Margins matter — RCV-IRV elects the third answer (Cocoa)¶

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

Method: RCV-IRV (Instant Runoff) · 1 seat · Expected winner: Cocoa

▶ Live on BetterVoting: vote · results ↗ (election kdjjkq · test BV2251).

Scenario¶

The same twelve gelato ballots, counted by instant runoff. First choices are Almond 5, Cocoa 4, Berry 3, so Berry — the BORDA winner and the margin-weighted Copeland winner — is eliminated FIRST. All three of Berry's ballots rank Cocoa next, so they transfer intact and Cocoa wins 7-5. This is the fourth distinct answer the same electorate produces: Plurality says Almond, RCV-IRV says Cocoa, Borda says Berry, and Copeland says nobody (a three-way tie). Not a center-squeeze case — there is no Condorcet winner for IRV to miss, because the pairwise contests form a cycle.

Ballots¶

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

Almond>Berry>Cocoa
Almond>Berry>Cocoa
Almond>Berry>Cocoa
Almond>Berry>Cocoa
Almond>Berry>Cocoa
Berry>Cocoa>Almond
Berry>Cocoa>Almond
Berry>Cocoa>Almond
Cocoa>Almond>Berry
Cocoa>Almond>Berry
Cocoa>Berry>Almond
Cocoa>Berry>Almond

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) ---
  Margins matter — RCV-IRV elects the third answer (Cocoa)
 Tabulating 12 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
Almond             5  Hopeful
Cocoa              4  Hopeful
Berry              3  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Cocoa              7  Elected
Almond             5  Rejected
Berry              0  Rejected


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

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): Almond, Berry, Cocoa
   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 Cocoa 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/copeland_vs_borda_margins/cases/margins_irv.yaml

Margins matter — RCV-IRV elects the third answer (Cocoa)¶

Scenario¶

Ballots¶

What the engine says¶

Full audit — preference matrix, Condorcet, and score distribution¶

See also¶