Successive elimination Ex.11 — after: a twin joins and costs their own side the win¶

Generated from succ_elim_ex11_twin_after.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: B

Scenario¶

The AFTER half of Felsenthal's successive-elimination twin example. Source: Dan S. Felsenthal (2010), Appendix A4, Example 11, crediting Moulin (1988b: 54) — see succ_elim_ex11_twin_before.yaml for the setup. The same six voters plus one more casting C>B>A, an exact copy of a ballot already present: 7 voters, 2×(A>B>C), 2×(B>C>A), 1×(C>A>B), 2×(C>B>A). The extra ballot breaks the A/B tie that had been carrying A into round 2: B now beats A 4:3 and beats C 4:3, so B is the Condorcet winner and successive elimination elects B from any agenda at all. Before the twin arrived, C won. The twin ranks C first. So the voter whose position was duplicated — and the duplicate themselves — both end up with their SECOND choice instead of their first, purely because one more person voted exactly as they did. That is the twin paradox. It is worth being precise about why this is more than a curiosity: no voter changed a preference, no candidate entered or left, and the added ballot was not strategic or insincere. It was the most ordinary thing a supporter can do, and it backfired. Labels are Felsenthal's own, capitalized, so the case can be read beside the paper's table. Tabulated as Ranked Robin, which elects B — here agreeing with the agenda, since a Condorcet winner exists and both methods are Condorcet-consistent. Run the procedure with tools_adam/pref_voting_tabulation_engine/successive_elimination_report.py --agenda A,B,C.

Ballots¶

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

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

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 7 ballots (ranked ballots).

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

Round-Robin — every pair, head-to-head (For – Against):
   B  beats A   4 – 3
   C  beats A   5 – 2
   B  beats C   4 – 3

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
      |     A     |    B     |    C     |
-----------------------------------------
  A > |    ---    |3 - 0 - 4 |2 - 0 - 5 |
  B > | 4 - 0 - 3 |   ---    |4 - 0 - 3 |
  C > | 5 - 0 - 2 |3 - 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  B          2–0–0         2      +2  C, A
    2  C          1–1–0         1      +2  A
    3  A          0–2–0         0      -4  —

Winner — Ranked Robin (RCV-RR): B
   beats every opponent head-to-head — the Condorcet winner.

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 (1 of 3): B
   Outside (2):        A, C
   One member ⇒ B is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner B 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_ex11_twin_after.yaml

Successive elimination Ex.11 — after: a twin joins and costs their own side the win¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶