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Minimal tilted cycle — 5 voters, margins 3–1–1 (RCV-IRV)

Generated from tilted_cycle_c3_b5_irv.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.

Method: rcv-irv · 1 seat · Expected winner: Cara

Scenario

The same five ballots as tilted_cycle_c3_b5_rr.yaml — the minimal tilted Condorcet cycle from Brandt, Dong & Peters (arXiv:2411.19857), Fig. 1 — counted by instant runoff instead.

Ben holds just one first choice, so IRV eliminates him first; his ballot (Ben > Cara > Ada) transfers to Cara, who wins 3–2 over Ada.

Worth noting what IRV does NOT see: Ada's 4–1 crushing of Ben is the largest majority anywhere on these ballots, and it never enters the count. IRV reads first preferences; the cycle lives in the pairwise margins.

In a cycle there is no Condorcet winner, so IRV cannot be accused of missing one — this is a legitimate answer, not a failure. It simply lands on a different candidate than Copeland's margins tiebreak (Ada) and than leximin (Ada), and agrees with Nanson (Cara). Five voters, four defensible answers: that is what a cycle costs. See the folder README.

Ballots

Each row is one voter's ranking, most-preferred first (N: prefix = N identical ballots).

2:Ada>Ben>Cara
1:Ben>Cara>Ada
2:Cara>Ada>Ben

What the engine says

Round-by-round Sankey diagram: each candidate's votes as a band, and where the votes of an eliminated candidate transferred to.

Where the votes went. Band thickness is votes; a band leaving an eliminated candidate lands on whoever that ballot ranked next, or on inactive if it ranked nobody who was left.

The count, step by step — the rounds and how the winner is reached:

--- RCV / Instant-Runoff Voting (single winner) ---
  Minimal tilted cycle — 5 voters, margins 3–1–1 (RCV-IRV)
 Tabulating 5 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
Ada                2  Hopeful
Cara               2  Hopeful
Ben                1  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Cara               3  Elected
Ada                2  Rejected
Ben                0  Rejected


Winner(s) — RCV / Instant-Runoff Voting (single winner)
  Cara

Full audit — preference matrix, Condorcet, and score distribution

--- Smith Set (the generalized Condorcet winner) ---
The smallest group whose every member beats every candidate outside it —
the honest answer to "who is even in contention?".
   Smith set (3 of 3): Ada, Ben, Cara
   Outside (0):        —
   More than one member ⇒ NO Condorcet winner: the top of the tournament is a
   cycle, so the strongest "candidate" is a set, not a person. Which member of
   the set should win is exactly what Minimax / Ranked Pairs / Schulze disagree
   about — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.
   RCV-IRV winner Cara is INSIDE the Smith set. ✓
      Not guaranteed — RCV-IRV is not Smith-efficient — but it holds here.
   More: 07_Concepts/topics/smith_set.md

Everything in one file: the _tabulated mirror (regenerated on every run; every analysis forced on).

Run it yourself:

python STARVote_LH_tabulation_engine/starvote_larry_hastings.py method_comparisons/minimal_tilted_cycle/cases/tilted_cycle_c3_b5_irv.yaml

See also

More cases in this set: tilted_cycle_c3_b5_rr