Felsenthal Ex.3 District II — Runoff/IRV: Bruno wins in round one¶

Generated from bv2148_h87k6v_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 h87k6v · test BV2148).

Scenario¶

Race 1 of 2 in District II of the Felsenthal Reinforcement-paradox trio (BV2148, bvid h87k6v; 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 II: 15 voters — 6×(Alma>Cora>Bruno), 8×(Bruno>Cora>Alma), 1×(Cora>Alma>Bruno). Bruno is ranked first by an absolute majority (8 of 15) and wins in the first round; no runoff is needed. Bruno is also this district's Condorcet winner (beats Alma 8–7, Cora 8–7). Bruno wins District I too (BV2147) — yet the amalgamated electorate (BV2149) elects Alma under the same procedure. Live results: https://bettervoting.com/h87k6v/results

Ballots¶

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

6:Alma>Cora>Bruno
8:Bruno>Cora>Alma
1:Cora>Alma>Bruno

What the engine says¶

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

--- RCV / Instant-Runoff Voting (single winner) ---
  Felsenthal Ex.3 District II — Runoff/IRV: Bruno wins in round one
 Tabulating 15 ballots (ranked ballots).

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Bruno              8  Elected
Alma               6  Rejected
Cora               1  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 (1 of 3): Bruno
   Outside (2):        Alma, Cora
   One member ⇒ Bruno is the Condorcet winner, beating every rival head-to-head.
   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/bv2148_h87k6v_irv.yaml

See also¶