Felsenthal Ex.8 — IRV: a third winner, Clara¶

Generated from bv2154_wq6yv7_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: Clara

▶ Live on BetterVoting: vote · results ↗ (election wq6yv7 · test BV2154).

Scenario¶

Race 2 of 3 in the three-winners election (BV2154, bvid wq6yv7; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A3, Example 8 — see bv2154_wq6yv7_approval.yaml for the setup. The same 15 voters' full rankings under instant runoff: first choices April 6, Bruce 4, Clara 5, so BRUCE — the Condorcet winner — is deleted first, and Clara beats April 9–6. IRV elects Clara: neither the approval race's April (the absolute loser) nor the pairwise winner Bruce. One electorate, three winners across the three races. Live results: https://bettervoting.com/wq6yv7/results

Ballots¶

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

6:April>Bruce>Clara
4:Bruce>Clara>April
1:Clara>April>Bruce
4:Clara>Bruce>April

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.8 — IRV: a third winner, Clara
 Tabulating 15 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
April              6  Hopeful
Clara              5  Hopeful
Bruce              4  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Clara              9  Elected
April              6  Rejected
Bruce              0  Rejected


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

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): Bruce
   Outside (2):        April, Clara
   One member ⇒ Bruce is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner Clara is OUTSIDE the Smith set. ✗
      Every member of the set (Bruce) beats Clara head-to-head, yet
      RCV-IRV elected Clara 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/bv2154_wq6yv7_irv.yaml

See also¶