Successive elimination Ex.9 — the agenda elects B, whom every voter ranks below A¶

Generated from succ_elim_ex9_pareto.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: A

Scenario¶

Felsenthal's flagship successive-elimination example, and the densest case in the whole appendix: one 11-voter profile that yields four different paradoxes depending on which single datum you vary. Source: Dan S. Felsenthal, "Review of Paradoxes Afflicting Various Voting Procedures Where One Out of m Candidates (m ≥ 2) Must Be Elected", University of Haifa / LSE, revised 26 May 2010; Appendix A4, Example 9. 11 voters, four candidates: 3×(A>B>C>D), 2×(C>A>B>D), 1×(C>D>A>B), 5×(D>A>B>C). The majority preference cycles (B>C>D>A>B), which is the precondition for everything below. PARETO. Under the agenda D vs A, winner vs C, winner vs B: D beats A 6:5, C beats D 6:5, B beats C 8:3 — B is elected. But all 11 voters rank A above B, unanimously and without exception. A Pareto-dominated candidate wins. PATH INDEPENDENCE. Same ballots, agenda A vs B, winner vs C, winner vs D: A beats B 11:0, A beats C 8:3, then D beats A 6:5 — D wins. Under a cycle the agenda-setter picks the winner, not the electorate. SCC. Delete D, who wins nothing under the first agenda: A beats C 8:3 and then B 11:0, so A wins. A non-winner's mere presence decided the election. NO-SHOW is the companion file succ_elim_ex9_noshow.yaml, where two of the D-first voters stay home and get A, whom they prefer to B. Labels are Felsenthal's own, capitalized; this is an academic reproduction meant to be read beside the paper's table, not a scenario with a cast. Successive elimination exists in neither the LH engine nor BetterVoting — it is a parliamentary procedure, not a ballot-box method — so this file is tabulated as Ranked Robin, which reads the same pairwise matrix the agenda consumes one pair at a time. Ranked Robin elects A, the candidate the agenda buried. Run the procedure itself with tools_adam/pref_voting_tabulation_engine/successive_elimination_report.py, whose --agenda and --drop flags reproduce all four readings above.

Ballots¶

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

3:A>B>C>D
2:C>A>B>D
1:C>D>A>B
5: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 11 ballots (ranked ballots).

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

Round-Robin — every pair, head-to-head (For – Against):
   A  beats B   11 –  0
   A  beats C    8 –  3
   D  beats A    6 –  5
   B  beats C    8 –  3
   D  beats B    6 –  5
   C  beats D    6 –  5

--- 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 > |     ---      |11 -  0 -  0 | 8 -  0 -  3 | 5 -  0 -  6 |
  B > |  0 -  0 - 11 |    ---      | 8 -  0 -  3 | 5 -  0 -  6 |
  C > |  3 -  0 -  8 | 3 -  0 -  8 |    ---      | 6 -  0 -  5 |
  D > |  6 -  0 -  5 | 6 -  0 -  5 | 5 -  0 -  6 |    ---      |

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  A          2–1–0         2     +15  B, C
    2  D          2–1–0         2      +1  A, B
    3  B          1–2–0         1      -7  C
    4  C          1–2–0         1      -9  D

Winner — Ranked Robin (RCV-RR): A
   *** 2 candidates tie for the most wins (A, 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): A, D, B, C
   Outside (0):        —
   More than one member ⇒ NO Condorcet winner: the top of the tournament is a
   cycle, so the strongest "candidate" is a set, not a person. Which member of
   the set should win is exactly what Minimax / Ranked Pairs / Schulze disagree
   about — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.
   Note: the Copeland leaders (A, 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 A 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.
   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_ex9_pareto.yaml

Successive elimination Ex.9 — the agenda elects B, whom every voter ranks below A¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶