Successive elimination Ex.10 — District II: a single voter, C wins¶

Generated from succ_elim_ex10_district2.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¶

District II of Felsenthal's successive-elimination reinforcement example. Source: Dan S. Felsenthal (2010), Appendix A4, Example 10. One voter, ranking C>D>B>A. With a single ballot every pairwise majority is that voter's own preference, so the agenda B vs D, winner vs A, winner vs C runs D beats B 1:0, D beats A 1:0, C beats D 1:0 and C — the voter's first choice — is elected. C is trivially the Condorcet winner. The one-voter district is not a mistake or a simplification: it is the smallest thing that can be amalgamated with District I, and Felsenthal uses it precisely because nothing about it is controversial. Both districts elect C. Their union (succ_elim_ex10_amalgamated.yaml) ties in every round, and under one tie-break reading elects B, which is the reinforcement failure. Labels are Felsenthal's own, capitalized, so the case can be read beside the paper's table. Tabulated as Ranked Robin, which also elects C — with one ballot there is nothing for the two methods to disagree about. Run the procedure with tools_adam/pref_voting_tabulation_engine/successive_elimination_report.py --agenda B,D,A,C.

Ballots¶

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

1:C>D>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 1 ballots (ranked ballots).

Ballots:
     1 × C > D > B > A

Round-Robin — every pair, head-to-head (For – Against):
   C  beats D   1 – 0
   C  beats B   1 – 0
   C  beats A   1 – 0
   D  beats B   1 – 0
   D  beats A   1 – 0
   B  beats A   1 – 0

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

Winner — Ranked Robin (RCV-RR): C
   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 4): C
   Outside (3):        D, B, A
   One member ⇒ C is the Condorcet winner, beating every rival head-to-head.
   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.
   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_ex10_district2.yaml

See also¶