One Vote, Several Parliaments: An Empirical Analysis of the Algorithmic Ambiguity of the Italian Electoral Law on the 2022 General Election Data

2026-07-13

AI Summary

This study addresses an algorithmic ambiguity in Article 83(1)(h) of Italy’s Rosatellum electoral law, which governs proportional seat allocation and may yield different elected candidates from identical vote totals. Leveraging official open data from the 2022 Chamber of Deputies election, the authors empirically replicate and compare the effects of three legally plausible interpretations of the provision—the first such analysis in a real nationwide election. Through end-to-end seat allocation implementation, Monte Carlo simulations, and sequential sensitivity analysis—validated against official results (matching 389 of 391 seats)—they demonstrate that this ambiguity can generate up to 560 distinct parliamentary compositions, altering the election outcomes for six to eight specific candidates. Crucially, these effects remain robust under data perturbations, revealing how textual vagueness in electoral statutes can substantively undermine democratic representation.

Abstract

Crafa's algorithmic analysis of the Italian electoral law (D.P.R. 361/1957, as amended by Law 165/2017, the Rosatellum) showed that the statutory text distributing proportional seats among territories (Art. 83(1)(h)) admits at least three algorithmic interpretations, which can elect different people from the same votes. We test this empirically: we implement the full seat-allocation pipeline (Arts. 77, 83, 83-bis, 84, 85) and run the three interpretations on the complete open data of the Italian general election of 25 September 2022 (Chamber of Deputies). The implementation reproduces the official national apportionment exactly from raw municipal data, matches by name 389 of the 391 seats it models (99.5%), and agrees step by step with the official minutes of the National Central Electoral Office; the two residual mismatches fall on seats that the Chamber's Committee on Elections placed under formal investigation in 2025. On these validated data, the sequential interpretation (Algorithm A) is order-dependent: reversing the constituency order replaces 6 deputies with 6 others, and 1000 random orders produce 560 distinct outcomes; in 29% of orders A strands one or two seats the text cannot assign, and in a further 9% it changes the party composition. The interpretation applied in practice (Algorithm C) is order-independent, provably so absent ties, but differs from A by 8 deputies. The Mattarella-style interpretation (Algorithm B) leaves two seats unassignable under every order. Under the executions documented in practice the statutory compensation preserves every party's national seat total, and a Monte Carlo analysis shows the named differences between interpretations are robust to input noise well beyond the residual uncertainty of the data: the ambiguity changes which persons are elected and where, not party strength. On real data, this confirms Crafa's central claim.

Problem

• electoral law
• algorithmic ambiguity
• seat allocation
• Italian general election
• proportional representation

Innovation

• algorithmic ambiguity
• electoral law
• seat allocation
• empirical validation
• Monte Carlo analysis