======================================================================
SOURCE FILE:     bv2282_hf3ckp_brams_irv.yaml
TABULATED FILE:  bv2282_hf3ckp_brams_irv_tabulated.txt
======================================================================

election_title: "Brams 1982 — twenty-one voters, and the Condorcet winner goes out second"

scenario_description: |-
  A 21-voter, 4-candidate profile from Stephen J. Brams, "The AMS Nomination
  Procedure Is Vulnerable to 'Truncation of Preferences'," Notices of the
  American Mathematical Society 29:2 (February 1982), 136-138 — reproduced via
  rangevoting.org, which cites it as an RCV-IRV example.

  Counted by Hare: B leads on 7 first choices, F (3) is eliminated and sends 3
  to N, then G is eliminated on 6 and sends all 6 to B, who wins 13 of 21. But
  G beats B head-to-head 14-7, and beats N 13-8 and F 18-3 — G is the Condorcet
  winner, and is eliminated one round before the finish.

  It is the smallest example in this folder: 21 ballots, checkable on paper in
  about a minute, which is what makes it the one to hand someone who does not
  want to take a 303-voter profile on trust.

  PROVENANCE, STATED CAREFULLY. The profile is Brams's; the RCV-IRV reading is
  rangevoting.org's. Brams's paper is about vulnerability to PREFERENCE
  TRUNCATION — voters ranking only some candidates — which is a different
  argument from the Condorcet failure shown here, and we could not confirm from
  the abstract whether the AMS procedure of the day was Hare specifically. So:
  cite Brams for the ballots, and cite this file for what Hare does with them.
  Do not write "Brams showed that IRV..." — he did not, in this paper.

  Candidate labels B, G, N, F are Brams's own and are kept for traceability to
  the source, which is why they are neither alphabetical nor in reading order.

  BV-CONFIRMED. Race 1 of live election hf3ckp (Test ID BV2282) is these 21
  ballots counted by BetterVoting's own IRV tabulator, and it elects B, matching
  this file exactly; race 2 is the same ballots under Ranked Robin and elects G.
  tieBreakType 'none' in both. Frozen export: bv2282_hf3ckp_bv_export.json.

  Live on BetterVoting: https://bettervoting.com/hf3ckp
  Live results: https://bettervoting.com/hf3ckp/results
bv_test_id: BV2282
bv_election_id: hf3ckp
bv_results_url: https://bettervoting.com/hf3ckp/results
voting_method: RCV_IRV
num_winners: 1

# Source profile: Brams (1982), via https://rangevoting.org/rangeVirv.html
# section 12. Claim-checked in this folder's README.md.
ballots: |-
  7:B>G>N>F
  6:G>B>N>F
  5:N>G>B>F
  3:F>N>G>B

expected_winners:
  - B

# file: bv2282_hf3ckp_brams_irv.yaml

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TABULATION RESULTS
======================================================================

--- RCV / Instant-Runoff Voting (single winner) ---
  Brams 1982 — twenty-one voters, and the Condorcet winner goes out second
 Tabulating 21 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
B                  7  Hopeful
G                  6  Hopeful
N                  5  Hopeful
F                  3  Rejected

ROUND 2
Candidate      Votes  Status
-----------  -------  --------
N                  8  Hopeful
B                  7  Hopeful
G                  6  Rejected
F                  0  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
B                 13  Elected
N                  8  Rejected
G                  0  Rejected
F                  0  Rejected


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

--- 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): G
   Outside (3):        B, N, F
   One member ⇒ G is the Condorcet winner, beating every rival head-to-head.
   RCV-IRV winner B is OUTSIDE the Smith set. ✗
      Every member of the set (G) beats B head-to-head, yet
      RCV-IRV elected B 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