Felsenthal Ex.3 District I — Runoff/IRV: Bruno wins the runoff¶

Generated from bv2147_9gdrqg_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: Bruno

▶ Live on BetterVoting: vote · results ↗ (election 9gdrqg · test BV2147).

Scenario¶

Race 1 of 2 in District I of the Felsenthal Reinforcement-paradox trio (BV2147, bvid 9gdrqg; BV-confirmed; the trio is BV2147/48/49). Source: Dan S. Felsenthal, "Review of Paradoxes Afflicting Various Voting Procedures Where One Out of m Candidates (m ≥ 2) Must Be Elected", University of Haifa / LSE, revised 26 May 2010; Appendix A2, Example 3 (the Reinforcement paradox). District I: 17 voters. No first-round majority (Alma 4, Bruno 6, Cora 7), so plurality-with-runoff — run as IRV, identical for three candidates — deletes Alma, and Bruno beats Cora 10–7. Note the district's pairwise preferences form a Condorcet CYCLE (Alma>Bruno 10–7, Bruno>Cora 10–7, Cora>Alma 12–5): no Condorcet winner exists here. Bruno also wins District II (BV2148) outright — yet the amalgamated electorate (BV2149) elects Alma under the same procedure. Live results: https://bettervoting.com/9gdrqg/results

Ballots¶

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

4:Alma>Bruno>Cora
1:Bruno>Alma>Cora
5:Bruno>Cora>Alma
6:Cora>Alma>Bruno
1:Cora>Bruno>Alma

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) ---
  Felsenthal Ex.3 District I — Runoff/IRV: Bruno wins the runoff
 Tabulating 17 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
Cora               7  Hopeful
Bruno              6  Hopeful
Alma               4  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Bruno             10  Elected
Cora               7  Rejected
Alma               0  Rejected


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

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): Alma, Bruno, Cora
   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 Bruno 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/felsenthal_paradoxes/cases/bv2147_9gdrqg_irv.yaml

See also¶