Felsenthal Ex.2 after the raise — Runoff/IRV: Ben loses by GAINING support¶

Generated from bv2146_krk2px_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: Ada

▶ Live on BetterVoting: vote · results ↗ (election krk2px · test BV2146).

Scenario¶

Race 1 of 3 in the Felsenthal runoff-paradoxes election, part 2 of 2 (BV2146, bvid krk2px; BV-confirmed). 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 2 (continued). Identical to BV2145 except one datum, ceteris paribus: the two Cleo>Ben>Ada voters RAISE Ben to first (Ben>Cleo>Ada) — strictly more support for Ben, nothing else changes. First choices become Ada 5, Ben 8, Cleo 4, so the runoff procedure (IRV; identical for three candidates) now eliminates CLEO instead of Ada — and Ada beats Ben 9–8. Ben, who won BV2145, loses precisely because two voters moved him UP: the lack-of-monotonicity (more-is-less) paradox, Felsenthal's model CONDITIONAL paradox. Confirmed live on BetterVoting. Live results: https://bettervoting.com/krk2px/results

Ballots¶

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

3:Ada>Ben>Cleo
2:Ada>Cleo>Ben
4:Ben>Ada>Cleo
2:Ben>Cleo>Ada
4:Cleo>Ada>Ben
2:Ben>Cleo>Ada

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.2 after the raise — Runoff/IRV: Ben loses by GAINING support
 Tabulating 17 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
Ben                8  Hopeful
Ada                5  Hopeful
Cleo               4  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Ada                9  Elected
Ben                8  Rejected
Cleo               0  Rejected


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

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): Ada
   Outside (2):        Ben, Cleo
   One member ⇒ Ada is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner Ada 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/bv2146_krk2px_irv.yaml

See also¶