H2: Opponent-sponsored polls understate the opposing candidate

H2: Opponent-sponsored polls understate the opposing candidate

When a Brazilian mayoral candidate's opponent commissions an electoral poll, the poll's reported share for candidate c is systematically lower than what other polls of the same race report for the same candidate. The within-candidate gap is again the quantity of interest, with the sign flipped: holding the candidate fixed, does sponsorship by a rival's campaign push the reported number down? The sender-side mirror of H1: if the same Bayesian-persuasion logic that inflates the sponsor also deflates the sponsor's opponents, the coefficient on OpponentSponsored_c should enter with the opposite sign of SponsoredBy_c. The asymmetry in magnitude is itself informative about whether boosting one's own candidate and attacking a rival are equally costly to fabricate.

Evidence strength: Confirmed by AN-001 (2026-06-02). Within- candidate FE on the analysis panel gives β_opp = −1.93 pp (SE 0.89, p = 0.030) on 1,048 opponent-sponsored candidate-poll rows. The symmetry test gives β_self − β_opp ≈ +9.7 pp — the mirror direction is confirmed, but the magnitudes are sharply asymmetric: boosts are ~4× the size of attacks.

Theory

Same framework as H1: Polls as Bayesian persuasion (theory.md §"Polls as Bayesian persuasion"). The sender chooses a signal structure to maximize the receivers' posterior over the sponsor's preferred outcome. For the opponent-sponsored case the preferred outcome is suppressing receivers' posterior over the rival — moving voters, donors, and coalition partners off the rival's viability. The same disclosure-regime commitment (Kamenica & Gentzkow (2011)) that gives the supply-side prediction its sharpness for H1 applies here.

The asymmetry between β_self and β_opp is the interesting object. Two non-exclusive readings: (i) commission opportunity is asymmetric — a candidate has one self to boost but several opponents to attack, so any given opponent's share of total slant attention is diluted; (ii) attack-slant carries a higher detection / reputational cost than boost-slant, so the sender's optimal τ is smaller in the negative direction. The current design does not separate (i) and (ii).

Prediction

A regression of reported candidate share on an OpponentSponsored_c indicator, absorbing candidate fixed effects, yields a negative coefficient on the order of −1 to −5 pp. The mechanism is supply-side and sender-specific: the sponsor commissions slant against rivals; the candidate FE strips out the confounder that opponents of strong candidates might attract different sponsorship patterns.

Competing predictions

Generic pollster house effect. If the +7 pp self-sponsor coefficient reflects firm-level house effects rather than sender-specific bias, then opponent-sponsored polls — which run through the same pollster firms — should show the same sign as self-sponsored, not the opposite. β_opp = −1.93 rules this out: the bias is tied to who paid, not which firm fielded the poll. See sender-specific interpretation.

Symmetric mirror (|β_opp| ≈ |β_self|). If boost-slant and attack-slant were equally costly to fabricate and equally demanded, β_opp and β_self should mirror in magnitude as well as in sign. The data reject symmetry: |β_opp| ≈ 1.9, |β_self| ≈ 7.75, a ~4× asymmetry. The strong asymmetry is itself evidence that the supply-side cost / demand for attack-slant differs from that for boost-slant.

Prior research

No prior estimate of opponent-sponsor bias in the Brazilian setting. Available anecdotes show campaigns attacking polls that hurt them rather than commissioning attack-polls directly: the 2022 PT coalition in Bahia challenged a Datafolha poll commissioned by rádio Metrópole on methodology grounds [stories.csv #078]; Boulos's 2024 SP campaign attempted to censor an unfavorable Datafolha poll [stories.csv #133]. These are reactions to disliked outputs, not the kind of commissioned attack-polls H2 tests. The closest direct analog in the sponsor-bias literature is the online opinion-survey experimental work [cite:leeper2019sponsorship; cite:crabtree2020sponsorship], which manipulates declared sponsor identity but does not separate boost-sponsor from attack-sponsor effects.

Evidence

Analysis Bearing Key takeaway
AN-001 Confirms Within-candidate FE: β_opp = −1.93 pp (SE 0.89, p = 0.030) on 1,048 opponent-sponsored rows. Sign matches the H2 prediction; symmetry test β_self − β_opp ≈ +9.7 pp confirms the bias is sender-specific (not a generic firm-level house effect).

Open tests

Asymmetry decomposition: opportunity vs cost

The 4× gap between |β_self| and |β_opp| could reflect either sender opportunity (one self vs many opponents to attack) or asymmetric detection cost (attacks invite scrutiny that boosts do not). A natural sharpening is to estimate β_opp separately for the candidate's closest rival (the main two-way contest) vs more distant opponents; if opportunity dominates, the closest-rival β_opp should be most negative.

Independent-design replication

The H1 evidence stack rests on three independent designs (within- candidate FE, race × week FE, pre-poll trajectory placebo). The opponent coefficient currently has only the within-candidate FE estimate. Re-estimating the race × week FE spec (AN-002) and the trajectory placebo (AN-003) with OpponentSponsored_c as the focal coefficient would upgrade H2 from single-design to triangulated. This is the lightest-touch upgrade available.

Channel A vs Channel B for attack-slant

The H1 mechanism decomposition (see H10 methodology-flexibility-a) asks whether boost-slant flows through declared methodology or residual fabrication. The same decomposition applied to β_opp would test whether attack-slant uses the same supply-side levers — or whether it concentrates differently (e.g., more in non-response handling, more in scenario selection). Blocked on the same poll_methodology LLM extractor.