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Similarity of Information and Collective Action

T0 review · 0 major / 3 minor · reviewed 2026-05-23 · grok-4.3

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Pith's one-line read More similar information helps groups achieve challenging collective goals but hinders them when goals are easy.

desk verdict The paper cleanly derives a threshold reversal on signal correlation in a standard collective action game and sketches two applications, but the core result follows directly from the usual setup. read the letter →

arxiv 2407.14773 v2 submitted 2024-07-20 econ.GN q-fin.EC

Deepal Basak , Joyee Deb , Aditya Kuvalekar This is my paper
classification econ.GNq-fin.EC
keywords collectiveactioninformationsimilaritycoordinationfree-ridingglobalgamesprotestscommitteesincomplete
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 examines a collective action game where individuals must decide whether to participate or free-ride based on private signals about a shared fundamental. It establishes that raising the similarity of those signals raises the chance of successful coordination only when the required participation level is high. A sympathetic reader would care because the result resolves the tension between the coordination benefit and the free-riding cost of shared information and supplies concrete explanations for observed patterns in protests and committee voting.

What carries the argument

The threshold effect of signal correlation on coordination success when payoffs contain both coordination value and free-riding temptation.

What would settle it

A laboratory experiment in which subjects play the game under high versus low signal correlation crossed with high versus low participation thresholds and success rates are compared to the predicted switch.

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Extended reading notes

Core claim

In a canonical collective action game with incomplete information, where individuals decide whether to participate while receiving correlated signals about a common fundamental, more similar information facilitates achieving a common goal when achieving the goal is sufficiently challenging and impedes it when the goal is easy.

Load-bearing premise

The payoff structure creates both coordination value and free-riding temptation in a simultaneous-move game with signals about a common value.

Editorial extensions

If this is right

  • Insufficiently powerful authoritarian governments may face larger protests when restricting press freedom.
  • Informational diversity in committees is beneficial when each vote carries more weight.
  • The effect of information similarity on success reverses exactly at a critical difficulty threshold of the collective goal.

Reading between the lines

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

  • Algorithms that increase information similarity on platforms could raise mobilization on difficult issues while lowering it on easy ones.
  • Efforts to diversify news sources may be more useful for low-stakes than high-stakes collective actions.
  • The same threshold logic could be tested in field settings such as online petitions with varying signature requirements.
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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

0 major / 3 minor

Summary. The manuscript studies a canonical collective action game with incomplete information. Agents simultaneously choose whether to participate in a shared goal while receiving private signals about a common fundamental; the correlation of these signals parameterizes information similarity. The central result is a threshold characterization: higher signal correlation facilitates (impedes) equilibrium participation when the participation threshold implied by payoffs is sufficiently high (low). The paper applies the result to explain larger protests under weak authoritarian press restrictions and the value of informational diversity in high-stakes committee voting.

Significance. If the threshold result holds, the paper supplies a clean comparative-static explanation for the dual effects of information similarity in settings with both strategic complementarity and free-riding. The applications are policy-relevant and grounded in the model. Credit is due for deriving the reversal directly from the standard global-game payoff structure and indifference condition without auxiliary restrictions.

minor comments (3)
  1. Abstract: the phrase 'consuming more similar information' is nonstandard; 'observing more correlated signals' would align better with the model primitives used later.
  2. Introduction, paragraph 2: the literature discussion omits recent contributions on information design in global games (e.g., papers on signal correlation and coordination); adding two or three targeted citations would strengthen positioning.
  3. Section 4 (applications): the mapping from the model's correlation parameter to 'press freedom restriction' is stated qualitatively; an explicit comparative-static exercise linking the parameter shift to the threshold would make the claim sharper.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and constructive report. The recommendation for minor revision is appreciated, and we note that no specific major comments were raised for response.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; derivation self-contained

full rationale

The paper's central result—that information similarity facilitates collective action when the goal is sufficiently challenging—emerges from solving the standard indifference condition in a canonical global-game collective-action model with binary actions, a common fundamental, and correlated signals. The threshold reversal follows directly from the tension between strategic complementarity and free-riding once payoffs and signal correlation are specified; no equation reduces to a fitted parameter renamed as prediction, no self-citation chain bears the load-bearing premise, and no ansatz or uniqueness claim is smuggled in via prior work by the same authors. The model is externally falsifiable against the usual coordination-game benchmarks and contains no self-definitional steps.

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

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the canonical game structure itself is treated as background.

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Cite this review

Pith. "Pith review of Similarity of Information and Collective Action." pith.science (2026). https://pith.science/paper/2407.14773

@misc{pith2026240714773,
  author       = {Pith},
  title        = {Pith review of: Similarity of Information and Collective Action},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2407.14773}},
  note         = {Machine review of arXiv:2407.14773}
}
read the original abstract

We study a canonical collective action game with incomplete information. Individuals attempt to coordinate to achieve a shared goal, while also facing a temptation to free-ride. Consuming more similar information about the fundamentals can help them coordinate, but it can also exacerbate free-riding. Our main result shows that more similar information facilitates (impedes) achieving a common goal when achieving the goal is sufficiently challenging (easy). We apply this insight to show why insufficiently powerful authoritarian governments may face larger protests when attempting to restrict press freedom, and why informational diversity in committees is beneficial when each vote carries more weight.

Figures

Figures reproduced from arXiv: 2407.14773 by the authors.

Figure 1
Figure 1. Increasing similarity when θ “ 1 How does this increased similarity in the realized private signals affect players’ incentives to work in equilibrium? The answer to this question depends on the value of q. A player works on a signal 1 if p1 ´ qq P1 1 pX´i “ 1q looooooomooooooon Ò with more similarity `q P1 1 pX´i “ 0q looooooomooooooon Ó with more similarity ě c. When q is high, with high likelihood one player’s eff… view at source ↗
Figure 2
Figure 2. Encouragement and discouragement environments. Here, ψpn, x ¯ q “ e´xx n¯ n¯! is the Poisson pmf at ¯n with mean x. The peak of these pmfs occurs at ¯n. In both the environments, N ă n¯ ă 2N. However, in encouragement environments, ¯n is much larger than N. Therefore, Λo “ ψpn, N ¯ q ă ψpn, ¯ 2Nq “ Λb in encouragement environments (left), while the reverse holds in discouragement environments (right). Our result sug… view at source ↗
Figure 3
Figure 3. Pivotal probabilities To see this, suppose that ψpn, βN ¯ q ą ψpn, ¯ 2βNq (as in [PITH_FULL_IMAGE:figures/full_fig_p026_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Information Similarity and Maximal Equilibrium [PITH_FULL_IMAGE:figures/full_fig_p056_4.png]

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Reference graph

Works this paper leans on

23 extracted references · 23 canonical work pages

  1. [1]

    P ˆ tθ “ 1u č tA´ g ě ¯nu ˇ ˇ ˇ ˇXg “ x ˙ ´ c´ P ˆ tθ “ 1u č tA´ g ě ¯n ` 1u ˇ ˇ ˇ ˇXg “ x ˙ “ Ppθ “ 1|Xg “ xq

    1, 5, 7, 18 C. R. Taylor and H. Yildirim. Public information and electoral bias. Games and Economic Behavior , 68(1):353–375, 2010. 7 M. Taylor and H. Ward. Chickens, whales, and lumpy goods: alternat ive models of public-goods provision. Political Studies, 30(3):350–370, 1982. 1 The Economist. Political protests have become more widespread and more frequ...

    work page 2010

  2. [2]

    σgpxq “ 1 ù ñ ∆gpx;σq ě 0

    work page

  3. [3]

    The expression in the proposition follows from noting that according to an agent in group g, Ng ´ 1 ` N´ g „ ηA 2 p¨q , Ng ´ 1 „ ηAp¨q , N´ g „ ηp¨q , and ¯n „ φp¨q

    σgpxq “ 0 ù ñ ∆gpx;σq ď 0. The expression in the proposition follows from noting that according to an agent in group g, Ng ´ 1 ` N´ g „ ηA 2 p¨q , Ng ´ 1 „ ηAp¨q , N´ g „ ηp¨q , and ¯n „ φp¨q . A.3. Proof of Theorem 1 Proof. We prove this result using two steps. In Step 1, we establish that th e max- imal equilibrium is symmetric. In step 2, we show that ...

    work page

  4. [4]

    P 1 xpP pσqq ě xP 1 xpP pσqq for all x PP pσq

    work page

  5. [5]

    elementary transformation along identical intervals

    P 1 xpP pσqq ď xP 1 xpP pσqq for all x PNP pσq. Consider ( IC:P), the incentive constraint for an agent who participates. The left hand side is a convex combination of Λ b and Λ o. In encouragement environments, a higher weight on Λ b increases the LHS of ( IC:P), making the constraint easier to satisfy. Therefore, P 1 xpP pσqqΛb ` p 1 ´ P 1 xpP pσqqqΛo ě...

    work page 1990

  6. [6]

    V ˚ pPq ě V ˚ p xPq if Λo ą Λb. And, 41

    work page

  7. [7]

    V ˚ pPq ď V ˚ p xPq if Λb ą Λo. Proof. Let σ ˚ be a maximal equilibrium under P with associated participation and nonparticipation sets P ˚ and NP ˚ respectively. Suppose that Λ o ą Λb. Then, for all x PP ˚ P ´ 1 x pP ˚ qΛb ` p 1 ´ P ´ 1 x pP ˚ qqΛo ď xP ´ 1 x pP ˚ qΛb ` p 1 ´ xP ´ 1 x pP ˚ qqΛo And, for all x R P ˚ , µpxqP 1 xpP ˚ q ă c by Assumption 2. ...

    work page 1990

  8. [8]

    If ψ p¯n,GN q ě ψ p¯n,kN q for all k ă G ´ 1, then V ˚ pPq ě V ˚ p xPq. 42

    work page

Show all 23 references
  1. [9]

    If ψ p¯n,GN q ă ψ p¯n,kN q for all k ă G ´ 1, and xP satisfies condition M, then V ˚ pPq ď V ˚ p xPq. Proof. For any set T Ă X , we define IpT q as the random variable denoting the number of other groups that receive a signal x PT . Formally, for any group g “ 1 (say), IpT q :“ ...

  2. [10]

    For x PT , P 1 xpT,k q ď xP 1 xpT,k q for all k “ 0, 1, 2...G ´ 2 and P 1 xpT,G ´ 1q ě xP 1 xpT,G ´ 1q

  3. [11]

    For x RT , P 1 xpT,k q ď xP 1 xpT,k q for all k “ 0, 1, 2...G ´ 1 Let σ ˚ be the maximal participation equilibrium in xP, and let P ˚ and NP ˚ be the associated participation and not-participation sets respec tively. For more than 2 groups, the IC for protesting and not-protes...

    2022

  4. [12]

    If l ď β ă ¯l, then information does not aggregate if P 1 has conditionally independent signals (denoted by P 1,CI ) as long as c ą 0; and Dc ą 0 and a signal P 1 ě CAD P 1,CI , such that information aggregates under P 1

  5. [13]

    maximally informative turnout

    If β ą ¯l, then information does not aggregate for any P 1 ě CAD P 1,CI and any c ą 0. Proof of Proposition 8. Substituting the expression for Poisson pdf, we get β pk, P, ¯P q “ µ 1 ´ µ P 1p ¯P, ¯P qψ pk, 2Nq ` 2P 1p ¯P, ¯NP qψ pk,N q P 0p ¯P, ¯P qψ pk, 2Nq ` 2P 0p ¯P, ¯NP qψ...

  6. [14]

    If ψ p¯n˚, 2Nq ą 2ψ p¯n˚,N q, then IpPq ě Ip xPq if maxT Ă X P 1pT,T q ´ xP 1pT,T q is sufficiently small

  7. [15]

    pDpi,j q ´ α pi,j q /BD i‰ j ` ÿ k‰ i α pi,k q/BD i“ j If D P ∆pX ˆ X q, then we say that “ D is obtained from pD by an ETI given by α

    If ψ p¯n˚, 2Nq ă ψ p¯n˚,N q, then it is possible that IpPq ă Ip xPq. Proof of Proposition 9. Let σ ˚ be the maximally informative equilibrium under xP. If the policymaker continues to use ¯ n˚ as the cutoff, then σ ˚ continues to remain an equilibrium under P due to Theorem 1. ...

    1990

  8. [16]

    If P 1 1 pX´ i “ 1q ą 1 2, a player’s incentive to work is more influenced by whether the other player works, making the LH S on the incentive constraint decreasing in q

    This makes P 1 1 pX´ i “ 1q “ 1. If P 1 1 pX´ i “ 1q ą 1 2, a player’s incentive to work is more influenced by whether the other player works, making the LH S on the incentive constraint decreasing in q. Therefore, if σ 1 is an equilibrium for some q, it is an equilibrium for a...

  9. [17]

    51 In the introduction, we only considered the symmetric pure strate gy profile σ 1 in which both Abe and Bob work with probability 1 after seeing Xi “ 1

    If I 0p˜p,q q,I 1p˜p,q q ă c, then I β p˜p,q q ă c for all β . 51 In the introduction, we only considered the symmetric pure strate gy profile σ 1 in which both Abe and Bob work with probability 1 after seeing Xi “ 1. Now let σ β denote symmetric mixed strategy profiles in which...

  10. [18]

    Therefore, the region where σ 1 is the maximal equilibrium is increasing in the set order in ˜p

    If q ă 1 2 then (a) for ˜p ă c, σ 0 is the maximal equilibrium (b) for ˜p ą c, there exists a threshold q˚˚ such that, σ 1 is the maximal equilibrium whenever q P p0,q ˚˚ q and σ 0 is the maximal equilibrium in q P pq˚˚ , 1 2q The threshold q˚˚ is increasing in ˜p. Therefore, ...

  11. [19]

    max " min

    If q ą 1 2, then there exist two thresholds, pq,q ˚ such that the following holds: (a) for ˜p ă 1 ´ c, σ 0 is the maximal equilibrium in q P p 1 2,c q, σ a is the maximal equilibrium in q P pc, pqq, σ β is the maximal equilibrium in q P p pq,q ˚ q, σ 1 is the maximal equilibri...

  12. [20]

    On the other hand, for any ˜ p, q˚˚ p˜pq ď q˚˚ p1q “ 1 ´ c ă 1

  13. [21]

    /BV/D0/CP/CX/D1 3/BM For any ˜p P rp, 1s, σ 1 is the maximal equilibrium if q ě q˚ p˜pq or if q ď q˚˚ p˜pq

    Also, note that q˚ p1 ´ cq “ 1 and q˚˚ pcq “ 0. /BV/D0/CP/CX/D1 3/BM For any ˜p P rp, 1s, σ 1 is the maximal equilibrium if q ě q˚ p˜pq or if q ď q˚˚ p˜pq. Moreover, if ˜p P p 1 ´ c,c q, then q˚ p˜pq “ 1 and q˚˚ p˜pq “ 0, and σ 1 is not an equilibrium for any q P r0, 1s. Proof...

  14. [22]

    Therefore, there exists q˚ p˜pq (defined above) such that for q ě q˚ p˜pq, I 1p˜p,q q ě c, i.e, σ 1 is the maximal equilibrium

    Then, I 1p˜p,q q is increasing in q. Therefore, there exists q˚ p˜pq (defined above) such that for q ě q˚ p˜pq, I 1p˜p,q q ě c, i.e, σ 1 is the maximal equilibrium. Next, suppose that ˜ p ě 1

  15. [23]

    Therefore, there exists q˚˚ p˜pq (defined above) such that for q ď q˚˚ p˜pq, I 1p˜p,q q ě c, i.e, σ 1 is the maximal equilibrium

    Then, I 1p˜p,q q is decreasing in q. Therefore, there exists q˚˚ p˜pq (defined above) such that for q ď q˚˚ p˜pq, I 1p˜p,q q ě c, i.e, σ 1 is the maximal equilibrium. If ˜p ă 1 ´ c, then q˚˚ p˜pq “ 0 and q˚ p˜pq P p c, 1q. Therefore, σ 1 is not an equilibrium for q ă 1 2, where...

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Reviewed May 23, 2026 · model on record in the stance chip above.