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Persuasion Gains and Losses from Peer Communication

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Pith's one-line read In critical-mass Bayesian persuasion on networks, adding communication links among receivers can strictly increase a sender's payoff, and in several natural network families it reaches the maximum value achievable with private signaling.

desk verdict Novel and mostly convincing non-monotonicity results, but Proposition 4 (clusters) is false as stated and needs a real repair before the paper is publishable. read the letter →

arxiv 2509.09099 v1 pith:2AHUCP2Y submitted 2025-09-11 cs.GT econ.TH

Toygar T. Kerman , Anastas P. Tenev , Konstantin Zabarnyi This is my paper · ORCID
classification cs.GTecon.TH MSC 91A2891B1291D30
keywords Bayesianpersuasioncommunicationnetworkscriticalmasspeerinformationspilloversdominationnon-monotonicvaluevoting
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper studies a strategic sender—a campaign, firm, or platform—who wants to push a critical mass of receivers to take one action, and each receiver sees his own private message plus those of his immediate neighbors. The common-sense view is that more communication among receivers should make them harder to manipulate. The authors show this can fail: for hierarchical stellar networks, multi-center constellations, disconnected galaxies, and clustered cliques, there are link additions that strictly raise the sender's expected payoff, often to V_n^k, the maximum value the sender could get in an empty network. Thus the sender's value is not monotone in network density, and who observes whom matters more than how many links exist. The paper also exhibits networks in which no extension helps and notes that these sender-beneficial additions worsen receivers' ability to learn the true state.

What carries the argument

The central tool is the notion of information domination: receiver i information-dominates j if j's neighborhood is a subset of i's. The paper relies on Lemma 3, a cited sufficient condition, which says that if a network has no information-dominating pairs, the sender can achieve the empty-network upper bound V_n^k. The constructive half of the paper builds link additions that break every information-dominating pair, then invokes Lemma 3 to conclude the upper bound is reached.

What would settle it

For a small instance of Theorem 1 (e.g., n=8, k=4, lambda0(X)=0.3, with a stellar component of six nodes of depth 2 and two external nodes), explicitly build the extension described in the proof and numerically optimize the sender's experiment over finite message sets; if the optimum is strictly below V_8^4 = 0.9, the central claim fails. More directly, any network with no information-dominating pairs whose optimal value is below V_n^k would refute the imported Lemma 3 and with it the paper's upper-bound constructions.

Watch

Extended reading notes

Core claim

The paper's central claim is that in a Bayesian persuasion problem where a sender needs a critical mass of receivers to choose a desired action, and where each receiver observes the messages sent to himself and to his direct neighbors, extending the communication network can strictly increase the sender's expected utility. For several natural families—stellar networks with a hierarchical center, constellations with multiple centers, galaxies built from disconnected star components, and cluster networks of equal-sized cliques—the paper constructs an explicit extension on which the sender achieves the upper bound V_n^k, the payoff of optimal private signaling on an empty network. The mechanism

Load-bearing premise

The upper-bound results depend on Lemma 3, a theorem imported from a cited paper: if a network has no information-dominating pairs, the sender can achieve the private-signaling value V_n^k; if that theorem is false or carries unstated conditions, the main constructions in Theorem 1, Theorem 2, Proposition 3, and Proposition 4 collapse.

Editorial extensions

If this is right

  • The sender's value is not monotone in network density: adding links can strictly increase the probability of reaching critical mass, even when starting from a network where the sender is constrained.
  • In stellar, constellation, galaxy, and cluster networks satisfying the stated conditions, an optimal experiment on the extension reaches V_n^k, the same value as in the empty network—so the sender loses nothing from communication if links are chosen well.
  • Such beneficial extensions come at the receivers' expense: the probability that the collective outcome matches the true state decreases.
  • Platform designers and policymakers should not equate more communication with greater consumer or voter protection; link recommendations can actually increase manipulability.
  • For marketing and voting, the results imply semi-connected sets of consumers or voters are not necessarily harder to persuade; the structure of the added links determines whether persuasion power rises or falls.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The information-domination condition suggests a general design principle: any network extension that makes all neighborhoods incomparable should restore private-signaling power; this may apply to random graph models or community detection beyond the specific families studied.
  • A testable behavioral prediction: in a lab experiment with a threshold voting task, adding a small number of cross-hierarchy links (e.g., connecting a peripheral member of one clique to an outsider) should increase the sender's success rate relative to the base network, while adding all links should lower it back to public-signaling levels.
  • For social media policy, this implies that recommender systems that create 'boundary spanner' connections—links between users of different hierarchical depths—may inadvertently amplify the platform's or advertisers' persuasive power; density alone will not reveal the risk.
  • The paper's non-monotonicity could also inform design of deliberation procedures: if an institution controls the communication graph (e.g., committee meetings, town halls), choosing which participants can talk to whom is itself a design instrument that can be used for manipulation.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 3 minor

Summary. The paper studies a multi-receiver Bayesian persuasion problem with network spillovers: each receiver observes the sender's private message to himself and to his neighbors, and the sender wants a critical mass k of receivers to choose the sender-favorable action. The main claim is that, contrary to the intuition that more communication helps receivers, extending the network can strictly increase the sender's value, and in several families (stellar, halo, constellation, galaxy, cluster) the sender can reach the empty-network upper bound V_n^k. The analysis uses a symmetry lemma, a circle construction, and a sufficient condition for attaining V_n^k based on the absence of information-dominating pairs. Section 4 also gives examples where no beneficial extension exists.

Significance. If correct, the paper would make a valuable and counterintuitive contribution: it would show that the sender's persuasion value is non-monotone in network density, with concrete structural families where denser communication helps the sender and hurts receivers. The constructive experiments, especially the two-message circle construction, are a useful strength, and the transparent reliance on the information-domination lemma makes the proof strategy easy to follow. However, the cluster-family result (Proposition 4) is false as stated, which materially weakens the paper's claim to cover 'general families' of networks. The stellar and galaxy results may still be salvageable, but the current manuscript overstates the scope of its conclusions.

major comments (3)
  1. [Appendix B, Proof of Proposition 4; Proposition 4] Proposition 4 is false as stated. The proof derives p|n and p|n-k, hence p|k, and then asserts that n/2<k<n forces gcd(n,k)=1. This is wrong: n=6, k=4, p=2 satisfies the hypotheses and gcd(6,4)=2. In that case, the network is three disjoint 2-cliques, and the sender can already achieve V_6^4. Send x to all receivers in state X; in state Y, with probability r = 6λ0/(4(1-λ0)), choose two of the three clusters uniformly and send x to those four receivers and y to the third cluster, and with probability 1-r send y to all. Each receiver in a targeted cluster has posterior 1/2, exactly four receivers choose x, and the value is (6/4+1)λ0 = V_6^4. Since V_n^k is the upper bound, no extension can strictly benefit. The proposition needs a divisibility condition such as p∤k, and the divisible case must be handled separately.
  2. [Lemma 3 and its uses in Theorem 1, Theorem 2, Proposition 3, Proposition 4] The paper's central positive results all conclude by invoking Lemma 3, imported from Babichenko et al. (2021), which asserts that a network with no information-dominating pairs attains V_n^k. Lemma 3 is therefore load-bearing. The manuscript should either prove it or provide a precise reference with all hypotheses verified. The Proposition 4 counterexample shows the importance of checking the lemma's precondition: if the original network already attains V_n^k, the lemma cannot be used to establish strict improvement. The current proofs do not independently verify this precondition in a way that rules out the counterexample.
  3. [Corollary 2 (Halo)] Corollary 2 is stated without proof. It is not an immediate corollary of the displayed results, and it is used to extend the paper's nonmonotonicity claim to halo networks. The authors should provide a proof or a precise reduction to Theorem 1; otherwise the claim should be labeled as a conjecture or removed.
minor comments (3)
  1. [Lemma 2 proof] The set T_i is defined as {i, i+1, ..., i+n-1-k} (mod n), which has n-k elements, not k. To obtain the claimed experiment, T_i should have exactly k elements, e.g., {i, ..., i+k-1}. As written, the construction does not reach the critical mass in state Y.
  2. [Proposition 4 proof, line 'p|pq=n'] The notation 'p|pq=n' is awkward; since n=pq, the authors mean p divides n. More importantly, the subsequent claim about relative primality is false, as noted above.
  3. [Example 2] The example sets λ0(X)=1/3, which equals k/(n+k) rather than satisfying the strict inequality assumed at the end of Section 2. The text acknowledges this, but it would be cleaner to choose a generic prior and adjust the probabilities.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's results are supported by independent constructions and externally cited lemmas, not by self-referential definitions or fitted predictions.

full rationale

The derivation chain is not circular. The upper bound V_n^k = (n/k+1)λ0(X) is cited as the known empty-network value from Kerman et al. (2024) / Arieli and Babichenko (2019), and the paper proves via a replication argument (Proposition 1 proof) that every network value lies between V_p and V_n^k. That bound is an independent mathematical fact, not an input that already contains the paper's main conclusions. The load-bearing no-information-domination sufficiency condition (Lemma 3) is imported from Babichenko et al. (2021) as a black-box theorem; it is parameter-free, its assumptions do not include any of the paper's target statements, and the paper supplies explicit link-addition constructions (circle experiment, stellar/halo/constellation/galaxy/cluster extensions) to satisfy it. Even though some citations overlap with the present authors (Zabarnyi in Babichenko et al. 2021; Kerman in Kerman et al. 2024), the cited results have independent proofs and are not derived from the current paper's claims. No parameter is fitted to data, and no predictive quantity is defined in terms of the quantity it is supposed to predict. The skeptic's concern about Proposition 4—that the gcd argument 'since n/2<k<n, we must have that n,k are relatively prime' is invalid (e.g., n=6,k=4,p=2) and that the cluster network may already attain V_n^k—is a mathematical-correctness issue, not a circularity: if correct, it would falsify a theorem, but it would not make the derivation equivalent to its inputs. Therefore the circularity score is 0.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The paper introduces no fitted parameters and no new physical or economic entities. It relies on cited theorems for the empty-network value and the no-information-domination condition, plus standard Bayesian updating and the stated prior/quota restrictions.

assumptions (4)
  • domain assumption V_n^k = ((n+k)/k) * lambda_0(X) is the value of the empty network (Kerman et al., 2024).
    Used to define the upper bound and in Lemma 4. The result is imported from prior work by the authors and not proved here.
  • domain assumption Babichenko et al. (2021) Theorem 3.5: a network with no information-dominating pairs admits an experiment achieving the private signaling upper bound.
    Formulated as Lemma 3 and used to show extensions reach V_n^k. This is an external theorem with overlapping authorship that the present paper does not prove.
  • standard math Receivers use Bayes updates and choose the action with posterior at least 1/2, with ties broken in the sender's favor.
    Standard Bayesian persuasion assumptions (Kamenica-Gentzkow).
  • domain assumption Prior lambda_0(X) < k/(n+k) and k >= floor((n+1)/2).
    Modeling restrictions in Section 2 that rule out trivial persuasion. The paper's proofs rely on these inequalities.

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Cite this review

Pith. "Pith review of Persuasion Gains and Losses from Peer Communication." pith.science (2026). https://pith.science/paper/2AHUCP2Y

@misc{pith2026250909099,
  author       = {Pith},
  title        = {Pith review of: Persuasion Gains and Losses from Peer Communication},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2AHUCP2Y}},
  note         = {Machine review of arXiv:2509.09099}
}
read the original abstract

We study a Bayesian persuasion setting in which a sender wants to persuade a critical mass of receivers by revealing partial information about the state to them. The homogeneous binary-action receivers are located on a communication network, and each observes the private messages sent to them and their immediate neighbors. We examine how the sender's expected utility varies with increased communication among receivers. We show that for general families of networks, extending the network can strictly benefit the sender. Thus, the sender's gain from persuasion is not monotonic in network density. Moreover, many network extensions can achieve the upper bound on the sender's expected utility among all networks, which corresponds to the payoff in an empty network. This is the case in networks reflecting a clear informational hierarchy (e.g., in global corporations), as well as in decentralized networks in which information originates from multiple sources (e.g., influencers in social media). Finally, we show that a slight modification to the structure of some of these networks precludes the possibility of such beneficial extensions. Overall, our results caution against presuming that more communication necessarily leads to better collective outcomes.

Figures

Figures reproduced from arXiv: 2509.09099 by the authors.

Figure 1
Figure 1. The optimal experiment for fully private signaling (left); a possible network [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. A stellar network and the induced graph of the information-domination re [PITH_FULL_IMAGE:figures/full_fig_p019_2.png] view at source ↗
Figure 3
Figure 3. The intuition behind the second step of the proof of Theorem [PITH_FULL_IMAGE:figures/full_fig_p021_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Non-monotonicity of the network value in Example [PITH_FULL_IMAGE:figures/full_fig_p023_4.png]
Figure 5
Figure 5. Figure 5: A halo network (left) with n = 5; a constellation network (right) with two centers (the black nodes), three nodes with depth 1 (white), and two nodes with depth 2 (gray). In Example 2, receiver 5 forming a link with receiver 6 allows the sender to employ a rougher part…
Figure 6
Figure 6. Figure 6: The construction in the proof of Proposition [PITH_FULL_IMAGE:figures/full_fig_p027_6.png]
Figure 7
Figure 7. Figure 7: An example of a constellation described in Example [PITH_FULL_IMAGE:figures/full_fig_p029_7.png]
Figure 8
Figure 8. Figure 8: The extension of g with ℓ = 1 when |P|= |N \ C| (left) and |P|> |N \ C| (right). The nodes in P are in black, while the nodes in N \C are in gray; the original network is given by the solid lines, while its extension is given by the dashed lines. Assume now ℓ > 1. Let …
Figure 9
Figure 9. Figure 9: The extension of the network g with ℓ ≥ 2 when |N \ (C ∪ {v1, . . . , vℓ})|≥ 2 (left) and |N \ (C ∪ {v1, . . . , vℓ})|= 1 (right). The nodes of depth 1 in C are given in black, the nodes of depth 2 in C – in brown, the nodes in N \ (C ∪ {v1, . . . , vℓ}) – in gray; the…

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Works this paper leans on

66 extracted references · 1 linked inside Pith

  1. [1]

    Ali, S. N. and D. A. Miller (2016). Ostracism and forgiveness. American Economic Review\/ 106\/ (8), 2329--2348

    2016

  2. [2]

    Alonso, R. and O. C \^a mara (2016). Persuading voters. American Economic Review\/ 106\/ (11), 3590--3605

    2016

  3. [3]

    Anderson, L. R. and C. A. Holt (1997). Information cascades in the laboratory. The American economic review\/ , 847--862

    1997

  4. [4]

    Angeletos, G.-M. and A. Pavan (2004). Transparency of information and coordination in economies with investment complementarities. American Economic Review\/ 94\/ (2), 91--98

    2004

  5. [5]

    Anunrojwong, J. and N. Sothanaphan (2018). Naive Bayesian learning in social networks . In Proceedings of the 2018 ACM Conference on Economics and Computation , pp.\ 619--636

    2018

  6. [6]

    Arieli, I. and Y. Babichenko (2019). Private Bayesian persuasion . Journal of Economic Theory\/ 182 , 185--217

    2019

  7. [7]

    Athanassopoulos, A. D. (2000). Customer satisfaction cues to support market segmentation and explain switching behavior. Journal of business research\/ 47\/ (3), 191--207

    2000

  8. [8]

    Talgam-Cohen, H

    Babichenko, Y., I. Talgam-Cohen, H. Xu, and K. Zabarnyi (2021). Multi-Channel Bayesian Persuasion . arXiv preprint arXiv:2111.09789\/

    arXiv 2021

Show all 66 references
  1. [9]

    Backstrom, L. and J. Leskovec (2011). Supervised random walks: predicting and recommending links in social networks. In Proceedings of the fourth ACM international conference on Web search and data mining , pp.\ 635--644

    2011

  2. [10]

    Bala, V. and S. Goyal (2000). A noncooperative model of network formation. Econometrica\/ 68\/ (5), 1181--1229

    2000

  3. [11]

    Bardhi, A. and Y. Guo (2018). Modes of persuasion toward unanimous consent. Theoretical Economics\/ 13\/ (3), 1111--1149

    2018

  4. [12]

    Aloini, P

    Benevento, E., D. Aloini, P. Roma, and D. Bellino (2025). The impact of influencers on brand social network growth: Insights from new product launch events on Twitter . Journal of Business Research\/ 189 , 115123

    2025

  5. [13]

    Hirshleifer, and I

    Bikhchandani, S., D. Hirshleifer, and I. Welch (1992). A theory of fads, fashion, custom, and cultural change as informational cascades. Journal of political Economy\/ 100\/ (5), 992--1026

    1992

  6. [14]

    Birkinshaw, and R

    Bresman, H., J. Birkinshaw, and R. Nobel (1999). Knowledge transfer in international acquisitions. Journal of international business studies\/ 30\/ (3), 439--462

    1999

  7. [15]

    Broderick, A. J., G. E. Greenley, and R. D. Mueller (2007). The behavioural homogeneity evaluation framework: Multi-level evaluations of consumer involvement in international segmentation. Journal of International Business Studies\/ 38\/ (5), 746--763

    2007

  8. [16]

    Burt, R. S. (1992). Structural holes . Harvard University Press

    1992

  9. [17]

    Burt, R. S. (2004). Structural holes and good ideas. American Journal of Sociology\/ 110\/ (2), 349 – 399

    2004

  10. [18]

    Candogan, O. (2019). Persuasion in networks: Public signals and k-cores. New York, NY, USA. Association for Computing Machinery

    2019

  11. [19]

    Guo, and H

    Candogan, O., Y. Guo, and H. Xu (2020). On information design with spillovers. Available at SSRN 3537289\/

    2020

  12. [20]

    Gupta, F

    Chan, J., S. Gupta, F. Li, and Y. Wang (2019). Pivotal persuasion. Journal of Economic Theory\/ 180 , 178--202

    2019

  13. [21]

    Church, J. and N. Gandal (1992). Network effects, software provision, and standardization. The journal of industrial economics\/ , 85--103

    1992

  14. [22]

    Colla, P. and A. Mele (2010). Information linkages and correlated trading. The Review of Financial Studies\/ 23\/ (1), 203--246

    2010

  15. [23]

    Colman, H. L. and A. Rouzies (2019). Postacquisition boundary spanning: A relational perspective on integration. Journal of Management\/ 45\/ (5), 2225--2253

    2019

  16. [24]

    Cooperman, A. D. (2024). Bloc voting for electoral accountability. American Political Science Review\/ 118\/ (3), 1222--1239

    2024

  17. [25]

    Corten, R. and V. Buskens (2010). Co-evolution of conventions and networks: An experimental study . Social Networks\/ 32\/ (1), 4--15

    2010

  18. [26]

    Ursino, and A

    Currarini, S., G. Ursino, and A. Chand (2020). Strategic transmission of correlated information. The Economic Journal\/ 130\/ (631), 2175--2206

    2020

  19. [27]

    de Fine Licht, J. (2014). Transparency actually: how transparency affects public perceptions of political decision-making. European Political Science Review\/ 6\/ (2), 309--330

    2014

  20. [28]

    Dong, Y., J. Tang, N. V. Chawla, T. Lou, Y. Yang, and B. Wang (2015). Inferring social status and rich club effects in enterprise communication networks. PloS one\/ 10\/ (3), e0119446

    2015

  21. [29]

    Mengel, and C

    Drago, F., F. Mengel, and C. Traxler (2020). Compliance behavior in networks: Evidence from a field experiment. American Economic Journal: Applied Economics\/ 12\/ (2), 96–133

    2020

  22. [30]

    Egorov, G. and K. Sonin (2020). Persuasion on networks. Technical report, National Bureau of Economic Research

    2020

  23. [31]

    Eguia, J. X. (2011). Voting blocs, party discipline and party formation. Games and economic behavior\/ 73\/ (1), 111--135

    2011

  24. [32]

    Galeotti, A. and S. Goyal (2010). The law of the few. American Economic Review\/ 100\/ (4), 1468--92

    2010

  25. [33]

    Galperti, S. and J. Perego (2025). Games with information constraints: seeds and spillovers. Theoretical Economics\/ 20 , 667–711

    2025

  26. [34]

    Gatewood, J. B. (1984). Cooperation, competition, and synergy: information-sharing groups among Southeast Alaskan Salmon seiners . American Ethnologist\/ 11\/ (2), 350--370

    1984

  27. [35]

    Gavazza, A. and A. Lizzeri (2009). Transparency and economic policy. The Review of Economic Studies\/ 76\/ (3), 1023--1048

    2009

  28. [36]

    Goeree, J. K., A. Riedl, and A. Ule (2009). In search of stars: Network formation among heterogeneous agents. Games and Economic Behavior\/ 67\/ (2), 445--466

    2009

  29. [37]

    Gormley, I. C. and T. B. Murphy (2008). Exploring voting blocs within the irish electorate: A mixture modeling approach. Journal of the American Statistical Association\/ 103\/ (483), 1014--1027

    2008

  30. [38]

    Marble, and C

    Grimmer, J., W. Marble, and C. Tanigawa-Lau (2025). Measuring the contribution of voting blocs to election outcomes. The Journal of Politics\/ 87\/ (3), 905--921

    2025

  31. [39]

    Gupta, P., A. Goel, J. Lin, A. Sharma, D. Wang, and R. Zadeh (2013). Wtf: The who to follow service at twitter. In Proceedings of the 22nd international conference on World Wide Web , pp.\ 505--514

    2013

  32. [40]

    Hansen, M. T. (1999). The search-transfer problem: The role of weak ties in sharing knowledge across organization subunits. Administrative science quarterly\/ 44\/ (1), 82--111

    1999

  33. [41]

    Jackson, M. O. and B. W. Rogers (2007). Meeting strangers and friends of friends: How random are social networks? The American Economic Review\/ 97\/ (3), 890--915

    2007

  34. [42]

    Br \'o dka, and J

    Jankowski, J., P. Br \'o dka, and J. Hamari (2016). A picture is worth a thousand words: an empirical study on the influence of content visibility on diffusion processes within a virtual world. Behaviour & Information Technology\/ 35\/ (11), 926--945

    2016

  35. [43]

    Kamenica, E. and M. Gentzkow (2011). Bayesian persuasion. American Economic Review\/ 101\/ (6), 2590--2615

    2011

  36. [44]

    Stolarczyk, Z

    Karamched, B., S. Stolarczyk, Z. P. Kilpatrick, and K. Josic (2020). Bayesian evidence accumulation on social networks. SIAM journal on applied dynamical systems\/ 19\/ (3), 1884--1919

    2020

  37. [45]

    Katona, Z., P. P. Zubcsek, and M. Sarvary (2011). Network effects and personal influences: The diffusion of an online social network. Journal of marketing research\/ 48\/ (3), 425--443

    2011

  38. [46]

    Katz, M. L. and C. Shapiro (1994). Systems competition and network effects. Journal of economic perspectives\/ 8\/ (2), 93--115

    1994

  39. [47]

    Kerman, T. and A. P. Tenev (2021). Persuading communicating voters. Available at SSRN 3765527\/

    2021

  40. [48]

    Kerman, T. T., P. J.-J. Herings, and D. Karos (2024). Persuading sincere and strategic voters. Journal of Public Economic Theory\/ 26\/ (1), e12671

    2024

  41. [49]

    Kerman, T. T. and A. P. Tenev (2025). Information design for weighted voting. Economic Theory\/ 79 , 809--852

    2025

  42. [50]

    Kerman, T. T., A. P. Tenev, and Y. Tsodikovich (2025). Bayesian persuasion in networks: Divisibility and network irrelevance. Available at SSRN 5131130\/

    2025

  43. [51]

    Levy, G. (2007). Decision making in committees: Transparency, reputation, and voting rules. American economic review\/ 97\/ (1), 150--168

    2007

  44. [52]

    Liporace, M. (2021). Persuasion in networks. Working Paper\/

    2021

  45. [53]

    Marmaros, D. and B. Sacerdote (2006, 02). How Do Friendships Form? The Quarterly Journal of Economics\/ 121\/ (1), 79--119

    2006

  46. [54]

    Perego, and I

    Mathevet, L., J. Perego, and I. Taneva (2020). On information design in games. Journal of Political Economy\/ 128\/ (4), 1370--1404

    2020

  47. [55]

    Jamtveit, and K

    Mathiesen, J., B. Jamtveit, and K. Sneppen (2010). Organizational structure and communication networks in a university environment. Physical Review E—Statistical, Nonlinear, and Soft Matter Physics\/ 82\/ (1), 016104

    2010

  48. [56]

    Friedman, and J

    Mengel, F., D. Friedman, and J. Kov \'a r \' k (2024). Influence in social networks. Available at SSRN 5059047\/

    2024

  49. [57]

    Molavi, P. and A. Jadbabaie (2011). Aggregate observational distinguishability is necessary and sufficient for social learning. In 2011 50th IEEE Conference on Decision and Control and European Control Conference , pp.\ 2335--2340. IEEE

    2011

  50. [58]

    Noam, E. M. (2016). Who Owns the World's Media? Media Concentration and Ownership around the World . Oxford University Press

    2016

  51. [59]

    Noble, G. and R. Jones (2006). The role of boundary-spanning managers in the establishment of public-private partnerships. Public administration\/ 84\/ (4), 891--917

    2006

  52. [60]

    Nora, V. and E. Winter (2024). Exploiting social influence in networks. Theoretical Economics\/ 19\/ (1), 1--27

    2024

  53. [61]

    Sun, J., A. J. Schram, and R. Sloof (2023). Public persuasion in elections: Single-crossing property and the optimality of censorship. Available at SSRN 4028840\/

    2023

  54. [62]

    Taneva, I. (2019). Information design. American Economic Journal: Microeconomics\/ 11\/ (4), 151--85

    2019

  55. [63]

    Titova, M. (2022). Persuasion with verifiable information. Technical report, Working Paper

    2022

  56. [64]

    Vizcarrondo, T. (2013). Measuring concentration of media ownership: 1976--2009. International Journal on Media Management\/ 15\/ (3), 177--195

    2013

  57. [65]

    Wang, Y. (2013). Bayesian persuasion with multiple receivers. Available at SSRN: https://ssrn.com/abstract=2625399\/

    2013

  58. [66]

    Williams, P. (2012). We are all boundary spanners now? In Collaboration in Public Policy and Practice , pp.\ 95--118. Policy Press

    2012

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