Media Bias and Reputation

• p. 10 Section III, model assumptions

  We also assume that

• p. 17 Proposition 1

  For any

• p. 32 Appendix, proof of Proposition 1, comparative statics on the feedback probability

  For the comparative statics on

• p. 14 Section III.B, no-feedback case

  since a truthful normal firm reports r̂ with probability (1 −

Only the authors can say what is right here.

Judge's note: I looked at p010 (θ ∈ [1/2, π), π < 1), p014 (the no-feedback argument and footnote 18), p017 (Proposition 1) and p032 (the comparative statics on μ in the proof). My own working: (1−θ)(1−π)+θπ−θ = 1−π−2θ+2θπ = (1−π)(1−2θ). This is strictly negative only when θ > 1/2 and equals 0 at θ = 1/2. At θ = 1/2, footnote 18's formula gives σ_l(r̂) = 0, so truthful reporting is not ruled out at a parameter value the model allows. Lemma 1 and Proposition 1 do assume θ > 1/2, so the stated results stand. Proposition 1's range (1/2, 1) runs past π, outside the assumed set. The argument (Δ^nf > 0 for θ > 1/2; Δ^f(l) does not depend on θ) still seems to go through there, so this is a range inconsistency, not a false result. Only the authors can say which range they intend.

Second check: another model agreed

• p. 15 Section III.C, expected payoff difference

  Δ(s) = (1 − μ)Δⁿᶠ + μΔᶠ(s)

• p. 34 Definition preceding (A2) and equation (A2)

  conditional on feedback

• p. 34 Equation (A2), right-hand side

  −Δᶠ(r)

Only the authors can say what is right here.

Judge's note: Page 15 image: Δ(s) = (1−μ)Δ^nf + μΔ^f(s). Page 34 image: Δ^f(r) is "the relative payoff to reporting r̂ after r conditional on feedback", and (A2) reads (2/3)[...] + (1/3)[...] = −Δ^f(r). My reworking: indifference needs (1−μ)N + μΔ^f(r) = 0, so N = −[μ/(1−μ)]Δ^f(r). This equals −Δ^f(r) only when μ = 1/2, which the proof does not assume. The factor is missing as printed. I did not re-derive the reviewer's numerical example. The genericity argument (two equations, one unknown) and Proposition 5 still stand, hence S3.

Second check: another model agreed

• p. 18 Figure 4 caption

  given that the newspaper with the scoop receives a signal of

• p. 19 Section IV

  has a “scoop” on the true state of the world

• p. 19 Section IV, second paragraph

  One of these firms has a “scoop” on the true state of the world

Judge's note: Page 18 image: caption as quoted. Page 17 image: Figure 4 is introduced directly after Proposition 1 in the monopoly section. Page 19 image: "One of these firms has a 'scoop'" first appears in Section IV. The text search finds no earlier use of "scoop". The scoop firm's problem is later said to be equivalent to the monopoly problem, so only the label is affected.

Second check: another model agreed

• p. 18 Footnote 22, continuation-welfare argument

  an unbiased signal provides strictly more information about the firm’s type

• p. 18 Footnote 22

  eliminating bias must also at least weakly increase this payoff

Only the authors can say what is right here.

Judge's note: Page 18 image, footnote 22. I reworked the counterexample with π = .7, θ = .6, θ^F = .5, λ = .3, f(x) = x and bias σ_l(r̂) = .1. The posterior on quality after (l̂, feedback L) is .3/(.3 + .7·.63) = .4049. Under truthful reporting the largest posterior over all report and feedback events is .3/(.3 + .7·.7) = .3797. A biased-equilibrium posterior lies outside the range of the truthful posteriors, so the biased experiment is not a garbling of the truthful one with respect to firm type. I also checked that this bias is an equilibrium: Δ^nf = .30498 − .29283 > 0, Δ^f(l) = .3·.3699 − .7·.4049 < 0, giving an interior μ ≈ .066. A consumer decision that pays 1{high quality} − .4 has value 0 under truthful reporting and positive value under bias. The claim is an aside in a footnote about a model the paper does not specify; Proposition 2 as stated is not affected, hence S3.

Second check: another model agreed

• p. 20 Section IV, top of page

  that the true state is revealed after all re-

• p. 21 Section IV, joint-ownership equilibrium argument

  This occurs with positive

Judge's note: Page 20 image: μ̃ > 0 is the only restriction given when the probability is introduced. Page 21 image: the argument invokes μ̃ < 1. The text search finds no statement of the upper bound elsewhere in Section IV. This is an unstated assumption that is plainly intended; no result is affected.

Second check: another model agreed

• p. 33 Proof of Proposition 5, opening

  each firm must distort at most one signal with positive probability

• p. 25 Effective-monopoly equilibrium construction

  firm 2 will be indifferent about its report (since it has no consumers)

Only the authors can say what is right here.

Judge's note: Page 33 image: the universal claim and its strict-payoff justification. Page 25 image: in the effective-monopoly equilibrium "firm 2 will be indifferent about its report (since it has no consumers)" and may play "any strategy with a positive probability of distortion". An unread firm's payoff does not depend on its report or signal, so the strict inequality is false for it and it may distort both signals. Example: firm 2 reports a fair coin regardless of signal, which satisfies σ_r(r̂) ≥ σ_l(r̂). All consumers then strictly prefer honest firm 1, and firm 1 with equal numbers of each type reports honestly by the paper's own argument on pages 24-25. The step holds once restricted to firms with positive readership, and the classification in Proposition 5 stands, hence S3.

Second check: another model agreed

• p. 36 References

  Kaplan, Martin, and Matthew Hale. Local TV Coverage of the 2000 General Election.

• p. 29 Section VI.B

  (Kaplan and Hale 2001)

• p. 30 Table 1 note

  (Kaplan and Hale 2001)

Judge's note: Page 36 image: the entry runs straight from the authors to the italic title with no year; every other entry on the page gives the year after the authors. The text layer shows the citation "(Kaplan and Hale 2001)" in Section VI.B and in the Table 1 note; I did not open the page 29 or page 30 images. The missing year is evidently 2001.

Second check: none (judge only)