Felsenthal Ex.4 full electorate — Ranked Robin: the Condorcet winner Beth¶

Generated from bv2150_dxg8pb_ranked_robin.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: Beth

▶ Live on BetterVoting: vote · results ↗ (election dxg8pb · test BV2150).

Scenario¶

Race 2 of 3 in the No-Show-paradox pair, part 1 of 2 (BV2150, bvid dxg8pb; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A2, Example 4 — see bv2150_dxg8pb_irv.yaml for the setup. The same 11 ranked ballots counted by Ranked Robin (Copeland): Beth wins both her head-to-heads (Andy 6–5, Carl 7–4) — the Condorcet winner, elected directly. No cycle here, so the count is fully deterministic on BetterVoting too. Live results: https://bettervoting.com/dxg8pb/results

Ballots¶

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

4:Andy>Beth>Carl
3:Beth>Carl>Andy
1:Carl>Andy>Beth
3:Carl>Beth>Andy

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:
     4 × Andy > Beth > Carl
     3 × Beth > Carl > Andy
     1 × Carl > Andy > Beth
     3 × Carl > Beth > Andy

Round-Robin — every pair, head-to-head (For – Against):
   Beth  beats Andy   6 – 5
   Carl  beats Andy   7 – 4
   Beth  beats Carl   7 – 4

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
         |   Andy    |  Beth    |  Carl    |
--------------------------------------------
  Andy > |    ---    |5 - 0 - 6 |4 - 0 - 7 |
  Beth > | 6 - 0 - 5 |   ---    |7 - 0 - 4 |
  Carl > | 7 - 0 - 4 |4 - 0 - 7 |   ---    |

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  Beth       2–0–0         2      +4  Carl, Andy
    2  Carl       1–1–0         1      +0  Andy
    3  Andy       0–2–0         0      -4  —

Winner — Ranked Robin (RCV-RR): Beth
   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): Beth
   Outside (2):        Andy, Carl
   One member ⇒ Beth is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner Beth 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/bv2150_dxg8pb_ranked_robin.yaml

See also¶