Theory

Theory

Theoretical apparatus motivating the empirical design. The paper is primarily empirical — measuring sponsor bias in TSE-registered polls — but the why does this matter hinges on how polls actually shape voter behavior. This file collects the framework theories that make poll content consequential. As additional theories enter the project (e.g., bandwagon dynamics, candidate-quality signaling, fundraising-cascade models), they get sibling ## sections.

Polls as coordination devices (strategic voting)

The cleanest motivation for why polls matter at all: in plurality systems, instrumentally-rational voters do not want to "waste their vote" on candidates with no chance of finishing in the seat-winning set. Polls are the common-knowledge signal that lets voters coordinate on who is viable. Multiple equilibria collapse onto one.

Setup

Brazilian institutional detail

Predictions

Strategic-voting + polls-as-coordination jointly imply that the marginal viability threshold is the political quantity that matters:

  1. Polls move voters most when the marginal-viability identity is uncertain. A candidate clearly in 4th in a small-muni poll has little to gain from strategic-vote shifts no matter what; a candidate near the 2nd-place threshold (small munis) or 3rd-place threshold (large munis) has the most to gain from appearing viable.

  2. Sponsor-bias incentive is heterogeneous in the same direction. Sponsors of candidates near the viability cutoff have the largest marginal return to slanted polls (move voters across the wasted-vote frontier); sponsors of front-runners or hopeless candidates have weaker incentives. This is the testable coordination-theory prediction in the sponsor-bias setting: β should be larger for candidates near the cutoff than for the very top or very bottom of the field.

  3. The cutoff itself shifts at the 200k-voter institutional boundary. In small munis, the cutoff is between 2nd and 3rd place; in large munis, between 3rd and 4th. If the coordination theory is right, the position of the largest β should shift accordingly across the institutional discontinuity. This is the cleanest design-level test the project can support — RD-style at the 200,000-voters threshold, with the position of peak β across final-rank quintiles as the heterogeneity object.

  4. Polls matter more in small munis (in absolute consequence). Coordination problems are more acute when N is large relative to M+1 viable spots; smaller plurality elections (M+1=2) have a sharper coordination cliff than runoff-eligible ones (M+1=3). This is in tension with the slant-incentive prediction — the demand for slanted polls (from sponsors) and the effect of slanted polls (on voters) are predicted to peak at different places.

Mapping to the empirical design

Open testability concern

Per the project framing: every candidate has a strategic-vote incentive to commission slanted polls regardless of their position, because slant could in principle move voters across any viability threshold the voter is using. The coordination-theory prediction is not that "only borderline candidates slant" but that "the voter-side return to slant peaks at the threshold." Whether sponsors internalize this in their commissioning decisions is itself an empirical question — which limits the within-paper test of coordination theory to the heterogeneity-in-β across final-rank position. See docs/thinking.md for sketches on tighter tests.

Why this theory belongs in the motivation

The descriptive finding — Brazilian sponsor-paid polls overstate the sponsor by 6–7 pp on average — gains its policy weight only if those polls then shape voter behavior. The coordination-devices theory is the most prosaic and well-evidenced channel through which poll content moves votes. The companion empirical literature is rich and agrees on the qualitative claim:

The Brazilian-context piece Lloyd et al. (2016) documents non-random poll error operating through strategic voting specifically — the closest substantive predecessor for the claim that poll-induced voter coordination is consequential in Brazil.

References

All entries in paper/references.bib; expand docs/literature.md with the three classics (Cox, Duverger, Myerson-Weber) next time the literature pass runs.

Polls as bandwagon triggers

Related to coordination but mechanistically distinct: voters do not explicitly compute who's pivotal but are nonetheless pulled toward the candidate who appears to be leading. Mechanisms in the literature:

  1. Conformity / social desirability — desire to be on the winning side ex post; psychological, not instrumental.
  2. Expressive utility from voting for a winner — utility payoff from the act of supporting the eventual winner, independent of marginal pivotal probability.
  3. Mobilization asymmetry — supporters of the apparent leader exert more effort because the win looks within reach; supporters of trailers stay home (a turnout channel rather than a vote-choice channel).

The underdog effect is the counter-prediction: sympathy for the trailing candidate, pulling votes the other way. Documented in lab experiments (less so in field data); the net behavioral pattern in any given setting is empirical. The fact that we observe sponsors overstating (rather than understating) their candidates is itself weak evidence the underdog effect is not the dominant force in the Brazilian 2024 mayoral setting — sponsors would slant down if underdog dominated bandwagon.

Setup

Predictions

  1. β should be largest for sponsors of candidates just below the front-runner. These are the candidates with the most to gain from appearing to be leading — slant them up by ~7 pp and they cross from "close 2nd" to "apparent 1st," triggering the bandwagon premium. Sponsors of a clear 4th-place candidate gain less from slant (they can't realistically be made to look like leaders); sponsors of clear 1st-place candidates also gain less (they already appear leading).

  2. Bandwagon prediction differs from coordination prediction sharply in runoff-eligible munis. In large munis (≥200k voters), coordination predicts β peaks near final rank 3 (the M+1 cutoff for the runoff first round); bandwagon predicts β peaks near final rank 2 (candidates trying to look like front-runner). This is the cleanest discriminating test the project can run — the same heterogeneity analysis distinguishes the two voter-side theories.

  3. β should be larger in tighter races. Where front-runners are not visibly far ahead, slant has more room to flip the apparent leader identity. Predicts a competitiveness × sponsored_by interaction with positive sign. (Coordination would predict the same sign through a different channel — tight races also have more strategic-vote movement.)

Mapping to the empirical design

Open testability concern

The two voter-side theories can coexist — bandwagon and coordination operate through different cognitive channels and may both shape behavior. The within-paper test is which one dominates the heterogeneity pattern, not which is "real." A null discriminating result is consistent with both forces operating.

References

Polls as quality cues (Bayesian information)

A third voter-side mechanism: voters take a candidate's poll standing as a Bayesian signal about candidate quality, distinct from both strategic coordination (who's viable) and bandwagon (conformity). Closest framing: "if many voters seem to like candidate X, then X likely has qualities I might not have observed directly." This is the low-information-rationality / cue-taking tradition.

Setup

Predictions

  1. β should be largest for sponsors of new / lesser-known candidates. First-time candidates, non-incumbents, candidates without prior elected office — these are the candidates for whom voters have weak priors, so a poll signal has the most posterior-shifting weight. This contrasts with both coordination (predicts peak at viability cutoff regardless of candidate experience) and bandwagon (predicts peak just below front-runner regardless of candidate experience).

  2. Candidates with strong endorsement / media coverage should show smaller β. Their quality priors are already informed from other sources, so a slanted poll has less posterior weight.

  3. Repeat candidates (returning to a previous office) should show smaller β than newcomers — voters have direct prior experience to anchor the quality prior.

Mapping to the empirical design

Open testability concern

"Quality signal" is a posited cognitive process — we don't directly observe voter inference. The heterogeneity test (β by candidate experience) is the indirect test; alternative explanations exist for any difference observed (e.g., new candidates may also have more volatile sponsors).

References

Why bias survives voter discounting (information frictions)

A standard objection threatens the whole enterprise: if every voter observes who paid for a poll, and sponsor identity is a public field on every TSE registration, rational voters can subtract the expected slant and the sponsor gets no return from biasing. In equilibrium sponsors should pay for unbiased polls and β should be zero. The data say β ≈ +7 pp. So something in the rational-discount chain is broken.

This section walks through the obvious resolutions, eliminates the ones that don't survive scrutiny, and lands on information frictions on the voter side as the load-bearing assumption that ties the four voter-side / supply-side theories above into a coherent picture.

Obvious resolutions that don't survive

  1. "Voters can't see the methodology so they can't discount Channel A." Voters don't need to parse the 1,600-char DS_PLANO_AMOSTRAL to discount. They could just run the regression this paper runs — observe historical sponsor-poll error and apply a sponsor- conditional discount. Or update anecdotally from past episodes of sponsor-poll error. So design opacity per se does not protect the slant. The bias produces an observable historical pattern that a sufficiently motivated voter could in principle estimate.

  2. "Sponsor's payoff is on rank, not level — rank can't be discounted away." Once sponsor identity is observed, voters can apply the discount to whichever target the sponsor cares about, including rank. "This poll says X is in 2nd, sponsored by X, probably X is in 4th" is a rank discount, not a level discount.

  3. "Sponsors are short-horizon so the unraveling discipline doesn't bite." Pollsters are not — they run hundreds of polls across cycles and do face long-run reputational stakes. So the intermediary in the contract has skin in the game even if the principal does not.

What survives: voters are not fully informed about β

What the three eliminations leave is a single resolution: voters do not have, and do not acquire, the information they would need to discount the slant precisely. This is the information-friction story. Five operational sub-mechanisms make it concrete and (mostly) testable:

  1. Rational inattention. Acquiring a precise estimate of sponsor-specific bias is costly — it requires aggregating across thousands of polls and final results. The marginal voter's instrumental stake in any single race is small, so the cost-benefit calculation does not justify the acquisition. Voters end up with diffuse priors over β and under-discount in expectation. [cite:sims2003implications]

  2. Anecdotal updating is biased. What voters do instead is update from salient episodes — the 2018 polls miss, a pundit's accusation that a particular firm slants. Anecdotal samples are small, selected on what got media attention, and weighted toward recent/vivid cases. The resulting estimate of β can be off in either direction and is unlikely to coincide with the academic-regression estimate. The data set for the rational discount does not, in practice, exist in any voter's head.

  3. Channel A produces heterogeneous bias across polls. Even a voter who has internalized "sponsored polls overstate by 7 pp on average" cannot back out this poll's bias, because Channel A bias depends on design choices that differ across sponsored polls (urban-only vs full-coverage, education-quota vs not, etc.). The variance of per-poll bias around the mean is large; a constant-discount rule overcorrects for honest sponsored polls and undercorrects for heavily-designed ones. This refines the eliminated argument (1) above: design opacity does not protect the average β, but it does protect per-poll dispersion of β that an ideal voter would need to discount well.

  4. The marginal pivotal voter is less informed than the average voter. Sponsors care about the voter who tips the race. In close mayoral races, that voter is disproportionately low-engagement, low-political-knowledge, and unlikely to be the one who computes a sponsor-conditional discount. The sponsor's marginal return is on the marginal voter, not the average.

  5. Pollster long-run reputation is multi-dimensional. Pollsters are long-run players, but their reputation function rewards aggregate accuracy on final-week, headline-race polls — the ones used in the post-election "who called it right" press — far more than per-poll accuracy on sponsored mid-cycle polls. A firm can sustain sponsor-poll inflation in early/mid-cycle polls and still close the cycle with a clean final-week poll that defends its public reputation. This is consistent with the customer-mix-sorting prediction in the pollster-reputation section below: the reputation incentive bites where it is observable to the headline-poll audience, not where it isn't.

Mapping to the empirical design

The information-friction story has within-paper consequences but is not itself fully testable here:

Open testability concerns

References

All four are candidates for a literature-pass addition; the information-friction argument is foundational enough that the paper should cite the standard references when writing it up.

Polls as Bayesian persuasion (supply-side / Channel A)

Why a sponsor would commission a slanted poll in the first place: the sponsor (sender) chooses a signal structure to maximize the receivers' posterior belief about their candidate, subject to a disclosure constraint. In the Brazilian setting, the disclosure constraint is the mandatory PesqEle registration regime — every methodology choice is publicly filed before the poll's results can be released.

Setup

Predictions

  1. Channel A vs Channel B decomposition is the core supply-side prediction. Total β = β^A (movement through methodology) + β^B (residual). After conditioning on the structured methodology features (sample size, days-to-election, ST_PESQUISA_PROPRIA) and the LLM-extracted methodology features (coverage_class, quota variables, population frame), β should shrink to β^B. If β shrinks substantially → Channel A dominates (Bayesian persuasion through disclosed methodology). If β stays roughly constant → Channel B dominates (residual / fabrication, outside the disclosure regime).

  2. β^A should be larger where methodology flexibility is greater. Rural-heavy munis (where coverage_class choice matters more), races with demographic skew (where quota choice matters more) should show larger Channel-A contribution.

  3. β^B should be larger where verifiability is weaker. Polls far from the election (less ex-post verification) should show larger Channel-B contribution. Polls in races with weaker media scrutiny should also.

Mapping to the empirical design

Refined Channel-A lever inventory

The canonical lever-inventory table — concrete-design differences, opacity differences, ruled-out alternatives — lives in docs/source-of-bias.md. That doc also documents the size-mismatch problem (the measured magnitudes of the documented levers do not add up to +7 pp) and the open agenda of probes (non-response handling, weighting structure, mode, question-order priming, interviewer-supervision detail) that would either identify a sharp design lever or leave "opacity is genuinely the answer" as the well-earned default.

The empirical highlights flowing into the inventory:

Open testability concern

The decomposition is identified only up to the observable methodology features. Residual β^B contains both "fabrication" (actual numerical manipulation) and "design slant via dimensions we didn't extract." Sharpening the dictionary of extracted methodology features matters — see docs/todo.md § Mechanism decomposition for the queued schema.

References

Pollster reputation: volume vs customer mix (supply-side)

Pollsters' equilibrium slant choice is disciplined by reputation, which has two distinct components: (i) absolute volume — the aggregate stake a firm has in being publicly seen as accurate, and (ii) customer-mix sorting — which segment of clients the firm primarily serves. AN-018 establishes that volume dominates customer mix as the empirical predictor of within-firm sponsor bias. The section is organized accordingly: volume-discipline first, with customer-mix sorting as the secondary refinement.

Setup

Reputation is the firm's product. Three mechanisms shape how much slant a firm tolerates when paid for a sponsored poll:

The first two of these mechanisms can co-move: small firms tend to attract candidate-heavy customers, big firms tend to attract media-heavy customers. The empirical question AN-018 settled is which axis is load-bearing once both are observable.

Predictions

P1 — Volume discipline (the dominant axis). Per-firm β within the within-candidate FE design should decrease in log(firm's total poll volume in the cycle). Mechanism: aggregate reputation cost scales with exposure; big firms face higher absolute stakes from a public miss. Confirmed: AN-018 univariate OLS δ = −4.28 (p = 0.017, R² = 0.18); WLS δ = −5.74 (p = 0.0005, R² = 0.35). Each doubling of firm volume associates with β falling by ~4-5 pp. The relationship is monotone across firm-size tertiles: small (n_total ~13) β = +11.98; medium (~41) β = +8.64; large (~118) β = −0.93.

P2 — Pollster-self share (reputation-as-product). Firms that primarily publish their own marketing polls (the pollster_self customer type) face the sharpest reputation sanction from slant, because their brand is the product. Their β when paid by a sponsor should be lower than firms with mixed customer composition. Confirmed (marginally): AN-017 γ_pollster_self = −19.9 (p = 0.10, n = 31) in the regression of β on customer-mix shares.

P3 — Customer-mix sorting (the secondary, weaker, axis). Conditional on volume, β should increase in the firm's candidate-share of customer mix. The customer-mix axis is real but is empirically subordinate to volume. Univariate AN-017 γ_candidate_share = +7.6 (p = 0.27, R² = 0.04) — right direction but not significant on its own. Joint AN-018 regression with log_n_total: γ_candidate becomes statistically indistinguishable from zero (and flips sign — see "Open issues" below). The candidate-share/slant correlation that AN-007 first reported appears to be primarily volume confounding.

P4 — Equilibrium bimodality. The pollster market should be bimodal in either size or customer mix rather than uniformly distributed, because firms cannot sustain both reputations simultaneously. The current 31-firm sample is not large enough to test this sharply, but AN-016's forest plot shows a visible cluster near β = 0 for the large-firm tertile and a cluster near β = +12 for the small-firm tertile, with relatively thin mass between them.

Empirical mapping

The size-discipline mechanism is the cleanest first-order empirical story for the cross-firm β heterogeneity surfaced by the robustness battery. The cascade of findings:

  1. AN-016 (within-firm β refit on 31 firms with ≥ 5 self- sponsored polls each). β range across firms = [−10.95, +35.20]; sd 10.3. 19 of 31 firms individually significant. PDF style and LLM extraction held strictly fixed within firm, so the cross-firm dispersion cannot be a data-quality artifact.
  2. AN-017 (refresh of AN-007's per-firm β vs candidate-share on the AN-016 sample). γ_candidate_share = +7.6 unweighted (R² = 0.04) — right direction but statistically weak. pollster_self coefficient γ = −19.9 (p = 0.10) is the cleanest single piece of mixed-customer evidence.
  3. AN-018 (firm size vs customer mix). log(n_total) coefficient dominates: univariate R² leaps to 0.18–0.35; joint WLS regression gives δ_log_n_total = −7.09 (p = 0.0002) and γ_candidate becomes non-significant (p = 0.13). R² in the joint WLS is 0.40.

Tertile pattern (AN-018): small firms (n_total median ~13) β mean = +11.98 (9 of 12 individually significant); medium (~41) β = +8.64 (8 of 10 significant); large (~118) β = −0.93 (only 2 of 9 significant). The "large" tertile contains every big-name 2024 pollster (CENSUS, IIP, INSTITUTO PARANÁ, Verita, AR7, AGILI); the "small" tertile contains METHODUS, CAMARGO, INTENÇÃO, DATA SC, VISÃO, RADAR, BRASLOPES, SEND, and analogous niche firms.

Substantive read for the paper

The headline +7.85 pp sponsor bias is not a uniform industry property. It is concentrated in small, low-volume firms; the big-name Brazilian polling industry appears to self-discipline at the within-candidate level. The headline is a weighted cross-firm average; the variance is the substantively interesting fact.

This sharpens the policy reading two ways:

Open issues

References

Empirical anchors:

Polls as verifiable disclosure

A supply-side complement to ## Polls as Bayesian persuasion: the sender faces a future cost of slanting that scales with how verifiable the claim is at the time the receiver consumes it. In the canonical Bayesian-persuasion setup the sender commits a signal structure and bears no ex-post cost. Brazilian electoral polls violate that assumption: the election day eventually arrives and returns a public, granular check on the poll's headline numbers.

Status: drafted 2026-06-02.

Setup

Predictions

  1. β^B declines with proximity to election day. After Channel A controls, the residual sponsor bias should be monotonically decreasing in proximity to election day. Polls in the final 1–2 weeks should show β^B ≈ 0; the action is at the longer horizon, where detection is far off and discounted.

  2. β is larger where scrutiny is weaker. Munis with no major-firm poll in the race (less cross-firm cross-check), low media density, or low EJ injunction activity — i.e., low P(detection) — should show higher β. Operationalizable via coarse proxies (presence of a Datafolha / Quaest / Ipec poll in the race; muni population; race-level injunction count).

  3. Enforcement events suppress β. A TSE / MPF investigation into a pollster firm should suppress β in that firm's subsequent polls — a Bayesian update on enforcement intensity. Testable in principle if an enforcement-event panel materializes; flagged conjectural for now.

Mapping to the empirical design

Open testability concern

The verifiable-disclosure prediction opposes the bandwagon-incentive prediction (theory.md §"Polls as bandwagon triggers", prediction 3): near-election polls have larger voter-side bandwagon return → sponsor's demand for slant is higher near the election; verifiable disclosure says the sponsor's cost of slant is also higher near the election. The two effects pull in opposite directions on the days_to_election × sponsored_by interaction. The observed sign discriminates between them, but a null is consistent with both operating and roughly cancelling — a perennial cost/demand-decomposition problem.

References

Polls as career-concerns games

Second supply-side complement to ## Polls as Bayesian persuasion: the pollster firm is a repeat player whose long-run revenue depends on accuracy reputation among future clients. Slanting any individual poll trades short-run sponsor revenue against long-run accuracy reputation; the trade-off varies with how much reputational capital the firm has accumulated.

Status: drafted 2026-06-02.

Setup

Predictions

  1. β is smaller for major national firms. Pollster fixed effects in the headline spec already absorb each firm's average house effect; the prediction here is on the interaction sponsored_by × major_firm — slant per unit of sponsorship is smaller for firms with more reputational capital. Predicted sign: negative.

  2. Newcomer firms show the largest β. First-electoral-cycle pollsters have no reputation to protect. Operationalize as years-since-first-TSE-registration of the pollster CNPJ.

  3. Visible methodology defense as reputation maintenance. When a major firm is challenged on methodology (e.g., Datafolha responded to Russomanno's 2020 censorship attempt with a detailed 35-year-old-methodology defense [stories.csv #131]), the defense itself is reputation-maintenance behavior the model predicts. Small firms with sponsorship-heavy portfolios should defend less and settle more.

Mapping to the empirical design

Open testability concern

Pollster volume mixes reputation stock and capacity: a major firm has many polls because clients trust it AND because it has the field operations to deliver them. Both predict the same heterogeneity sign through different channels. A sharper test would need a pollster-level shock that changes reputation without changing capacity (loss of a major media contract, statistician-level audit finding) — the data don't support that yet.

A second concern: Brazilian polling firms are often vertically linked to media outlets (Datafolha ↔ Folha; Globo's polling partnerships) [institutions.md §"Major firms"]. The media outlet's reputation may be the binding constraint rather than the polling firm's own — the model's predictions hold but the unit of accumulation is the outlet-pollster pair, not the pollster CNPJ.

References

Discriminating among the voter-side theories

The three voter-side theories above (coordination, bandwagon, information-cue) predict different positions of peak β across final-rank quintiles and candidate-experience bins. Summarized in one table:

Theory Where β peaks Discriminating heterogeneity
Coordination At M+1 viability cutoff (rank 2 in small munis, rank 3 in large) Position of peak shifts at 200k institutional cutoff
Bandwagon Just below front-runner (rank 2, regardless of muni size) Same peak position in small and large munis
Information cue Among lesser-known / first-time candidates, regardless of rank β larger for non-incumbents

The β-by-(rank × runoff-eligibility × first-time-candidate) cube is the within-paper test that distinguishes them. The Bayesian persuasion theory operates on the supply side and is orthogonal: its decomposition (Channel A vs B) is testable independently of the voter-side discriminating test.