message to everyone. In environments with linear payoffs, the paper fully characterizes the best test the principal should run in each regime and identifies the exact condition under which public messaging delivers strictly better results for the principal.

Core claim

Any outcome implementable under private messaging can also be implemented under public messaging. In a canonical linear-payoff setting, the principal's optimal test is characterized for both regimes, and public messaging is strictly dominant if and only if two agents are the principal's conflicting allies.

What carries the argument

The weak dominance of public cheap-talk messaging over private cheap-talk messaging after the principal chooses an information test in a collective approval game.

If this is right

  • Any approval probability vector achievable with private messages is also achievable with public messages.
  • In linear-payoff environments the principal's optimal test differs between the two regimes.
  • Strict improvement from public messaging occurs exactly when the principal has two conflicting allies among the agents.

Where Pith is reading between the lines

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

  • Principals facing group approval problems may be able to simplify their communication strategy without losing control.
  • The result suggests that public disclosure rules could substitute for private briefings in committees or partnerships.
  • Experiments could test the conflicting-allies condition by varying whether two agents have opposing stakes relative to the principal.

Load-bearing premise

Agents update beliefs rationally from the messages they receive in a cheap-talk game where the principal cannot commit in advance to any future action.

What would settle it

A concrete payoff structure and agent preferences in which some approval outcome can be achieved with private messages but no public message strategy works would disprove the weak dominance result.

Figures

Figures reproduced from arXiv: 2605.03621 by Boli Xu, Yingkai Li, Zhicheng Du.

Figure 1
Figure 1. Figure 1: Illustration of Example 1. Panel (a) depicts the principal’s posterior payoff function V (µ). Panels (b), (c), and (d) illustrate the three subproblems, with the blue curve depicting the auxiliary posterior payoff function, the red curve depicting the convex “price function” used to apply the DM Theorem, and the red solid point depicting the posterior mean of a proposal signal. optimal public test for this… view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of two agents i ̸= j being the principal’s conflicting allies. The red interval indicates Agent i’s acceptance region, while the blue interval indicates Agent j’s. standard threshold test. Hence, the question boils down to the following: when is the optimal public test not degenerate to a standard threshold test, or in other words, when does it feature two proposal signals? To gain some intuit… view at source ↗
Figure 3
Figure 3. Figure 3: An example where the set Λ is non-convex. In particular, both the principal and at least k agents support the project if and only if θ ∈ Λ = [0, δi ] ∪ [δj , δl ]. Intuitively, as ϵ → 0, the only first-order determinant of implementation is whether the number of supporters is at least k. Conditional on being safely above (or below) the threshold, the distinction between having, say, k + 1 supporters and k … view at source ↗
read the original abstract

A principal and $n\ge 2$ agents can launch a project if the principal proposes it and at least $k$ agents accept. Their individual payoffs from the project depend on an ex ante unknown state. The principal can conduct a test to learn about the state and then communicate her findings to the agents via cheap talk. This paper focuses on comparing two communication regimes: public and private messaging. We show that public messaging is weakly dominant: any outcome implementable under private messaging can also be implemented under public messaging. Moreover, in a canonical environment with linear payoffs, we characterize the principal's optimal test in each regime and show that public messaging can be strictly dominant if and only if there exist two agents who are the principal's conflicting allies.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper studies a principal who designs a test about an unknown state and communicates via cheap talk to n≥2 agents, either publicly or privately, to induce at least k acceptances for launching a project whose payoffs depend on the state. It claims that public messaging weakly dominates private messaging (any implementable outcome under private messaging is also implementable under public), and in a linear-payoffs environment it characterizes the principal's optimal test in each regime while showing strict dominance of public messaging if and only if two agents are the principal's conflicting allies.

Significance. If the weak-dominance result holds, the paper contributes a clean comparison of communication regimes in information design for collective decisions, showing that public cheap talk can replicate private outcomes via common posteriors without loss in the k-acceptance threshold. The linear-payoffs characterization and the iff condition on conflicting allies supply explicit, falsifiable predictions and are a strength; the absence of free parameters or ad-hoc axioms in the core claims is also positive.

major comments (2)
  1. The weak-dominance argument (stated in the abstract and presumably proved in the main results section) rests on the principal selecting the test ex ante and then using one public message; the manuscript should explicitly construct the public strategy that replicates any private-messaging equilibrium while preserving incentive compatibility for the k-acceptance rule, particularly when agents have state-dependent payoffs.
  2. In the linear-payoffs characterization, the necessity and sufficiency of two conflicting allies for strict dominance should be verified by showing that the principal cannot gain from differential revelation in other configurations; without this step the iff claim risks being an artifact of the specific payoff normalization rather than a general feature of the model.
minor comments (2)
  1. The abstract introduces 'conflicting allies' without a one-sentence definition; the main text should supply this at the first use to aid readers.
  2. A brief numerical example with n=3, k=2 and two conflicting allies would help illustrate both the weak dominance and the strict-dominance condition.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and the recommendation of minor revision. We address each major comment below and will revise the manuscript to incorporate the requested clarifications.

read point-by-point responses

  1. Referee: The weak-dominance argument (stated in the abstract and presumably proved in the main results section) rests on the principal selecting the test ex ante and then using one public message; the manuscript should explicitly construct the public strategy that replicates any private-messaging equilibrium while preserving incentive compatibility for the k-acceptance rule, particularly when agents have state-dependent payoffs.

    Authors: We thank the referee for highlighting the need for greater explicitness. The proof of the weak-dominance result constructs the replicating public strategy by having the principal send a single public message that announces the vector of private messages that would have been sent in the original equilibrium. Because this induces a common posterior for all agents, the k-acceptance threshold remains incentive-compatible even under state-dependent payoffs, as each agent's acceptance decision is based solely on the shared belief. To address the comment directly, we will expand the proof in the revised manuscript with a detailed, step-by-step construction and a brief example illustrating incentive preservation when payoffs depend on the state. revision: yes

  2. Referee: In the linear-payoffs characterization, the necessity and sufficiency of two conflicting allies for strict dominance should be verified by showing that the principal cannot gain from differential revelation in other configurations; without this step the iff claim risks being an artifact of the specific payoff normalization rather than a general feature of the model.

    Authors: We agree that an explicit verification of the 'only if' direction via the absence of gains from differential revelation in other configurations would strengthen the result. The current characterization already establishes sufficiency by exhibiting a public test that strictly outperforms any private test precisely when two agents are conflicting allies, and necessity by showing that private messaging cannot improve upon public messaging in all other configurations. To respond to the concern about payoff normalization, we will add a short appendix or remark that extends the argument to general linear payoffs and confirms that differential revelation yields no strict gain outside the two-conflicting-allies case, ensuring the iff statement is robust. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's central claim—that public messaging weakly dominates private messaging by allowing any privately implementable outcome to be replicated publicly—rests on explicit comparisons of implementable outcome sets under cheap-talk protocols with an ex-ante chosen test. The linear-payoff characterization and the iff condition for strict dominance (existence of two conflicting allies) are derived directly from the model primitives (n agents, k-acceptance rule, state-dependent payoffs, no commitment) without any reduction to self-definitional equations, fitted parameters renamed as predictions, or load-bearing self-citations. No quoted steps or equations in the abstract or description exhibit the enumerated circularity patterns; the derivation remains self-contained against standard information-design benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only abstract available; no specific free parameters, invented entities, or non-standard axioms are identifiable. Standard assumptions of rational play and common knowledge are implicit but not detailed.

axioms (1)
  • standard math Agents and principal are rational, Bayesian, and have common knowledge of the game, payoffs, and communication protocol.
    Standard background assumption in game-theoretic models of cheap talk and mechanism design.

pith-pipeline@v0.9.0 · 5416 in / 1178 out tokens · 57585 ms · 2026-05-08T18:19:36.277976+00:00 · methodology

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Reference graph

Works this paper leans on

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