Source
Besley and Prat, “Handcuffs for the Grabbing Hand? Media Capture and Government Accountability”, American Economic Review 96(3) (2006), LIT-1333, read in full in NOTE-1031 from the LSE working paper of 2005 (PEPP/7). The result is its Proposition 1, proved in its appendix. The derivation below is the record’s.
What was actually shown
Setup. The incumbent is good with probability γ, else bad. If she is bad, all n outlets receive the same verifiable signal s = b with probability q > 0; otherwise they see s = ∅. Only verifiable news can be printed. An outlet reporting news earns a/m when m outlets report it. The incumbent sees the signal and makes private offers tᵢ ≥ 0, each costing her tᵢ and worth tᵢ/τ to the outlet. She receives r from re-election, minus what she paid. If any outlet reports s = b, every voter learns it.
Step 1, voting. After s = b the posterior is 0 < γ, so voters replace her (strictly dominant). Suppose voters also replaced her after s = ∅. Then a bad incumbent gains nothing by paying, no one is paid, the media report truthfully, and Pr(good | ∅) = γ / (γ + (1 − γ)(1 − q)) > γ, so voters should keep her after ∅, a contradiction. In every pure-strategy equilibrium she is re-elected iff no outlet reports.
Step 2, all or none. Since one report informs every voter, paying fewer than all informed outlets buys nothing. She pays all n or none.
Step 3, the price. Take a profile in which all n are silenced. An outlet that rejects its offer becomes the only one reporting, m = 1, and earns a. It therefore accepts iff tᵢ/τ ≥ a, so the cheapest offer that works is tᵢ = τa, and not τa/n. Conversely no outlet can earn more than a, so any offer worth at least a is accepted.
Step 4, the condition. Silencing costs nτa and gains r. The bad incumbent buys silence iff nτa < r, that is n < r/(τa), and is indifferent at equality.
Consequences. Under capture s = ∅ always, so Pr(good | ∅) = γ: the voters’ posterior equals the challenger’s prior, they are indifferent, and by Step 1 they keep the incumbent. Turnover is 0 and expected voter utility is γ in each period. Without capture a bad incumbent is caught with probability q, turnover is q(1 − γ), second-period utility is γ + q(1 − γ)γ, and audience revenue is qa rather than 0.
What could have failed: the price could have been the outlet’s share, a/n, as a reimbursement of lost revenue would suggest. Then the total cost would be a, independent of n, and plurality would not protect. It fails because the deviation payoff of a lone reporter is a.
What this does not say
- Not that voters are fooled. Under capture the voters’ inference is correct: silence is uninformative and they know it. The incumbent wins because the tie goes to her, not because anyone believes something false. This is the record’s gloss, and it is what separates the model from Bayesian persuasion (THEORY-404), where a receiver who knows the design is moved.
- Not about soft news or partial capture. With unverifiable news, or readers who see one outlet only, buying some outlets can pay. The paper’s segmented-audience extension needs to silence only enough outlets to keep half the voters uninformed, and the plurality result then holds cleanly only when at least half the viewers switch outlets.
- Not dynamic. Capture is a one-shot comparison. Nothing in the model lets capture change n, a, τ or r later, so it has no interpretation–authority loop.
- Not an empirical finding. The paper’s Table 1 compares means across 88 countries and is called “crude” and non-causal by its authors.
- Not the published text. The working paper was read. Its appendix writes the acceptance threshold once as a, not τa, a slip that does not affect the conclusion.
Connections
- THEORY-851 and THEORY-850. The two empirical readings of this batch take the model as their frame. Di Tella and Franceschelli’s transfers are advertising, and Szeidl and Szucs’s δ, the government’s ability to reward slant, plays the part of τ.
- THEORY-404. Two ways to govern a rational evaluator through its evidence: commit to a signal that moves it, or remove the signal and leave it at its prior.