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SOURCE FILE:     succ_elim_ex12_truncated.yaml
TABULATED FILE:  succ_elim_ex12_truncated_tabulated.txt
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election_title: "Successive elimination Ex.12 — truncated: naming only A turns last place into first"
scenario_description: |-
  The TRUNCATED half of Felsenthal's successive-elimination truncation example. Source: Dan S. Felsenthal (2010), Appendix A4, Example 12 — see succ_elim_ex12_sincere.yaml for the sincere profile.
  The same six voters, except the one who sincerely ranked A>B>C>D now names only A. Under the same agenda B vs C, winner vs D, winner vs A: with that voter no longer expressing a B-vs-C preference, round 1 goes to C 3:2 instead of tying; C then beats D 3:2; and the final round ties A against C 3:3, where A survives on the earlier-letter convention. A is elected.
  Sincerely, this voter got D — their last choice. Truncating, they get A — their first. Saying less about the bottom of the ballot was worth three places at the top: the truncation paradox.
  Two honest caveats. The final round is a 3:3 tie, so A's win rests on the earlier-letter convention; under the earlier-on-the-agenda reading C would survive instead, and the paradox would be a smaller one (C rather than D, still an improvement for the truncator, but not their first choice). And the mechanism is specific to procedures that let a ballot sit out a round: the voter is not misrepresenting a preference, only withholding one.
  Labels are Felsenthal's own, capitalized, so the case can be read beside the paper's table.
  Tabulated as Ranked Robin for the pairwise matrix. Run the procedure with tools_adam/pref_voting_tabulation_engine/successive_elimination_report.py --agenda B,C,D,A, and add --tiebreak agenda to see the other reading.
paradoxes: [truncation, condorcet-cycle]
voting_method: RankedRobin
num_winners: 1
ballots: |-
  1:A
  1:C>B>A>D
  2:C>D>B>A
  2:D>A>B>C
expected_winners:
  - C

# file: succ_elim_ex12_truncated.yaml

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TABULATION RESULTS
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--- Ranked Robin (RCV-RR / Copeland) Method (single winner) ---
 Tabulating 6 ballots (ranked ballots).

Ballots:
     1 × A
     1 × C > B > A > D
     2 × C > D > B > A
     2 × D > A > B > C

Round-Robin — every pair, head-to-head (For – Against):
   A  ties  C   3 – 3
   A  ties  B   3 – 3
   D  beats A   4 – 2
   C  beats B   3 – 2
   C  beats D   3 – 2
   D  beats B   4 – 1

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
      |     A     |    C     |    B     |    D     |
----------------------------------------------------
  A > |    ---    |3 - 0 - 3 |3 - 0 - 3 |2 - 0 - 4 |
  C > | 3 - 0 - 3 |   ---    |3 - 1 - 2 |3 - 1 - 2 |
  B > | 3 - 0 - 3 |2 - 1 - 3 |   ---    |1 - 1 - 4 |
  D > | 4 - 0 - 2 |2 - 1 - 3 |4 - 1 - 1 |   ---    |

Win–loss record — Copeland score = wins + ½·ties (highest score wins; ties broken by total margin, then lot order):
    #  Candidate  W–L–T  Copeland  Margin  Beats
    1  C          2–0–1       2.5      +2  D, B
    2  D          2–1–0         2      +4  A, B
    3  A          0–1–2         1      -2  —
    4  B          0–2–1       0.5      -4  —

Winner — Ranked Robin (RCV-RR): C
   unbeaten, but draws A — a *weak* Condorcet winner, not a strict one (highest Copeland score, 2.5).

--- 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 (4 of 4): C, D, A, B
   Outside (0):        —
   More than one member ⇒ NO Condorcet winner: the top of the tournament is a
   group held open by draws, so the strongest "candidate" is a set, not a
   person. Some members DO beat others, but no member beats them all — a draw
   blocks the sweep. No loop closes either, so there is no cycle for Minimax /
   Ranked Pairs / Schulze to resolve: which member wins is left to the
   tiebreak, not to a cycle rule. See
   05_Ranked_Robin/01_Learn/rr_tiebreak_lh_vs_bv.md.
   Note: the Copeland leaders (C) are only part of the set — the
   win–loss table's top block understates how wide the contention is.
   Ranked Robin (RCV-RR) winner C is INSIDE the Smith set. ✓
      Guaranteed: Ranked Robin (Copeland) is Smith-efficient — every member of
      the set outscores every outsider, so the top of the win–loss table is
      always inside the set, however the tie among them is then broken.
   Fine print: this set contains a pairwise DRAW, and a draw is enough to keep a
   candidate in the Smith set but not in the tighter Schwartz set — so Schwartz
   may be smaller here.
   More: 07_Concepts/topics/smith_set.md