Nine candidates, 25 voters — ranking all nine, counted by Ranked Robin¶

Generated from bv2280_37yf8x_rr_full.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: Finn

▶ Live on BetterVoting: vote · results ↗ (election 37yf8x · test BV2280).

Official tie-break (lot) order: Ada > Ben > Cleo > Dev > Emma > Finn > Gus > Hugo > Iris — consulted only if every deterministic tiebreaker stays tied (how the ladder works).

Scenario¶

THE CONTROL. Every voter ranks all nine candidates, nothing truncated and nothing rounded, and Ranked Robin returns Finn — the candidate who beats each of the other eight head-to-head.

This is the full-resolution ranked ballot that Condorcet-efficiency simulations normally hand to ranked methods. It is also an idealization: no large-field jurisdiction issues it. bv2280_37yf8x_rr_top5.yaml cuts it down to five ranks, which is what a real ranked ballot looks like, and the winner changes.

Compare with bv2280_37yf8x_star.yaml: the 0–5 score ballot agrees with this one. Compare with bv2280_37yf8x_irv_full.yaml: the SAME ballots, counted by instant runoff, do not — which is the cleanest evidence in this folder that the paper and the count are separate things.

Construction: build_cases.py in this folder. 25 voters and 9 candidates at frozen positions on one spectrum — Ada −0.73 · Ben −0.37 · Cleo −0.18 · Dev −0.17 · Emma −0.11 · Finn +0.24 · Gus +0.41 · Hugo +0.80 · Iris +0.84; utility = minus the distance; scores = each voter's own min-max scaling onto 0–5; rankings = those same utilities in order. Nothing is tuned to the result, and no count in this folder is settled by a tie-break — that was a search constraint, so every winner here survives any lot rule.

Ballots¶

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

Ben>Cleo>Dev>Ada>Emma>Finn>Gus>Hugo>Iris    # voter at -0.43
Gus>Hugo>Iris>Finn>Emma>Dev>Cleo>Ben>Ada    # voter at +0.60
Ada>Ben>Cleo>Dev>Emma>Finn>Gus>Hugo>Iris    # voter at -0.67
Iris>Hugo>Gus>Finn>Emma>Dev>Cleo>Ben>Ada    # voter at +0.89
Finn>Gus>Emma>Dev>Cleo>Ben>Hugo>Iris>Ada    # voter at +0.18
Emma>Dev>Cleo>Ben>Finn>Gus>Ada>Hugo>Iris    # voter at -0.13
Gus>Hugo>Iris>Finn>Emma>Dev>Cleo>Ben>Ada    # voter at +0.59
Hugo>Iris>Gus>Finn>Emma>Dev>Cleo>Ben>Ada    # voter at +0.72
Gus>Finn>Emma>Hugo>Iris>Dev>Cleo>Ben>Ada    # voter at +0.34
Hugo>Iris>Gus>Finn>Emma>Dev>Cleo>Ben>Ada    # voter at +0.69
Finn>Gus>Emma>Dev>Cleo>Hugo>Iris>Ben>Ada    # voter at +0.23
Ben>Cleo>Dev>Emma>Ada>Finn>Gus>Hugo>Iris    # voter at -0.30
Ben>Ada>Cleo>Dev>Emma>Finn>Gus>Hugo>Iris    # voter at -0.51
Iris>Hugo>Gus>Finn>Emma>Dev>Cleo>Ben>Ada    # voter at +0.89
Emma>Dev>Cleo>Finn>Ben>Gus>Ada>Hugo>Iris    # voter at -0.05
Gus>Hugo>Iris>Finn>Emma>Dev>Cleo>Ben>Ada    # voter at +0.60
Finn>Gus>Emma>Dev>Cleo>Hugo>Iris>Ben>Ada    # voter at +0.28
Ben>Cleo>Dev>Emma>Ada>Finn>Gus>Hugo>Iris    # voter at -0.40
Hugo>Gus>Iris>Finn>Emma>Dev>Cleo>Ben>Ada    # voter at +0.62
Ada>Ben>Cleo>Dev>Emma>Finn>Gus>Hugo>Iris    # voter at -0.63
Finn>Gus>Emma>Dev>Cleo>Hugo>Iris>Ben>Ada    # voter at +0.27
Ada>Ben>Cleo>Dev>Emma>Finn>Gus>Hugo>Iris    # voter at -0.61
Ada>Ben>Cleo>Dev>Emma>Finn>Gus>Hugo>Iris    # voter at -1.33
Cleo>Dev>Emma>Ben>Finn>Ada>Gus>Hugo>Iris    # voter at -0.23
Ada>Ben>Cleo>Dev>Emma>Finn>Gus>Hugo>Iris    # voter at -1.82

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 25 ballots (ranked ballots).

Ballots:
     1 × Ben > Cleo > Dev > Ada > Emma > Finn > Gus > Hugo > Iris
     3 × Gus > Hugo > Iris > Finn > Emma > Dev > Cleo > Ben > Ada
     5 × Ada > Ben > Cleo > Dev > Emma > Finn > Gus > Hugo > Iris
     2 × Iris > Hugo > Gus > Finn > Emma > Dev > Cleo > Ben > Ada
     1 × Finn > Gus > Emma > Dev > Cleo > Ben > Hugo > Iris > Ada
     1 × Emma > Dev > Cleo > Ben > Finn > Gus > Ada > Hugo > Iris
     2 × Hugo > Iris > Gus > Finn > Emma > Dev > Cleo > Ben > Ada
     1 × Gus > Finn > Emma > Hugo > Iris > Dev > Cleo > Ben > Ada
     3 × Finn > Gus > Emma > Dev > Cleo > Hugo > Iris > Ben > Ada
     2 × Ben > Cleo > Dev > Emma > Ada > Finn > Gus > Hugo > Iris
     1 × Ben > Ada > Cleo > Dev > Emma > Finn > Gus > Hugo > Iris
     1 × Emma > Dev > Cleo > Finn > Ben > Gus > Ada > Hugo > Iris
     1 × Hugo > Gus > Iris > Finn > Emma > Dev > Cleo > Ben > Ada
     1 × Cleo > Dev > Emma > Ben > Finn > Ada > Gus > Hugo > Iris

Round-Robin — every pair, head-to-head (For – Against):
   Cleo  beats Ben    16 –  9
   Dev   beats Ben    16 –  9
   Ben   beats Ada    20 –  5
   Emma  beats Ben    16 –  9
   Finn  beats Ben    14 – 11
   Gus   beats Ben    13 – 12
   Ben   beats Hugo   13 – 12
   Ben   beats Iris   13 – 12
   Dev   beats Cleo   15 – 10
   Cleo  beats Ada    19 –  6
   Emma  beats Cleo   15 – 10
   Finn  beats Cleo   13 – 12
   Gus   beats Cleo   13 – 12
   Cleo  beats Hugo   16 –  9
   Cleo  beats Iris   16 –  9
   Dev   beats Ada    19 –  6
   Emma  beats Dev    15 – 10
   Finn  beats Dev    13 – 12
   Gus   beats Dev    13 – 12
   Dev   beats Hugo   16 –  9
   Dev   beats Iris   16 –  9
   Emma  beats Ada    18 –  7
   Finn  beats Ada    16 –  9
   Gus   beats Ada    15 – 10
   Hugo  beats Ada    13 – 12
   Iris  beats Ada    13 – 12
   Finn  beats Emma   13 – 12
   Gus   beats Emma   13 – 12
   Emma  beats Hugo   17 –  8
   Emma  beats Iris   17 –  8
   Finn  beats Gus    16 –  9
   Finn  beats Hugo   17 –  8
   Finn  beats Iris   17 –  8
   Gus   beats Hugo   20 –  5
   Gus   beats Iris   21 –  4
   Hugo  beats Iris   23 –  2

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
         |     Ben      |    Cleo     |    Dev      |    Ada      |    Emma     |    Finn     |    Gus      |    Hugo     |    Iris     |
-----------------------------------------------------------------------------------------------------------------------------------------
   Ben > |     ---      | 9 -  0 - 16 | 9 -  0 - 16 |20 -  0 -  5 | 9 -  0 - 16 |11 -  0 - 14 |12 -  0 - 13 |13 -  0 - 12 |13 -  0 - 12 |
  Cleo > | 16 -  0 -  9 |    ---      |10 -  0 - 15 |19 -  0 -  6 |10 -  0 - 15 |12 -  0 - 13 |12 -  0 - 13 |16 -  0 -  9 |16 -  0 -  9 |
   Dev > | 16 -  0 -  9 |15 -  0 - 10 |    ---      |19 -  0 -  6 |10 -  0 - 15 |12 -  0 - 13 |12 -  0 - 13 |16 -  0 -  9 |16 -  0 -  9 |
   Ada > |  5 -  0 - 20 | 6 -  0 - 19 | 6 -  0 - 19 |    ---      | 7 -  0 - 18 | 9 -  0 - 16 |10 -  0 - 15 |12 -  0 - 13 |12 -  0 - 13 |
  Emma > | 16 -  0 -  9 |15 -  0 - 10 |15 -  0 - 10 |18 -  0 -  7 |    ---      |12 -  0 - 13 |12 -  0 - 13 |17 -  0 -  8 |17 -  0 -  8 |
  Finn > | 14 -  0 - 11 |13 -  0 - 12 |13 -  0 - 12 |16 -  0 -  9 |13 -  0 - 12 |    ---      |16 -  0 -  9 |17 -  0 -  8 |17 -  0 -  8 |
   Gus > | 13 -  0 - 12 |13 -  0 - 12 |13 -  0 - 12 |15 -  0 - 10 |13 -  0 - 12 | 9 -  0 - 16 |    ---      |20 -  0 -  5 |21 -  0 -  4 |
  Hugo > | 12 -  0 - 13 | 9 -  0 - 16 | 9 -  0 - 16 |13 -  0 - 12 | 8 -  0 - 17 | 8 -  0 - 17 | 5 -  0 - 20 |    ---      |23 -  0 -  2 |
  Iris > | 12 -  0 - 13 | 9 -  0 - 16 | 9 -  0 - 16 |13 -  0 - 12 | 8 -  0 - 17 | 8 -  0 - 17 | 4 -  0 - 21 | 2 -  0 - 23 |    ---      |

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  Finn       8–0–0         8     +38  Gus, Emma, Dev, Cleo, Ben, Hugo, Iris, Ada
    2  Gus        7–1–0         7     +34  Emma, Dev, Cleo, Ben, Hugo, Iris, Ada
    3  Emma       6–2–0         6     +44  Dev, Cleo, Ben, Hugo, Iris, Ada
    4  Dev        5–3–0         5     +32  Cleo, Ben, Hugo, Iris, Ada
    5  Cleo       4–4–0         4     +22  Ben, Hugo, Iris, Ada
    6  Ben        3–5–0         3      -8  Hugo, Iris, Ada
    7  Hugo       2–6–0         2     -26  Iris, Ada
    8  Iris       1–7–0         1     -70  Ada
    9  Ada        0–8–0         0     -66  —

Winner — Ranked Robin (RCV-RR): Finn
   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 9): Finn
   Outside (8):        Ben, Cleo, Dev, Ada, Emma, Gus, Hugo, Iris
   One member ⇒ Finn is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner Finn 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/ballot_expressiveness/cases/bv2280_37yf8x_rr_full.yaml

Nine candidates, 25 voters — ranking all nine, counted by Ranked Robin¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶