Same-poll sponsor-vs-top-opponent DiD: +8.2 pp (t = 6.43, n = 239 pairs, 64% positive). The sponsor's candidate's error jumps MORE between matched independent and sponsored polls than the top opponent's error does. Large sponsor-specific shift consistent with either per-candidate slant or sample-design favoring the sponsor's voter base.
Question
GPT-5-pro's 2026-06-14 pre-submission review asked for a within-poll sponsor-vs-opponent gap test that complements the digit-frequency forensics in distinguishing per-candidate manipulation from whole-poll mechanisms.
Design
For each sponsored × matched-independent pair:
- contrast = sponsored_error − indep_error (the sponsor's candidate's jump, the AN-003 placebo at the pair level)
- opp_contrast = same construct for the top opponent in the same race
- DiD = contrast − opp_contrast
A positive DiD says the sponsor's candidate's error jumps MORE between the independent and sponsored polls than the opponent's error does. A whole-poll mechanism that shifts both candidates by the same amount (e.g., a common turnout assumption shift) cancels in the DiD.
Results
| Statistic | Value |
|---|---|
| Pairs with both contrast + opp_contrast | 239 |
| Mean sponsor contrast (per-candidate placebo jump) | +5.51 pp |
| Mean opp_contrast (top opponent's contrast) | −2.66 pp |
| Mean DiD (sponsor − opp) | +8.17 pp |
| sd DiD | 19.64 |
| One-sample t (H0: DiD = 0) | +6.43 |
| Share DiD > 0 | 64% |
| Median DiD | +5.57 pp |
Interpretation
The within-poll gap between the sponsor's candidate and the top opponent widens by +8.17 pp between matched independent polls and the sponsored polls themselves, with a one-sample t of 6.43 and 64% of pairs going in the direction of the headline. This is a strong sponsor-specific shift, but it does NOT cleanly separate per-candidate slant from sample-design-driven slant: both predict a positive DiD because both move sponsor up and opponent down in the sponsored poll relative to the matched independent.
The DiD's role in the mechanism story is to complement, not replace, the digit forensics:
- Digit forensics (§sec:digit) rule out crude per-candidate post-fielding edits (the kind that leave digit signatures).
- The DiD shows the within-poll gap is real and large, but is consistent with sophisticated per-candidate manipulation (no digit trace) or with sample-design slanting that mechanically shifts sponsor up and opponent down (zero-sum within-poll).
- Combined with the §sec:within-firm dispersion and the §sec:roadmap Channel-A inventory, the narrowed space is whole-poll sample-design choices (most plausible) or sophisticated per-candidate editing (cannot be ruled out, but the digit + firm evidence makes it less likely).
Caveats
- The "top opponent" is the candidate whose name maps to the second- highest mean error across the pair-side independent polls; small- muni pairs with sparse opponent coverage are noisier.
- A whole-poll mechanism that systematically shifts only the sponsor (e.g., adding voters who like only the sponsor) would also produce the observed DiD; the test does not require zero-sum within-poll shifts.
Follow-ups
- A within-poll three-way DiD using rank-2 and rank-3 opponents separately could sharpen the mechanism reading.
- A regression of DiD on observable design levers (mode, coverage class, ponderação specificity) would localize the carrier.