D voter gets their last choice¶

Generated from succ_elim_ex12_sincere.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.

Method: Ranked Robin (RCV-RR / Copeland) · 1 seat · Expected winner: C

Scenario¶

The SINCERE half of Felsenthal's successive-elimination truncation example. Source: Dan S. Felsenthal (2010), Appendix A4, Example 12. Six voters, four candidates: 1×(A>B>C>D), 1×(C>B>A>D), 2×(C>D>B>A), 2×(D>A>B>C). Under the agenda B vs C, winner vs D, winner vs A: round 1 ties 3:3 and B survives on the earlier-letter convention; D beats B 4:2; D beats A 4:2. D is elected — the dead last choice of the voter who ranked A>B>C>D. That voter can do better by revealing LESS. In succ_elim_ex12_truncated.yaml they name only A, dropping out of every round A does not contest. Their absence from round 1 lets C beat B, C then beats D, and the final round ties A against C with A surviving — so the truncating voter gets their FIRST choice instead of their last, by saying less. The truncation paradox. What makes the mechanism visible here is that truncation is not a lie: the voter still ranks A top and says nothing false. They simply decline to help resolve contests among candidates they did not rank, and under an agenda procedure declining to participate in a round is a lever. Labels are Felsenthal's own, capitalized, so the case can be read beside the paper's table. Successive elimination exists in neither the LH engine nor BetterVoting, so this file is tabulated as Ranked Robin, which elects C by a margin tiebreak inside a Copeland tie. Run the procedure with tools_adam/pref_voting_tabulation_engine/successive_elimination_report.py --agenda B,C,D,A.

Ballots¶

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

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

What the engine says¶

The count, step by step — the rounds and how the winner is reached:

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

Ballots:
     1 × A > B > C > D
     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  B   3 – 3
   A  ties  C   3 – 3
   D  beats A   4 – 2
   B  ties  C   3 – 3
   D  beats B   4 – 2
   C  beats D   4 – 2

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

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          1–0–2         2      +2  D
    2  D          2–1–0         2      +2  A, B
    3  A          0–1–2         1      -2  —
    4  B          0–1–2         1      -2  —

Winner — Ranked Robin (RCV-RR): C
   *** 2 candidates tie on the highest Copeland score (2): C, D — tied on the tally, not a cycle (some of them beat others head-to-head, but no loop closes). Resolved by total margin, then lot order.

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 (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, D) 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

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/succ_elim_ex12_sincere.yaml

Successive elimination Ex.12 — sincere: the A>B>C>D voter gets their last choice¶

Scenario¶

Ballots¶

What the engine says¶

Full audit — preference matrix, Condorcet, and score distribution¶

See also¶