====================================================================== SOURCE FILE: equal_rank_clone_with.yaml TABULATED FILE: equal_rank_clone_with_tabulated.txt ====================================================================== election_title: "Equal ranks — Costa joins Chen's ticket, and Split-IRV hands them the win" scenario_description: |- Figure 9 of Théo Delemazure & Dominik Peters, "Generalizing Instant Runoff Voting to Allow Indifferences" (EC'24, arXiv:2404.11407): the profile on which Split-IRV fails independence of clones. The paper's counts are tripled so every bloc clears the house minimum of 6; scaling every weight by the same factor leaves every winner unchanged. Chen and Costa are perfect clones — every voter rates them identically, which is what "clone" means, and why they share an initial here. The matched file equal_rank_clone_without.yaml is the SAME election with Costa withdrawn, so the pair reads as one election with one thing changed. Split-IRV, round 1 with Costa running: Bruno 12, Chen 12, Costa 12, Alma 9. The 27 voters who rate Alma, Chen and Costa equal-first split their one point three ways, which leaves Alma the lowest and eliminates her immediately; the clone pair goes on to win. Withdraw Costa and those same 27 voters split two ways instead: Chen 19.5, Alma 13.5, Bruno 12, so BRUNO goes out first and Alma wins the final pairing. Adding a clone of a loser changed the winner: that is exactly the spoiler effect independence of clones forbids, and Split-IRV is the generalization actually deployed in the field — the John Muir Trust and the London Mathematical Society have used it for trustee and council elections since the late 1990s. Approval-IRV is clone-independent (Theorem 3.2) and elects Alma in both files. So does STAR: the extra identical ballot column adds nothing to the scoring round that was not already there, which is the same reason Approval-IRV survives the test. One honest wrinkle the file shows rather than hides: perfect clones cast IDENTICAL ballots, so Chen and Costa post identical score totals and STAR's second finalist slot is a genuine tie. The runoff is unaffected — Alma beats either of them on the same ballots — but the tiebreaker banner in the report is real, not a defect in the case. For the Approval-IRV and Split-IRV counts run tools_adam/pref_voting_tabulation_engine/approval_irv_report.py; --drop Costa reproduces the companion file's count from this one. paradoxes: [clone-teaming, condorcet-winner] voting_method: STAR num_winners: 1 ballots: |- Count:Alma,Bruno,Chen,Costa 27:5,0,5,5 # Alma and the whole Chen/Costa ticket equal-first 12:3,5,0,0 # Bruno first, Alma second, the ticket last 6:3,0,5,5 # the ticket first, Alma second, Bruno last expected_winners: [Alma] # file: equal_rank_clone_with.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Equal ranks — Costa joins Chen's ticket, and Split-IRV hands them the win === Figure 9 of Théo Delemazure & Dominik Peters, "Generalizing Instant Runoff Voting to Allow Indifferences" (EC'24, arXiv:2404.11407): the profile on which Split-IRV fails independence of clones. The paper's counts are tripled so every bloc clears the house minimum of 6; scaling every weight by the same factor leaves every winner unchanged. Chen and Costa are perfect clones — every voter rates them identically, which is what "clone" means, and why they share an initial here. The matched file equal_rank_clone_without.yaml is the SAME election with Costa withdrawn, so the pair reads as one election with one thing changed. Split-IRV, round 1 with Costa running: Bruno 12, Chen 12, Costa 12, Alma 9. The 27 voters who rate Alma, Chen and Costa equal-first split their one point three ways, which leaves Alma the lowest and eliminates her immediately; the clone pair goes on to win. Withdraw Costa and those same 27 voters split two ways instead: Chen 19.5, Alma 13.5, Bruno 12, so BRUNO goes out first and Alma wins the final pairing. Adding a clone of a loser changed the winner: that is exactly the spoiler effect independence of clones forbids, and Split-IRV is the generalization actually deployed in the field — the John Muir Trust and the London Mathematical Society have used it for trustee and council elections since the late 1990s. Approval-IRV is clone-independent (Theorem 3.2) and elects Alma in both files. So does STAR: the extra identical ballot column adds nothing to the scoring round that was not already there, which is the same reason Approval-IRV survives the test. One honest wrinkle the file shows rather than hides: perfect clones cast IDENTICAL ballots, so Chen and Costa post identical score totals and STAR's second finalist slot is a genuine tie. The runoff is unaffected — Alma beats either of them on the same ballots — but the tiebreaker banner in the report is real, not a defect in the case. For the Approval-IRV and Split-IRV counts run tools_adam/pref_voting_tabulation_engine/approval_irv_report.py; --drop Costa reproduces the companion file's count from this one. --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist Note: Chen and Costa tied at 165 in the Scoring Round, and the lot rung (the ballots could not separate them) advanced Chen. The * marks who advanced, not who scored highest. | * Alma | Bruno | * Chen | Costa | --------------------------------------------------------------------------- * Alma > | --- |33 - 0 - 12 |12 - 27 - 6 |12 - 27 - 6 | Bruno > | 12 - 0 - 33 | --- |12 - 0 - 33 |12 - 0 - 33 | * Chen > | 6 - 27 - 12 |33 - 0 - 12 | --- | 0 - 45 - 0 | Costa > | 6 - 27 - 12 |33 - 0 - 12 | 0 - 45 - 0 | --- | [Condorcet Winner] Condorcet Winner: Alma — matches the STAR winner [Condorcet Loser] Condorcet Loser: Bruno — loses every head-to-head matchup --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 45 ballots. Count × Alma,Bruno,Chen,Costa 27 × 5, 0, 5, 5 12 × 3, 5, 0, 0 6 × 3, 0, 5, 5 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg Alma 27 0 18 0 0 0 | 189 4.2 Bruno 12 0 0 0 0 33 | 60 1.3 Chen 33 0 0 0 0 12 | 165 3.7 Costa 33 0 0 0 0 12 | 165 3.7 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Alma -- 189 -- First place Chen -- 165 -- Tied for second place Costa -- 165 -- Tied for second place Bruno -- 60 Alma advances, but there's a two-way tie for second. [STAR Voting: Scoring Round: First tiebreaker] The candidate preferred in the most head-to-head matchups advances. Chen -- 0 -- Tied for second place Costa -- 0 -- Tied for second place Equal Support -- 45 There's still a two-way tie for second. [STAR Voting: Scoring Round: Second tiebreaker] The candidate with the most votes of score 5 advances. Chen -- 33 -- Tied for second place Costa -- 33 -- Tied for second place There's still a two-way tie for second. *** No official tie-breaking lot numbers were provided. Ties are resolved using a fallback order: CSV column order. Lot-number priority order: ['Alma', 'Bruno', 'Chen', 'Costa'] [Tiebreaker: Lot Number Priority] Tie among: ['Chen', 'Costa'] Resolved: ['Chen'] (selected by lot-number priority). [Lot-decided tie — rare] ⚠ The ballots did not break this tie: the deterministic rungs (pairwise / score, then five-star) all came back equal, so the pre-published LOT order chose among the tied candidates — the result here was set by lot, not by the votes. Usually the "dead rung": no tied candidate held a score-5 vote (five-star counts fives, not fours). Verify the tied candidates' 5-counts. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Alma -- 12 -- First place Chen -- 6 Equal Support -- 27 Alma wins. Runoff math: 45 ballots cast − 27 Equal Support (no preference between the two finalists) ── 18 voters with a preference (majority = 10) Alma 12 (67%) · Chen 6 (33%) [STAR Voting: Winner — STAR Voting Method (single winner)] Alma