H4: Channel A contribution is larger where methodology flexibility is greater
The Bayesian-persuasion supply-side prediction has a heterogeneity corollary: the share of sponsor bias travelling through disclosed methodology choices — call it β^A — should be larger in races and on methodology dimensions that give the sender a wider choice set. Where the menu has bite (rural-share-high munis, demographically heterogeneous munis, levers with discretion left after the legal floor) Channel A can carry more slant; where the menu is constrained, β^A is forced toward zero and any residual bias must be Channel B. This page collects what the within-paper analyses say about the "more flexibility → more β^A" claim across the inventory of methodology levers that we can observe today.
Evidence strength: Refuted by AN-019, AN-020, AN-021, AN-022, AN-024, AN-033, AN-040 (2026-06-02). Across every measured Channel-A lever, the prediction is either null or wrong-signed: coverage class is 2 pp directional on n_candidate=25 (AN-019), the audit-percent KS test is p=1.00 (AN-021), the methodology completeness index runs the wrong way (AN-022, candidate-touched 0.43 vs independent 0.39), universe-scale deferral is wrong-signed at p=0.021 (AN-024), and the within-candidate FE deferral interaction is null and sign-inconsistent across specs (AN-033, AN-040). The original-design rural-share / demographic-heterogeneity interactions remain untested — blocked on IBGE Censo 2022 muni demographics — and are now lower-priority given the lever-by-lever nulls.
Theory
The framework is Polls as Bayesian persuasion (theory.md §"Polls as Bayesian persuasion (supply-side / Channel A)", prediction 2). The sender's signal-structure choice set determines the maximum slant that disclosed methodology can carry. Where the legal floor binds (audit ≥ 20%, mandatory disclosures), the sender has no room to flex; where the floor leaves discretion (which neighborhoods to sample, what population frame to claim, whether to defer the coverage-class declaration to a complementary filing), the sender can pick a signal structure that tilts the posterior toward their candidate without violating any single statutory standard [cite:kamenica2011bayesian; institutions.md §"TSE PesqEle / Divulgação Regime"]. The H4 prediction is therefore mechanical: the contribution of disclosed methodology to β should scale with the width of the realised choice set, both across races (rural-heavy munis, demographically heterogeneous munis) and across levers (coverage class > audit percent, where audit is floor-pinned).
Prediction
Two operationalisations.
Across races. Interact sponsored_by with race-level
flexibility proxies (rural_share, demographic Gini from IBGE
Censo 2022). Without Channel A controls the interaction is positive;
conditional on Channel A controls (coverage_class, population
reference, weighting bundle) it should attenuate toward zero — the
controls absorb the lever and the heterogeneity disappears.
Across levers. On the methodology-LLM sample, sponsor-conditional share of slant-permissive choices (specific_neighborhoods, urban_only, mixed population reference, deferred coverage, floor-pinned audit) should be elevated for candidate-touched polls relative to independent polls. The cross-lever ordering should follow the size of each lever's discretion: the more permissive the lever, the larger the candidate-vs-independent gap.
Competing predictions
Constant-menu null. Disclosed methodology is industry-standard boilerplate; pollsters file essentially identical descriptions regardless of sponsor. Under this null, candidate-touched and independent polls look indistinguishable on every observable methodology feature, and the entire +7 pp travels through Channel B (residual / fabrication, or design choices the disclosure regime does not require). AN-022's wrong-signed completeness index and AN-024's wrong-signed universe-scale deferral are both consistent with this null.
Channel A operating through unobserved design dimensions. The
extracted lever inventory may be insufficient: sponsors flex
quota-distribution detail, weighting-target choice, or
question-order priming — dimensions the current poll_methodology
schema does not capture — while looking identical on coverage,
audit, and population frame. Under this reading the null on
observed flexibility levers does not refute Channel A; it only
narrows the lever space.
Prior research
No direct empirical predecessor for "Channel A heterogeneity by
methodology-menu width" in the pre-election polling literature.
The closest formal anchor is Kamenica & Gentzkow (2011) applied to
the disclosure regime as the institutional commitment device
[institutions.md §"Statutory mapping"]; "área urbana"
DS_DADO_MUNICIPIO coverage is widespread and not by itself
disqualifying, so the lever has bite only where rural share is
nonzero. The Channel A vs B decomposition itself draws on
Dziuda (2011) (partial-verifiability) and
[cite:mullainathan2005market] (partial-discounting equilibrium with
heterogeneous receivers).
Evidence
| Analysis | Bearing | Key takeaway |
|---|---|---|
| AN-019 | Mixed | n=200 methodology subset: slant-permissive coverage classes (specific_neighborhoods + urban_only) at 12% in candidate-touched polls vs 10% in independent — direction matches Channel A but the gap is 2 pp on n_candidate=25. Decisive test deferred until the universe extraction lands. |
| AN-020 | Mixed (qualitative) | n=200, finer split by route. Committee polls (n=6) are 83% deferred-to-complement — hide via the complement channel, never selective. Party-route polls (n=4 total) are 50% specific_neighborhoods — small-n hint that party sponsors use the active coverage-restriction lever. CPF cell empty in this subset. |
| AN-021 | Mixed | n=200 audit_pct distribution. KS p = 1.00; ~76% of every bucket sits at the 20% legal floor. Candidate-touched polls (n=24) never exceed 30% audit; independent polls reach 100%. Right-tail gap is qualitative not statistical. |
| AN-022 | Against | n=200 completeness index (share of 12 ops-block fields filled). Candidate-touched mean = 0.43 vs independent = 0.39 — the OPPOSITE direction from "candidates hide methodology". t = +1.25, p = 0.22. If sustained at universe scale, Channel A on disclosure quantity is dead. |
| AN-024 | Against (significant) | Universe-scale n=14,876. Candidate-touched defer at 35.5% vs independent at 38.3%. Odds ratio 0.89 (95% CI [0.80, 0.98]), chi-square p = 0.021. The "candidates hide coverage via deferral" subprediction is statistically refuted at universe scale. |
| AN-033 | Against (null) | Spec B complement of AN-024 on the AN-001 analysis sample (n=27,907 candidate-poll rows). Within-candidate FE: γ on sponsored_by × deferred is +1.08 (SE 2.08, p=0.60); +2.05 (SE 2.18, p=0.35) with institute FE + controls; flips to −5.63 (SE 5.46, p=0.30) under race × week FE. Sign-inconsistent and never close to significance. Deferral is ruled out as a Channel-A lever in BOTH directions — neither selection nor amplification. |
| AN-040 | Against (null) | Heterogeneity follow-up to AN-033. The 3-way sponsored × deferred × I(final_rank=1) is null across all four specs (+2.03 / +4.09 / +0.46 / −12.51, SEs 3.3–10.5pp, sign-inconsistent). Leader-specific deferral amplification is not in the data. Closes the deferral lever. Incidental finding: split-sample sponsored_by has a sharp rank gradient (+5.58pp rank 1, +11.52pp rank 2, −2.81pp rank 3+) — consistent with AN-026/AN-027 coordination story but orthogonal to the deferral question. |
The cross-lever pattern across AN-019 through AN-040 narrows the residual Channel-A space to population frame, coverage class, and census-setor usage — the three dimensions poll-methodology-paired finding flagged on the 244-pair eyeball. The "more flexibility → more β^A" prediction is not vindicated on any measured lever; whether it survives on the three unmeasured ones is the remaining open question.
Open tests
Rural-share and demographic-heterogeneity interactions
The original H4 design — sponsored_by × rural_share and
sponsored_by × demographic_heterogeneity on Spec 3 residuals,
with and without Channel A controls — remains untested. Blocked on
IBGE Censo 2022 muni demographics not yet in repo. Given the
lever-by-lever nulls above, this is now lower priority than the
unmeasured-lever extraction below.
Sharpened lever extraction
The decomposition is identified only up to observable methodology features. AN-055 (coverage by candidate base) and AN-056/AN-057 (quota distance, weighting) extend the lever inventory toward weighting targets and quota-distribution detail. If those also come back null, the case for "Channel B carries the load" hardens and H4 collapses to "the flexibility prediction had nowhere to operate on the observable design space." See H3 channel-a-shrinkage for the parent shrinkage spec and H5 verifiability-decay-b for the Channel B side of the same decomposition.
Supporting analyses
Universe-scale n=14,876. Candidate-touched polls defer at 35.5% vs independent at 38.3% — candidate-touched are LESS likely to defer (odds ratio 0.89, 95% CI [0.80, 0.98], chi-square p = 0.021). The "candidates hide coverage via deferral" hypothesis is statistically refuted at universe scale.
Within-candidate FE on the AN-001 sample (n=27,907 candidate-poll rows from 8,917 protocols): the sponsored_by × deferred interaction γ is null and bouncing-signed across specs — +1.08 (SE 2.08, p=0.60) under candidate FE; +2.05 (SE 2.18, p=0.35) with institute FE + controls; −5.63 (SE 5.46, p=0.30) under race × week FE. Combined with AN-024 (sponsors do NOT disproportionately defer), deferral is ruled out as a load-bearing Channel-A lever in both directions.
3-way sponsored × deferred × rank1 is NULL across all four specs (+2.03 / +4.09 / +0.46 / −12.51, SEs 3.3–10.5pp, sign-inconsistent). The AN-033 null does NOT hide leader-specific deferral amplification. Incidental finding: split-sample sponsored_by has a sharp rank gradient — +5.58pp (rank 1, p<0.01), +11.52pp (rank 2, p<0.001), −2.81pp (rank ≥3, null) — consistent with the AN-026/AN-027 coordination story but orthogonal to the deferral lever question.
Sponsored polls never use phone (0/244) and use in-person at 95%; independent uses phone at 10%. χ² on the joint mode table p = 0.0003 in the *opposite* direction of cheap-mode-slant. The mode-substitution lever is refuted on this sample.
Sponsored polls describe interviewer training MORE than matched independent polls (84.4 % vs 72.5 %, McNemar p = 0.002) and supervisor role slightly more (92.6 % vs 87.3 %, p = 0.08). Bias contrast does not track which side describes (MW p ≈ 0.57 for both fields). The opacity gap is field-specific — sponsored polls under-document coverage but over-document interviewer-side rigor.
Sponsored polls dramatically under-document candidate-name rotation in the questionnaire (5.4 % vs 26.1 % when rotation+random+rotated combined; McNemar p < 10⁻⁷). Sponsored polls file FEWER vote-intention scenarios on average (3.73 vs 4.49, Wilcoxon p = 0.002) — refutes the within-poll scenario-selection / cherry-pick hypothesis. **[2026-06-02 update — see AN-052/AN-053:]** The rotation contrast is a between-firm composition effect, not a within-firm sponsor-choice effect (AN-052 firm-FE LPM p = 0.37). The direct candidate-position priming test refutes the sponsor-exploitation reading (AN-053: sponsored polls list sponsor's candidate LATER, McNemar p = 0.001 in WRONG direction). The AN-051 finding is recontextualized as a firm-tier composition signal — sponsors choose low-discipline firms that don't document rotation — rather than a within-firm Channel-A lever.
AN-051's −20.8 pp sponsored-vs-independent rotation gap vanishes within firm — LPM with firm FE gives sponsored coefficient +0.025 pp (cluster-SE 0.027, p = 0.37). 19 of 20 firms with both sponsored and independent pair-sides show identical rotation rates between sides. The rotation contrast is a between-firm composition effect, not a within-firm sponsor-choice effect.
The direct name-order priming test refutes the sponsor-exploitation reading. On 196 of 244 pairs (after fuzzy name-matching), the sponsor's own candidate appears LATER on the sponsored side than on the matched independent side — sp first-position rate 20.4 % vs ind 30.1 % (McNemar p = 0.001 in the WRONG direction). Sponsored polls do not strategically order their candidate to exploit first-position priming. The within-pair bias-carrier test IS significant (MW p = 0.019) but on the small 17-pair subset where sp lists the candidate earlier — when priming is used, bias is higher; sponsors generally do not use it.
AN-051's rotation contrast maps monotonically onto firm-size discipline. Across 124 questionnaire-pilot firms binned by universe-level poll volume, rotation-documented rates rise 3.7 % → 15.2 % → 19.4 % from small (median 11 universe polls) to large (median 67) tertiles — a 5× gradient matching AN-051's sp-vs-ind asymmetry. Closes the loop on AN-052: AN-051 is fully absorbed into the AN-018 firm-size discipline / AN-025 media-filter narrative.
On the 200-poll methodology subset, slant-permissive coverage classes (specific_neighborhoods + urban_only) appear in 12% of candidate-touched polls vs 10% of independent polls — direction matches Channel A but n_candidate=25 makes the gap noisy. Opaque coverage (deferred + not_specified) is 72% vs 80%, weakly contradicting the "candidates hide scope" prediction.
audit_pct distributions overlap heavily across sponsor types (KS p = 1.00). Both candidate-touched (n=24) and independent (n=124) cluster at the 20% legal floor (~76% of each). The qualitative gap is at the right tail — candidate-touched polls never exceed 30%, while independent polls reach 100% — but this is a few-poll difference.
Methodology completeness is HIGHER for candidate-touched polls (mean 0.43) than independent (0.39) — the opposite of Channel A's "candidates hide methodology" prediction. t = +1.25, p = 0.22 (wrong-signed and underpowered). Suggests Channel A on disclosure quantity is not the operative mechanism on this subset.
Cheap-Tier-2 structural test on coverage × candidate-base finds **no triple-interaction signal**. On the universe-scale within-candidate FE sample (n=20,393 cand-poll rows, 3,524 candidates, 1,665 muni clusters), the headline sponsor effect lands at **+7.70 pp (SE 1.44, p<10⁻⁷)**, but the flat `sponsored × narrow_coverage` interaction is null (β = +1.61, SE 4.93, p=0.74) and the wash-out-breaking triple `sponsored × narrow_coverage × base_lv_size_weighted` is also null (β = −0.54, SE 1.35, p=0.69). The 95 % CI on the triple is [−3.2, +2.1] in units of pp per unit of base_lv_dm — rules out large triples but not modest ones. Read: coverage class is unlikely to be the dominant Channel-A lever for the headline +7 pp; consistent with AN-032's reversed-sign bairro test. Directs attention to weighting / income-quota features (next AN).
Within-pair quota-distribution deltas (income / age / education) do **not** correlate with within-pair bias contrast. On 244 curated sponsored × independent pairs with cached `poll_sampling` extractions (338/338 protocols cached; quota distributions on 336): |Δ income (SM)| vs |contrast| r = +0.02 (p=0.75), |Δ age| r = +0.13 (p=0.10), |Δ pct-superior| r = −0.05 (p=0.45); signed Δ income vs signed contrast r = +0.06 (p=0.39). Across-stratum: |Δ income| ≈ 1.1-1.2 SM in all three strata (high_bias, well_behaved, understating). Only `population_reference differs` shows a directional pattern: 25.5 % of high_bias pairs vs 14.6 % of well_behaved (chi-square p = 0.12, not significant). Reading: at the cached-quota-distribution granularity, sponsored polls do not deviate from indep-media polls in income / age / education quotas in a way that correlates with the observed bias. Combined with AN-055 (coverage × candidate-base null), the structural Channel A search continues to come up empty on the coverage + quota axis. Live frontiers remain AN-051 (scenario rotation, positive) and the unextracted ponderação description.
Within-pair ponderação description **does** differ systematically between sponsored and indep polls — but in the AN-042 *selective-disclosure* direction, not the simple Channel A 'sponsors hide methodology' direction. On 244 curated sponsored × independent pairs (338/338 protocols extracted via the new poll_weighting LLM extractor at gpt-4o-mini): (i) the binary flag `described_differs` is **27.3 % in high_bias vs 16.9 % in well_behaved vs 11.1 % in understating** (chi-square p = 0.044, monotone), (ii) `postst_differs` (post_stratification_explicit binary differs between sides) correlates with |contrast| at r = +0.13 (p = 0.042), (iii) directional asymmetry: when post_stratification_explicit differs between sides, the *indep* side is MORE LIKELY to omit it (68 / 114 = 59.6 %, binomial p = 0.049). Reading: sponsored polls describe weighting AND post-stratification with greater specificity than the matched indep comparator. This matches AN-042's reframing — sponsored polls under-document sample-shape but over-document visible-rigor dimensions. The pattern is real but does not directly explain the +7 pp bias; the simplest reconciliation is that the *claimed* corrections do not actually neutralise the quota choices (claimed-but-ineffective ponderação), but identifying that would require a downstream effectiveness test we don't yet have.
Structured `nonresponse_handling` is 100 % `not_specified` on every pair. Diagnostic regex grep confirms the substantive null — undecided/refusal vocabulary appears in only 5 sponsored and 2 independent pair-sides out of 488. The probe is null-by-data-design: registration PDFs are pre-fielding planning documents and do not describe a post-fielding analytical choice. Testing the nonresponse-handling × sponsor lever requires the post-fielding *relatório* PDFs (currently outside the methodology extraction pipeline).
The 200-poll subset has 0 CPF polls. Committees (n=6) are 83% deferred-to-complement — hide scope via the complement channel, never selective. Party-route polls (n=4 total) are 50% specific_neighborhoods — small-n hint that party sponsors pick the selective channel.