[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85351-en":3,"doc-seo-85351-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},85351,13056703020460,"Valentina","https://ap-avatar.wpscdn.com/avatar/be000253dac470eee5d?_k=1778207105932848923",8,"Research & Report","One Vote, Several Parliaments","Electoral laws are algorithms whose natural-language descriptions can be ambiguous, yielding different parliamentary compositions from identical votes. This paper empirically studies the Italian electoral law for the 25 September 2022 general election (Chamber of Deputies), focusing on the territorial allocation of proportional seats that admits multiple algorithmic interpretations. A faithful implementation is validated against official apportionment records, enabling a quantitative comparison of three admissible algorithms and their effects on elected persons, territories, and party composition under robustness to input noise.","arXiv :2607 . 11676v1 [ cs .CY] 13 Jul 2026  \nOne Vote, Several Parliaments:  \nAn Empirical Analysis of the Algorithmic Ambiguity of the Italian Electoral Law on the 2022 General Election Data  \nPaolo Coppola  \nDepartment of Mathematics, Computer Science and Physics, University of Udine  \n[paolo.coppola@uniud.it](paolo.coppola@uniud.it)  \nJuly 2026  \nAbstract  \nCrafa’s algorithmic analysis of the Italian electoral law (D.P.R. 361/1957, as amended by Law 165/2017, the so-called 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 assign seats to different territories and hence 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 and 85) and run the three interpretations on the complete open data of the Italian general election of  \n25 September 2022 (Chamber of Deputies) . The implementation reproduces the official national apportionment exactly from the 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 disagreements fall on two of the four seats that the Chamber’s own Committee on Elections placed under formal investigation in July 2025: in one case because the official record itself reports the decisive percentage tallies in two inconsistent ways, in the other because the decisive decimal comparison lies within the uncertainty of the verified vote counts. 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; in 29% of the sampled orders A also strands one or two 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 electoral practice (Algorithm C) is order-independent, provably so in the absence of ties, but differs from A by 8 deputies.  \nUnder the Mattarella-style interpretation (Algorithm B) two seats cannot be assigned by the rules stated in the text under any order, as historically occurred in 1994, 1996 and  \n2001. Under the executions documented in practice the statutory compensation preserves the national seat totals of every coalition and list, and a Monte Carlo analysis shows that 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 in which territories, and leaves party strength untouched only where the text’s procedure completes. On real data, this confirms the central claim of Crafa’s analysis.  \n1 Introduction  \nElectoral laws are algorithms written in natural language. They take as input the votes cast by citizens and produce as output the composition of a parliament. When the naturallanguage description of this computation is ambiguous, the same electoral input may lead to different outputs, depending on which of the admissible readings of the text is executed. This is not a hypothetical concern: Crafa [2, 1] showed that the text of the Italian electoral  \nlaw currently in force, the consolidated law for the election of the Chamber of Deputies (D.P.R. 361/1957) as amended by Law 165/2017 (“Rosatellum”), admits several distinct algorithmic interpretations of the procedure that distributes proportional seats among the electoral constituencies (circoscrizioni), and that these interpretations can produce different territorial seat assignments. Crafa’s analysis identifies three algorithms, here called A, B and C (Section 4), all algorithmically admissible readings of the statutory text: a notion we define and delimit in Section 4.1, deli","cbCaid6yMYq4Suh4","https://ap.wps.com/l/cbCaid6yMYq4Suh4","pdf",661189,1,48,"English","en",105,"# Abstract\n# Introduction\n## Problem: ambiguous natural-language electoral procedures\n## Contributions and implementation approach","[{\"question\":\"What source of ambiguity does the paper analyze in the Italian electoral law?\",\"answer\":\"The ambiguity comes from the statutory text describing territorial distribution of proportional seats, which allows at least three distinct algorithmic interpretations to be executed.\"},{\"question\":\"How is the seat-allocation pipeline implemented and validated?\",\"answer\":\"The paper implements the full seat-allocation pipeline (including arts. 77, 83, 83-bis, 84, 85) on the raw municipal open data and validates results against official national apportionment and electoral office records.\"},{\"question\":\"How do different algorithmic interpretations affect election outcomes?\",\"answer\":\"Different interpretations can change which individuals are elected and in which territories, while party strength remains largely unchanged only when the text procedure completes.\"}]",1784202708,121,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"one-vote-several-parliaments","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/one-vote-several-parliaments/85351/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-20","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What source of ambiguity does the paper analyze in the Italian electoral law?","Question",{"text":75,"@type":76},"The ambiguity comes from the statutory text describing territorial distribution of proportional seats, which allows at least three distinct algorithmic interpretations to be executed.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is the seat-allocation pipeline implemented and validated?",{"text":80,"@type":76},"The paper implements the full seat-allocation pipeline (including arts. 77, 83, 83-bis, 84, 85) on the raw municipal open data and validates results against official national apportionment and electoral office records.",{"name":82,"@type":73,"acceptedAnswer":83},"How do different algorithmic interpretations affect election outcomes?",{"text":84,"@type":76},"Different interpretations can change which individuals are elected and in which territories, while party strength remains largely unchanged only when the text procedure 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