election_title: "Equal ranks — a bare majority puts Amira top, and Basil still wins"
scenario_description: |-
  Figure 10 of Théo Delemazure & Dominik Peters, "Generalizing Instant Runoff Voting to Allow Indifferences" (EC'24, arXiv:2404.11407), cast as a 200-member co-op electing a general manager. The paper's percentages are doubled so every bloc count clears the house minimum of 6; scaling every weight by the same factor leaves every winner unchanged.
  The profile is built to embarrass an axiom that sounds obvious. Amira sits in the TOP indifference class of 102 of 200 voters — 94 who rate her equal-first with Basil, plus 8 who put her alone on top — so a rule that promised "elect a candidate a majority ranks first" would have to elect Amira. But look at the same ballots the other way: 98 voters strictly prefer Basil to Amira, and only 8 strictly prefer Amira to Basil. The other 94 rate them equal. Basil is the Condorcet winner.
  This is the profile the paper uses to argue that "select some majority alternative" is the WRONG axiom for equal-rank ballots, and that its own weaker axiom — respect for cohesive majorities — is the right one. Split-IRV elects Amira (splitting the 94 equal-first ballots half a point each drops Basil to last and eliminates him in round 1). Approval-IRV elects Basil. So does STAR, and so does the pairwise count.
  Why the file is a SCORE case and not a ranked one: a 0-5 ballot expresses a weak order natively — two 5s are an equal-first, exactly as "Amira=Basil" is — so the paper's profile can be recorded here without inventing a ballot type. The scores below are one reading of the paper's ordinal profile, and a reading does add information the paper's weak order does not carry. That freedom was measured rather than assumed: across 20,000 random strictly-decreasing 0-5 encodings of this same weak order, STAR elects Basil in 98.5% and never elects anyone else (the remaining 1.5% are exact scoring ties). Basil is not an artifact of the numbers chosen.
  For the Approval-IRV and Split-IRV counts on these same ballots run tools_adam/pref_voting_tabulation_engine/approval_irv_report.py — nothing in the LH engine or on BetterVoting counts either rule, because deployed instant runoff rejects an equal rank as an overvote.
paradoxes: [condorcet-winner]
voting_method: STAR
num_winners: 1
ballots: |-
  Count:Amira,Basil,Cora,Dmitri
  94:5,5,2,0    # Amira and Basil equal-first, then Cora, then Dmitri
  8:5,4,2,0     # the only bloc that strictly prefers Amira to Basil
  50:0,4,5,2    # Cora first, Basil a strong second
  48:0,4,2,5    # Dmitri first, Basil a strong second
expected_winners: [Basil]

# file: equal_rank_majority_alternative.yaml