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

Abstract

Crafa's algorithmic analysis of the Italian electoral law (the "Rosatellum") showed that the statutory text describing the territorial distribution of proportional seats (Art. 83(1)(h)) admits at least three different algorithmic interpretations, which may elect different people from the same votes. We test that conclusion empirically: we implement the full seat-allocation pipeline of the law (Arts. 77, 83, 83-bis, 84, 85) and run the three interpretations on the complete open data of the 2022 Italian general election (Chamber of Deputies). The implementation reproduces the official national apportionment exactly, matches by name 389 of the 391 seats it models (99.5%), and agrees step by step with the official minutes. On these validated data, the sequential interpretation (Algorithm A) is order-dependent: reversing the processing order of the constituencies replaces 6 deputies with 6 others, and 1,000 random orders produce 560 distinct outcomes; a near-exhaustive sweep of 15 million orders closes the set of order-contingent deputies at 140, while 764 of the 1,139 candidates of the admitted lists (67%) are elected under no order at all. In 29% of the sampled orders A also strands seats it cannot assign by any rule stated in the text, and in a further 9% it fills the Chamber with a different party composition. The interpretation applied in practice (Algorithm C) is order-independent, provably so in the absence of ties, but differs from A by 8 deputies. Under the Mattarella-style interpretation (Algorithm B) the documented order leaves two seats unassignable, and 46% of sampled orders strand one to three seats. A Monte Carlo analysis shows the named differences robust to input noise well beyond the residual uncertainty of the data: the ambiguity changes which persons are elected and in which territories, and leaves party strength untouched only where the text's procedure completes.