Residual Robustness and Election Result Layer v1 — Methodology and Report

1. Executive Summary

This study evaluates whether an empirical poll-to-election residual layer applied in Additive Log-Ratio / Centered Log-Ratio space improves election hindcasts over the frozen state_plus_dynamics model (OpinionState v1.1 + Dynamics v2 = symmetric_all_history).

Key Findings

1. Window Robustness: The historical residual patterns (S outperformance, V/MP underperformance, KD/L underperformance) are highly robust across 7-day, 14-day, and 21-day trailing consensus windows.
2. Model Variant Comparison:
   • base (state_plus_dynamics): 8-party mean CRPS = 0.8494 (1.0623 in 2018, 0.6364 in 2022).
   • bias_only: 8-party mean CRPS = 6.1842 (severe degradation).
   • noise_only: 8-party mean CRPS = 2.5503 (severe degradation).
   • bias_plus_noise: 8-party mean CRPS = 1.9950 (severe degradation).
3. Recommendation: Retain base (state_plus_dynamics). Naive empirical CLR residual bootstrapping fails because historical structural transitions (specifically Sverigedemokraterna being unpolled at 0.0% in 2002) create severe log-ratio leverage that distorts the simplex when transferred to modern multi-party elections.

2. Residual-Window Robustness Audit (7d, 14d, 21d)

Historical residuals were recomputed across all six modern general elections ($2002, 2006, 2010, 2014, 2018, 2022$) for three trailing lookback windows:

Overall Window MAE

• 7-day Window: Overall 8-party MAE = 0.98 pp
• 14-day Window (Canonical): Overall 8-party MAE = 1.02 pp
• 21-day Window: Overall 8-party MAE = 1.01 pp

Conclusion: The 100% sign-consistent outperformance of S alongside the 100% sign-consistent underperformance of V and MP is completely invariant to the consensus window length.

3. Election Layer Mathematical Formulation

Starting from intermediate sample $z^{(i)}$ from state_plus_dynamics: \(\text{CLR}(z^{(i)}) = \text{CLR}(\theta_t^{(i)}) + S^{(i)}\mathbf{\Delta}_h^{(i)}\)

Four variants were evaluated:

1. base: \(\text{CLR}(z_E^{(i)}) = \text{CLR}(z^{(i)})\)
2. bias_only: \(\bar{\mathbf{r}} = \frac{1}{K} \sum_{k=1}^K \mathbf{r}_{e_k}, \quad \text{CLR}(z_E^{(i)}) = \text{CLR}(z^{(i)}) + \bar{\mathbf{r}}\)
3. noise_only: \(\text{CLR}(z_E^{(i)}) = \text{CLR}(z^{(i)}) + (\mathbf{r}_{e^{(i)}} - \bar{\mathbf{r}})\)
4. bias_plus_noise: \(\text{CLR}(z_E^{(i)}) = \text{CLR}(z^{(i)}) + \mathbf{r}_{e^{(i)}}\)

Chronological Training Sets

• 2018 Hindcasts: Training pool strictly ${2002, 2006, 2010, 2014}$ ($K=4$).
• 2022 Hindcasts: Training pool strictly ${2002, 2006, 2010, 2014, 2018}$ ($K=5$).

4. Empirical Hindcast Results (2018 and 2022)

Overall Performance Across Both Elections (12 Forecast Cases / 108 Party Rows per Variant)

By Election

5. Diagnostic Analysis: Why Non-Parametric CLR Bootstrapping Fails

1. Log-Ratio Outlier Leverage:
   • In 2002, SD was not reported as an individual category by major pollsters (0.0% polled, floored to 0.01% in CLR), but received 1.44% in certified returns.
   • This produced a CLR residual of $\mathbf{r}_{\text{SD}, 2002} = +4.48$.
   • When averaged into $\bar{\mathbf{r}}$ for 2018 ($+1.29$), it acts as a $3.6\times$ multiplier on SD’s modern ~18% support, projecting SD at ~48% and deflating all other parties.
2. Interval Ballooning in Noise Variants:
   • In noise_only and bias_plus_noise, drawing the 2002 residual introduces wild swings ($19.55$ pp interval widths), destroying sharp probabilistic resolution.
3. Double Counting:
   • The 14-day pre-election residual represents not only pure polling bias, but also late-breaking opinion movement and turnout. Because Dynamics v2 already explicitly models transition uncertainty over the forecast horizon, unconstrained residual bootstrapping partially double-counts late movement.

6. Substantive Clarification on Historical Patterns

1. Intra-Bloc Consolidation:
   • The historical pattern where S systematically outperforms pre-election polls (+1.97 pp) while V (-1.06 pp) and MP (-0.83 pp) underperform (-1.89 pp combined) is consistent with intra-bloc consolidation.
   • Aggregate residuals alone cannot prove individual tactical voter switching, as differential turnout or late decision-making within the left-green voting pool could produce similar net shifts.
2. Residual Composition:
   • 14-day poll-to-election residuals reflect a mixture of measurement error, house effects, turnout differential, and genuine late campaign shifts.

7. Recommendation for Production Simulator

• Retain base (state_plus_dynamics) as the standard production election forecast model.
• Do not apply unconstrained empirical CLR residual bootstrapping.
• Any future strategic voting or threshold adjustments must be modeled structurally rather than via historical whole-vector CLR replay.