AN-062: Sponsor effect shrinks with independent-poll density

Sponsor effect shrinks sharply with independent-poll density. Sharpening AN-060's all-polls visibility metric to count only credible independent benchmarks: tertile split is now monotone, β_sponsored = +8.08 in low-density races (median 2 indep polls), +8.54 in medium (6), and **+2.71** in high (22 indep polls). High-vs-low cross-tertile drop = 5.4 pp. Linear interaction with firm FE: β_sponsored × log(1 + n_indep_in_race_dm) = −1.47 (SE 0.90, p = 0.10). Prior-only variant restricting to independent polls fielded BEFORE the sponsored poll's field date: β interaction = **−1.92** (SE 1.16, p = 0.10) within firm --- each doubling of prior-indep count is associated with ~1.3 pp less bias. Direct support for the reputation-via-public-visibility mechanism: sponsors slant less when their poll will be visible against a thick set of independent benchmarks. Sponsored polls cluster in races with few independent benchmarks on average (mean n_indep = 1.9 vs sample-wide 9.4); the cand-FE interaction test absorbs that selection.

Question

AN-060 tested the reputation-via-visibility prediction using total polls per race as the visibility metric and found a directionally supportive but statistically loose interaction. A sharper version of the reputation mechanism: the sponsored poll is most exposed when there are many independent polls available for comparison, because those are the credible benchmarks against which the bias becomes visible. Counting same-side or pollster-self polls in the visibility metric dilutes the signal.

This analysis re-runs AN-060 with the visibility metric restricted to independent polls, and adds a temporal-credibility variant counting only the independent polls fielded before the sponsored poll.

Design

source/analysis/an-062-indep-poll-visibility.py:

1. Compute two visibility measures per row:
   • n_indep_in_race: total distinct independent-media protocols filed in the same muni (any field date).
   • n_indep_prior: number of independent protocols in the same muni with field_end strictly before this row's field_end.
2. Four nested specs (within-cand FE, muni-clustered SE):
   • A: headline replicate.
   • B: + sponsored × log(1+n_indep_in_race_dm) interaction.
   • C: same as B + firm FE.
   • D: + sponsored × log(1+n_indep_prior_dm) + firm FE (temporal credibility).
3. Tertile split by n_indep_in_race for narrative clarity.

Results

Visibility metric distributions

• n_indep_in_race: mean 9.4, median 4, max 60.
• n_indep_prior: mean 4.1, median 1, max 57.
• Among sponsored polls only: mean n_indep_in_race = 1.9, mean n_indep_prior = 0.9. Sponsors cluster heavily in races with few independent benchmarks --- a selection pattern the within-candidate FE design absorbs.

Interaction estimates

Spec	β_sponsored	β interaction (per log-unit)	p (interaction)
A: cand FE	+7.43 (SE 1.12)	—	—
B: + n_indep interaction	+6.31 (SE 1.09)	−1.36 (SE 0.87)	0.117
C: + firm FE	+6.75 (SE 1.17)	−1.47 (SE 0.90)	0.103
D: prior-indep + firm FE	+7.10 (SE 1.17)	−1.92 (SE 1.16)	0.099

Both Spec C (all-time indep density) and Spec D (prior-only indep density) deliver tighter and larger-magnitude interactions than AN-060's all-polls version (−0.78 in Spec B / −1.29 with firm FE). Within firm, each doubling of prior independent polls in a race is associated with about 1.3 pp less sponsor bias.

Tertile split --- monotone

tertile	median n_indep_in_race	n rows	n sponsored	β_sponsored	p
low	2	9,759	281	+8.08	<0.001
medium	6	7,475	28	+8.54	0.005
high	22	7,634	25	+2.71	0.001

The high-density tertile β = +2.71 vs low-density +8.08 is a 5.4 pp cross-tertile drop. In the AN-060 all-polls version the analogue was +6.78 to +4.93 (1.85 pp) with a non-monotone medium spike at +10.46.

Interpretation

The mechanism is clearer with the sharpened metric

The reputation-via-public-visibility prediction is that bias is constrained by the threat of comparison against credible benchmarks. Counting all polls --- including same-side or pollster-self polls --- dilutes the metric with non-comparators. Restricting to independent polls produces a substantially tighter result.

Spec D goes further: only independent polls fielded before this poll's field date count toward the credibility yardstick. This isolates the reputational pressure at the moment of commissioning: when a sponsor commissions a poll after a thick history of credible independent polls in the race, the sponsor slants less.

The directional and tertile patterns line up. The linear interaction is at p = 0.10 on the cleanest spec --- still not at conventional significance, but the cross-tertile contrast is sharp enough to read off the descriptive split alone.

Combined with AN-061 (within-firm-within-race)

AN-061 found that on the rare firm × race cells with both customer types, the sponsor effect attenuates to zero. AN-062 shows the complementary pattern: across all firms, sponsor effect shrinks sharply in races with thick independent benchmarks. Together they identify the reputational constraint at two grains:

• Within-race comparison constraint (AN-061): direct overlap between sponsored and indep polls of the same firm in the same race is rare and, when it happens, attenuates the bias.
• Across-firm comparison constraint (AN-062): the broader market visibility from many independent polls in the same race constrains all sponsored polls, not just the same firm's.

Selection note

Sponsored polls cluster in races with few independent benchmarks (mean n_indep_in_race = 1.9 vs sample-wide 9.4). This is itself a portfolio-differentiation signal: sponsors pick races where the public credibility comparison is thin. The within-candidate FE absorbs this --- the test identifies how bias varies within candidate, across rounds of the same candidate's race, conditional on the candidate appearing somewhere in the visibility distribution.

Follow-ups

1. News-coverage-weighted visibility. A poll's visibility is not the same as the count of polls; it depends on how many reach a public aggregator or news outlet. A weighted version would refine the metric further.
2. Heterogeneity by firm tier. Does the visibility-shrinkage effect differ for large-volume vs small-volume firms? The reputation story predicts it concentrates in firms with reputational stakes to lose; small slant-for-hire firms may be relatively visibility-insensitive.
3. Drop into the §6 synthesis as the primary reputation-mechanism evidence, demoting AN-060 to a robustness mention.