Felsenthal Ex.3 Combined — Runoff/IRV: Bruno won both districts, Alma wins the whole¶

Generated from bv2149_byk9v2_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: Alma

▶ Live on BetterVoting: vote · results ↗ (election byk9v2 · test BV2149).

Scenario¶

Race 1 of 2 in the Combined stage of the Felsenthal Reinforcement-paradox trio (BV2149, bvid byk9v2; 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). The amalgamated electorate: the 32 voters of Districts I (BV2147) and II (BV2148) together, ceteris paribus. No first-round majority (Alma 10, Bruno 14, Cora 8), so CORA is deleted — and Alma beats Bruno 17–15 in the runoff. Bruno won BOTH districts separately; amalgamating two electorates that each chose Bruno makes plurality-with-runoff (run as IRV, identical for three candidates) elect Alma. That violates the Reinforcement postulate — the multiple-districts / inconsistency paradox, live on BetterVoting. The combined pairwise preferences form a Condorcet CYCLE (Alma>Bruno 17–15, Bruno>Cora 18–14, Cora>Alma 21–11), so no Condorcet argument rescues the flip: the procedure simply disagrees with itself. Live results: https://bettervoting.com/byk9v2/results

Ballots¶

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

4:Alma>Bruno>Cora
6:Alma>Cora>Bruno
1:Bruno>Alma>Cora
13:Bruno>Cora>Alma
7: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 Combined — Runoff/IRV: Bruno won both districts, Alma wins the whole
 Tabulating 32 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
Bruno             14  Hopeful
Alma              10  Hopeful
Cora               8  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Alma              17  Elected
Bruno             15  Rejected
Cora               0  Rejected


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

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 Alma 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/bv2149_byk9v2_irv.yaml

See also¶