Nurmi Ex.16 truncated — Ranked Robin: unmoved, still B¶

Generated from bv2163_74j6vv_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: B

▶ Live on BetterVoting: vote · results ↗ (election 74j6vv · test BV2163).

Scenario¶

Race 3 of 3 in the RCV-IRV truncation pair, part 2 of 2 (BV2163, bvid 74j6vv; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A6, Example 16, due to Nurmi (1999: 63) — see bv2163_74j6vv_irv.yaml for the setup. The same rankings with the 17 truncated ballots (only D ranked; the unranked candidates count as tied-last, Equal Support among themselves): B still wins every head-to-head (A 53–33 among voters with a preference, C 62–24, D 86–17) — the Condorcet winner, elected with full ballots and with truncated ones. Pairwise counting gives these 17 voters no truncation incentive; the elimination order (the IRV race) is what their truncation exploits. Live results: https://bettervoting.com/74j6vv/results

Ballots¶

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

33:A>B>C>D
29:B>A>C>D
24:C>B>A>D
17:D

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 103 ballots (ranked ballots).

Ballots:
    33 × A > B > C > D
    29 × B > A > C > D
    24 × C > B > A > D
    17 × D

Round-Robin — every pair, head-to-head (For – Against):
   B  beats A   53 – 33
   A  beats C   62 – 24
   A  beats D   86 – 17
   B  beats C   62 – 24
   B  beats D   86 – 17
   C  beats D   86 – 17

--- 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 > |     ---      |33 - 17 - 53 |62 - 17 - 24 |86 -  0 - 17 |
  B > | 53 - 17 - 33 |    ---      |62 - 17 - 24 |86 -  0 - 17 |
  C > | 24 - 17 - 62 |24 - 17 - 62 |    ---      |86 -  0 - 17 |
  D > | 17 -  0 - 86 |17 -  0 - 86 |17 -  0 - 86 |    ---      |

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          3–0–0         3    +127  A, C, D
    2  A          2–1–0         2     +87  C, D
    3  C          1–2–0         1      -7  D
    4  D          0–3–0         0    -207  —

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 4): B
   Outside (3):        A, C, D
   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/bv2163_74j6vv_ranked_robin.yaml

See also¶