Territorial MRP: history and evidence

01 / Scope and electoral geography

The historical v4 implementation uses Rosatellum single-member constituencies. This document separates its reported backtests from an area-agnostic Stan prototype. An electoral reform requires new aggregation rules, not an automatic transfer of validation results.

As of 5 October 2026, the project’s anticipated 8 October enactment is not treated as an accomplished event. “Stabilicum” rules and geographical mappings require official verification.

02 / Territorial MRP specification

Multilevel Regression and Poststratification combines hierarchical shrinkage with population-weighted cell estimates. Here, poststratification cells are geographical units; individual MRP would require respondent-level survey data and joint demographic population counts. Ecological associations do not identify individual voting behaviour.

The Stan prototype models positive concentrations α = exp(η), with hierarchical effects and territorial predictors. Cell shares are α / sum(α); known weights aggregate them to area shares. A Dirichlet-Multinomial likelihood jointly models party counts and overdispersion, without guaranteeing unbiased estimates. A separate national-poll likelihood provides a probabilistic constraint and replicated polls support posterior predictive checks.

The supplied PyMC v4 aggregates covariates before regression. Explicit cell weights and the national-poll likelihood are A4 extensions. The weighted area concentration is a modelling closure, not the exact distribution of summed DM counts.

03 / Historical backtests: reported evidence

CDX = centre-right. MAE and RMSE are different metrics. White paper v1.2 describes out-of-sample predictions; these were not rerun here. Covariate reference years alone do not establish ex ante forecasting: release dates and auditable training/evaluation splits are required.

CI90 coverage: 39.2% across the full 252-observation validation set reported in the white paper. Undercoverage remains unresolved. Small samples may contribute, but the reported prior comparisons do not establish a unique cause. Liguria (N=4) is only indicative.

04 / Stan prototype: partial calibration evidence

A4, 2 October 2026: CmdStan 2.38.0; 20 synthetic areas, 4 parties; maximum R-hat 1.0041, minimum bulk/tail ESS 1746/1697, zero divergences. A4-bis, 5 October: 100 SBC simulations attempted, 95 complete fits, 73/95 satisfying all MCMC criteria.

Holm adjustment across 132 tests: no rejection at 5%; minimum adjusted p = 0.1467. Non-rejection does not establish uniformity. Completed fits include 14 divergences across 11 fits. Five native Windows crashes remain unexplained; completion-conditioned results may be subject to selection.

SBC tests computation under the assumed generative model, not real-world electoral performance. Linux replication and failure diagnosis remain outstanding.

05 / Layer 0: provenance and denominators

A2 identifies 20 candidate features. Effective dimension from the correlation spectrum is 7.16 unweighted and 5.07 population-weighted, not an optimal predictor count. A4-bis integrates ten provisional features using synthetic data.

Adult indicators use ages 20+: the 15–19 band cannot isolate ages 18–19, which are excluded. Employment and education retain their own denominators. Residents are not the electorate; validated denotes agent checks, not complete historical boundary harmonisation.

06 / Limitations and external validity

Area-level shares do not identify individual preferences. Historical undercoverage requires additional data and checks of model specification, dependence and temporal validation. Increasing sample size alone is not a demonstrated remedy.

Reanalysing 2022 votes with 2023–2024 covariates will be retrospective, not ex ante forecasting. SBC does not change that status. Electoral rules and coalition shifts threaten transportability; separate temporal backtests, posterior predictive checks and official mappings are prerequisites for public use of the new engine.

07 / References and provenance

Numerical sources: white paper v1.2 (§§5–6), A4 (2 October), A4-bis and A2 (5 October), Data Agent 0.2.1 (2 October 2026). The October audit reports are local artifacts without a linked public release.

White paper v1.2 EN · Methodology (IT) · Historical validation (IT) · Public repository (AGPL v3).

The inspected frontend clone does not contain the historical v4 engine source. A verified file permalink remains unavailable; the general repository link does not establish its availability.

08 / Living documentation; separate release

This page is intended to accompany the retirement of the “Sondaggio 2027” mode; it does not disable that interface. The new engine requires verified rules, geography and observed-data performance before release. Production readiness has not been established.