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SOURCE FILE:     bv2162_4htk44_irv.yaml
TABULATED FILE:  bv2162_4htk44_irv_tabulated.txt
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election_title: "Nurmi Ex.16 sincere — RCV-IRV: full rankings elect A, not the Condorcet winner"
scenario_description: |-
  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
bv_test_id: BV2162
bv_election_id: 4htk44
bv_results_url: https://bettervoting.com/4htk44/results
paradoxes: [truncation, condorcet-winner]
voting_method: IRV
num_winners: 1
ballots: |-
  33:A>B>C>D
  29:B>A>C>D
  24:C>B>A>D
  17:D>C>B>A
expected_winners:
  - A

# file: bv2162_4htk44_irv.yaml

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TABULATION RESULTS
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--- 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

--- 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