Felsenthal Ex.2 — Runoff/IRV: the Condorcet winner is eliminated first¶

Generated from bv2145_6fj2kg_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: Ben

▶ Live on BetterVoting: vote · results ↗ (election 6fj2kg · test BV2145).

Scenario¶

Race 1 of 3 in the Felsenthal runoff-paradoxes election, part 1 of 2 (BV2145, bvid 6fj2kg; 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 (plurality with runoff). 17 voters, three candidates. Ada is the Condorcet winner (beats Ben 9–8 and Cleo 9–8; social ordering Ada>Ben>Cleo) but has the FEWEST first choices (Ada 5, Ben 6, Cleo 6). Plurality-with-runoff — run here as IRV, which is identical for three candidates — eliminates Ada first, and Ben beats Cleo 9–8. The Condorcet winner paradox, plus Felsenthal's SCC note: had Cleo withdrawn, Ada would have won the first round outright (9 of 17). The non-monotonicity half of the lesson is the paired election BV2146. Live results: https://bettervoting.com/6fj2kg/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:Cleo>Ben>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 — Runoff/IRV: the Condorcet winner is eliminated first
 Tabulating 17 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
Ben                6  Hopeful
Cleo               6  Hopeful
Ada                5  Rejected

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


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

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 Ben is OUTSIDE the Smith set. ✗
      Every member of the set (Ada) beats Ben head-to-head, yet
      RCV-IRV elected Ben anyway. RCV-IRV is not Smith-efficient (nor
      Condorcet-efficient) — this is the shape a center squeeze leaves behind.
   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/bv2145_6fj2kg_irv.yaml

See also¶