Nurmi Ex.16 sincere — RCV-IRV: full rankings elect A, not the Condorcet winner¶

Generated from bv2162_4htk44_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: A

▶ Live on BetterVoting: vote · results ↗ (election 4htk44 · test BV2162).

Scenario¶

Race 2 of 3 in the RCV-IRV truncation pair, part 1 of 2 (BV2162, bvid 4htk44; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A6, Example 16, due to Nurmi (1999: 63) — see bv2162_4htk44_star.yaml for the setup. The same 103 full rankings under instant runoff: no first-count majority (33/29/24/17), D is eliminated and transfers to C (41), then B (29) is eliminated — and A wins 62. Sincere, complete ballots elect A over the Condorcet winner B; and part 2 (BV2163) shows the 17 D-first voters doing BETTER by ranking only D. Their reward for ranking honestly and fully is their third choice. Live results: https://bettervoting.com/4htk44/results

Ballots¶

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

33:A>B>C>D
29:B>A>C>D
24:C>B>A>D
17:D>C>B>A

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) ---
  Nurmi Ex.16 sincere — RCV-IRV: full rankings elect A, not the Condorcet winner
 Tabulating 103 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
A                 33  Hopeful
B                 29  Hopeful
C                 24  Hopeful
D                 17  Rejected

ROUND 2
Candidate      Votes  Status
-----------  -------  --------
C                 41  Hopeful
A                 33  Hopeful
B                 29  Rejected
D                  0  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
A                 62  Elected
C                 41  Rejected
B                  0  Rejected
D                  0  Rejected


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

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 4): B
   Outside (3):        A, C, D
   One member ⇒ B is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner A is OUTSIDE the Smith set. ✗
      Every member of the set (B) beats A head-to-head, yet
      RCV-IRV elected A 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/bv2162_4htk44_irv.yaml

See also¶