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

Going Public: Communication in Collective Decisions

Zhicheng Du , Yingkai Li , Boli Xu This is my paper

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

82 extracted references · 82 canonical work pages

  1. [1]

    arXiv preprint arXiv:2405.18521 , year=

    Learning and Communication Towards Unanimous Consent , author=. arXiv preprint arXiv:2405.18521 , year=

    work page arXiv

  2. [2]

    Available at SSRN 3471491 , year=

    Global manipulation by local obfuscation , author=. Available at SSRN 3471491 , year=

    work page

  3. [3]

    Games and Economic Behavior , volume=

    How to talk to multiple audiences , author=. Games and Economic Behavior , volume=. 2011 , publisher=

    work page 2011

  4. [4]

    Theoretical Economics , volume=

    Optimal persuasion via bi-pooling , author=. Theoretical Economics , volume=. 2023 , publisher=

    work page 2023

  5. [5]

    American Political science review , volume=

    Convicting the innocent: The inferiority of unanimous jury verdicts under strategic voting , author=. American Political science review , volume=. 1998 , publisher=

    work page 1998

  6. [6]

    arXiv preprint arXiv:2511.18662 , year=

    Bayesian Persuasion without Commitment , author=. arXiv preprint arXiv:2511.18662 , year=

    work page arXiv

  7. [7]

    American Economic Review , volume=

    Information design, Bayesian persuasion, and Bayes correlated equilibrium , author=. American Economic Review , volume=. 2016 , publisher=

    work page 2016

  8. [8]

    The Review of Economic Studies , volume=

    Informative cheap talk in elections , author=. The Review of Economic Studies , volume=. 2019 , publisher=

    work page 2019

  9. [9]

    American Journal of Political Science , volume=

    Informational lobbying and legislative voting , author=. American Journal of Political Science , volume=. 2017 , publisher=

    work page 2017

  10. [10]

    The American Economic Review , volume=

    Cheap talk with two audiences , author=. The American Economic Review , volume=. 1989 , publisher=

    work page 1989

  11. [11]

    arXiv preprint arXiv:1903.00129 , year=

    Persuading part of an audience , author=. arXiv preprint arXiv:1903.00129 , year=

    work page arXiv 1903

  12. [12]

    Audience Design , author=

    work page

  13. [13]

    Journal of Economic Theory , volume=

    Expert advice to a voting body , author=. Journal of Economic Theory , volume=. 2015 , publisher=

    work page 2015

  14. [14]

    Available at SSRN 4298890 , year=

    Sender-optimal learning and credible communication , author=. Available at SSRN 4298890 , year=

    work page

  15. [15]

    American Economic Review , volume=

    The limits of price discrimination , author=. American Economic Review , volume=. 2015 , publisher=

    work page 2015

  16. [16]

    Proceedings of the 25th ACM Conference on Economics and Computation , pages=

    Algorithmic Information Disclosure in Optimal Auctions , author=. Proceedings of the 25th ACM Conference on Economics and Computation , pages=

    work page

  17. [17]

    Econometrica , volume=

    Extreme points and majorization: Economic applications , author=. Econometrica , volume=. 2021 , publisher=

    work page 2021

  18. [18]

    Econometrica , volume=

    The interval structure of optimal disclosure , author=. Econometrica , volume=. 2019 , publisher=

    work page 2019

  19. [19]

    Econometrica , pages=

    Strategic information transmission , author=. Econometrica , pages=. 1982 , publisher=

    work page 1982

  20. [20]

    Theoretical Economics , volume=

    Modes of persuasion toward unanimous consent , author=. Theoretical Economics , volume=. 2018 , publisher=

    work page 2018

  21. [21]

    Evidence Acquisition and Voluntary Disclosure , author=

    work page

  22. [22]

    American Economic Review , volume=

    Test design and minimum standards , author=. American Economic Review , volume=

    work page

  23. [23]

    2010 , publisher=

    The theory of corporate finance , author=. 2010 , publisher=

    work page 2010

  24. [24]

    Journal of economic perspectives , volume=

    The venture capital revolution , author=. Journal of economic perspectives , volume=. 2001 , publisher=

    work page 2001

  25. [25]

    Journal of Economic Theory , volume=

    Bayesian persuasion with costly messages , author=. Journal of Economic Theory , volume=. 2021 , publisher=

    work page 2021

  26. [26]

    Journal of Political Economy , volume=

    Persuasion via weak institutions , author=. Journal of Political Economy , volume=. 2022 , publisher=

    work page 2022

  27. [27]

    American Economic Review , volume=

    Delegated expertise, authority, and communication , author=. American Economic Review , volume=. 2019 , publisher=

    work page 2019

  28. [28]

    Theoretical Economics , year=

    Adversarial coordination and public information design , author=. Theoretical Economics , year=

    work page

  29. [29]

    Journal of Political Economy , volume=

    The simple economics of optimal persuasion , author=. Journal of Political Economy , volume=. 2019 , publisher=

    work page 2019

  30. [30]

    Econometrica , volume=

    The Political Economy of Zero-Sum Thinking , author=. Econometrica , volume=. 2025 , publisher=

    work page 2025

  31. [31]

    Journal of Economic Theory , pages=

    Persuasion without ex-post commitment , author=. Journal of Economic Theory , pages=. doi:https://doi.org/10.1016/j.jet.2025.106058 , year=

    work page doi:10.1016/j.jet.2025.106058 2025

  32. [32]

    Journal of Economic Literature , volume=

    Information design: A unified perspective , author=. Journal of Economic Literature , volume=. 2019 , publisher=

    work page 2019

  33. [33]

    American Economic Review , volume=

    Persuading voters , author=. American Economic Review , volume=. 2016 , publisher=

    work page 2016

  34. [34]

    Journal of Economic theory , volume=

    Pivotal persuasion , author=. Journal of Economic theory , volume=. 2019 , publisher=

    work page 2019

  35. [35]

    2023 , journal=

    Endogenous information acquisition in cheap-talk games , author=. 2023 , journal=

    work page 2023

  36. [36]

    2024 , journal=

    Mechanism Design with Endogenous Principal Learning , author=. 2024 , journal=

    work page 2024

  37. [37]

    American Economic Journal: Microeconomics , year=

    (Reverse) Price Discrimination with Information Design , author=. American Economic Journal: Microeconomics , year=

    work page

  38. [38]

    Econometrica , volume=

    Test design under falsification , author=. Econometrica , volume=. 2022 , publisher=

    work page 2022

  39. [39]

    American Economic Review , volume=

    Bayesian persuasion , author=. American Economic Review , volume=. 2011 , publisher=

    work page 2011

  40. [40]

    arXiv preprint arXiv:2410.17503 , year=

    Commitment and Randomization in Communication , author=. arXiv preprint arXiv:2410.17503 , year=

    work page arXiv

  41. [41]

    Econometrica , volume=

    Envelope theorems for arbitrary choice sets , author=. Econometrica , volume=. 2002 , publisher=

    work page 2002

  42. [42]

    Proceedings of the 23rd ACM Conference on Economics and Computation , pages=

    Constrained majorization: Applications in mechanism design , author=. Proceedings of the 23rd ACM Conference on Economics and Computation , pages=

    work page

  43. [43]

    Journal of Political Economy , volume=

    Credible persuasion , author=. Journal of Political Economy , volume=. 2024 , publisher=

    work page 2024

  44. [44]

    arXiv preprint arXiv:2207.04929 , year=

    Information design in cheap talk , author=. arXiv preprint arXiv:2207.04929 , year=

    work page arXiv

  45. [45]

    Academy of Management Journal , volume=

    Predictors and consequences of delegation , author=. Academy of Management Journal , volume=. 1986 , publisher=

    work page 1986

  46. [46]

    IEEE transactions on Engineering Management , number=

    The design structure system: A method for managing the design of complex systems , author=. IEEE transactions on Engineering Management , number=. 1981 , publisher=

    work page 1981

  47. [47]

    Academy of management review , volume=

    An integrative model of organizational trust , author=. Academy of management review , volume=. 1995 , publisher=

    work page 1995

  48. [48]

    Available at SSRN 4298890 , year=

    Sender-Optimal learning and credible communication , author=. Available at SSRN 4298890 , year=

    work page

  49. [49]

    Journal of Economic Theory , volume=

    Informational control and organizational design , author=. Journal of Economic Theory , volume=. 2010 , publisher=

    work page 2010

  50. [50]

    Journal of Political Economy , volume=

    Informed information design , author=. Journal of Political Economy , volume=. 2023 , publisher=

    work page 2023

  51. [51]

    2023 , journal=

    Sequential mechanisms for evidence acquisition , author=. 2023 , journal=

    work page 2023

  52. [52]

    arXiv preprint arXiv:2403.08031 , year=

    Score-based mechanisms , author=. arXiv preprint arXiv:2403.08031 , year=

    work page arXiv

  53. [53]

    Available at SSRN 4003491 , year=

    Optimal Disclosure in Two-Sided Matching , author=. Available at SSRN 4003491 , year=

    work page

  54. [54]

    Working paper , year=

    Mechanism Design under Costly Signaling: the Value of Non-Coordination , author=. Working paper , year=

    work page

  55. [55]

    2025 , publisher=

    Fraud-proof non-market allocation mechanisms , author=. 2025 , publisher=

    work page 2025

  56. [56]

    Journal of Political Economy , volume=

    Muddled information , author=. Journal of Political Economy , volume=. 2019 , publisher=

    work page 2019

  57. [57]

    American Economic Journal: Microeconomics , volume=

    Scoring strategic agents , author=. American Economic Journal: Microeconomics , volume=. 2025 , publisher=

    work page 2025

  58. [58]

    Journal of Accounting Research , volume=

    Imperfect information and credible communication , author=. Journal of Accounting Research , volume=. 2001 , publisher=

    work page 2001

  59. [59]

    Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science , pages=

    Strategic classification , author=. Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science , pages=

    work page 2016

  60. [60]

    Econometrica , pages=

    Mechanism design by an informed principal , author=. Econometrica , pages=. 1983 , publisher=

    work page 1983

  61. [61]

    The Review of Economic Studies , volume=

    Mechanism design by an informed principal: Private values with transferable utility , author=. The Review of Economic Studies , volume=. 2014 , publisher=

    work page 2014

  62. [62]

    Econometrica , volume=

    Persuasion of a privately informed receiver , author=. Econometrica , volume=. 2017 , publisher=

    work page 2017

  63. [63]

    Theoretical Economics , volume=

    Censorship as optimal persuasion , author=. Theoretical Economics , volume=. 2022 , publisher=

    work page 2022

  64. [64]

    Econometrica , volume=

    Mechanism design with limited commitment , author=. Econometrica , volume=. 2022 , publisher=

    work page 2022

  65. [65]

    Theoretical Economics , year=

    Optimal mechanism for the sale of a durable good , author=. Theoretical Economics , year=

    work page

  66. [66]

    arXiv preprint arXiv:2304.07551 , year=

    Test-Optional Admissions , author=. arXiv preprint arXiv:2304.07551 , year=

    work page arXiv

  67. [67]

    Theoretical Economics , volume=

    Costly miscalibration , author=. Theoretical Economics , volume=. 2021 , publisher=

    work page 2021

  68. [68]

    Econometrica , volume=

    Cheap talk with transparent motives , author=. Econometrica , volume=. 2020 , publisher=

    work page 2020

  69. [69]

    Mathematics of Operations Research , volume=

    Constrained information design , author=. Mathematics of Operations Research , volume=. 2024 , publisher=

    work page 2024

  70. [70]

    2024 , institution=

    Strategic Ignorance and Information Design , author=. 2024 , institution=

    work page 2024

  71. [71]

    American Economic Review , volume=

    Buyer-optimal learning and monopoly pricing , author=. American Economic Review , volume=. 2017 , publisher=

    work page 2017

  72. [72]

    Theoretical Economics , volume=

    Optimal disclosure of information to privately informed agents , author=. Theoretical Economics , volume=. 2023 , publisher=

    work page 2023

  73. [73]

    Public Administration Review , volume=

    Information use in public administration and policy decision-making: A research synthesis , author=. Public Administration Review , volume=. 2023 , publisher=

    work page 2023

  74. [74]

    Journal of Small Business Management (pre-1986) , volume=

    The feasibility study as a tool for venture analysis , author=. Journal of Small Business Management (pre-1986) , volume=. 1979 , publisher=

    work page 1986

  75. [75]

    International Journal of project management , volume=

    Trust in project relationships—inside the black box , author=. International Journal of project management , volume=. 2004 , publisher=

    work page 2004

  76. [76]

    Construction economics and building , volume=

    The influence of trust on project management practice within the construction industry , author=. Construction economics and building , volume=

    work page

  77. [77]

    2024 , journal=

    The Optimal Menu of Tests , author=. 2024 , journal=

    work page 2024

  78. [78]

    Mathematics of Operations Research , volume=

    Extreme points of moment sets , author=. Mathematics of Operations Research , volume=. 1988 , publisher=

    work page 1988

  79. [79]

    Journal of economic literature , volume=

    Information avoidance , author=. Journal of economic literature , volume=. 2017 , publisher=

    work page 2017

  80. [80]

    The Review of Economic Studies , volume=

    Strategic ignorance as a self-disciplining device , author=. The Review of Economic Studies , volume=. 2000 , publisher=

    work page 2000

Showing first 80 references.