Nine candidates, 25 voters — ranking only five, counted by Ranked Robin¶
Generated from bv2280_37yf8x_rr_top5.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: Gus
▶ 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 CAP CHANGES THE WINNER. Same 25 voters, same Ranked Robin rule as bv2280_37yf8x_rr_full.yaml. The only difference is that each voter may name five candidates instead of nine — and Gus wins instead of Finn.
Finn is the Condorcet winner on the electorate's real preferences. What the cap removes is the evidence: only 16 of the 25 voters can fit Finn into five names at all. For the other 9 Finn is simply absent from the paper, and an absent candidate wins no head-to-head.
This is the reversal worth remembering. A ranked ballot is usually called the more expressive one, and at full resolution it is. Capped at five names out of nine it records 3,620 distinct opinions where the 0–5 score ballot records 10,077,696 — and here it loses an answer that six rungs kept.
Convention, stated: a candidate left unranked is counted as beaten by everyone the voter did rank, and tied with everyone else the voter left off. Other treatments split that unstated pair half-and-half. It is a choice, not arithmetic, and it belongs in any quotation of this result.
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 # voter at -0.43
Gus>Hugo>Iris>Finn>Emma # voter at +0.60
Ada>Ben>Cleo>Dev>Emma # voter at -0.67
Iris>Hugo>Gus>Finn>Emma # voter at +0.89
Finn>Gus>Emma>Dev>Cleo # voter at +0.18
Emma>Dev>Cleo>Ben>Finn # voter at -0.13
Gus>Hugo>Iris>Finn>Emma # voter at +0.59
Hugo>Iris>Gus>Finn>Emma # voter at +0.72
Gus>Finn>Emma>Hugo>Iris # voter at +0.34
Hugo>Iris>Gus>Finn>Emma # voter at +0.69
Finn>Gus>Emma>Dev>Cleo # voter at +0.23
Ben>Cleo>Dev>Emma>Ada # voter at -0.30
Ben>Ada>Cleo>Dev>Emma # voter at -0.51
Iris>Hugo>Gus>Finn>Emma # voter at +0.89
Emma>Dev>Cleo>Finn>Ben # voter at -0.05
Gus>Hugo>Iris>Finn>Emma # voter at +0.60
Finn>Gus>Emma>Dev>Cleo # voter at +0.28
Ben>Cleo>Dev>Emma>Ada # voter at -0.40
Hugo>Gus>Iris>Finn>Emma # voter at +0.62
Ada>Ben>Cleo>Dev>Emma # voter at -0.63
Finn>Gus>Emma>Dev>Cleo # voter at +0.27
Ada>Ben>Cleo>Dev>Emma # voter at -0.61
Ada>Ben>Cleo>Dev>Emma # voter at -1.33
Cleo>Dev>Emma>Ben>Finn # voter at -0.23
Ada>Ben>Cleo>Dev>Emma # 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
3 × Gus > Hugo > Iris > Finn > Emma
5 × Ada > Ben > Cleo > Dev > Emma
2 × Iris > Hugo > Gus > Finn > Emma
4 × Finn > Gus > Emma > Dev > Cleo
1 × Emma > Dev > Cleo > Ben > Finn
2 × Hugo > Iris > Gus > Finn > Emma
1 × Gus > Finn > Emma > Hugo > Iris
2 × Ben > Cleo > Dev > Emma > Ada
1 × Ben > Ada > Cleo > Dev > Emma
1 × Emma > Dev > Cleo > Finn > Ben
1 × Hugo > Gus > Iris > Finn > Emma
1 × Cleo > Dev > Emma > Ben > Finn
Round-Robin — every pair, head-to-head (For – Against):
Ben beats Cleo 9 – 7
Ben beats Dev 9 – 7
Ben beats Ada 7 – 5
Emma beats Ben 16 – 9
Gus beats Ben 13 – 12
Ben beats Hugo 12 – 9
Ben beats Iris 12 – 9
Finn beats Ben 14 – 11
Cleo beats Dev 10 – 6
Cleo beats Ada 10 – 6
Emma beats Cleo 15 – 10
Gus beats Cleo 13 – 12
Cleo beats Hugo 16 – 9
Cleo beats Iris 16 – 9
Finn beats Cleo 13 – 12
Dev beats Ada 10 – 6
Emma beats Dev 15 – 10
Gus beats Dev 13 – 12
Dev beats Hugo 16 – 9
Dev beats Iris 16 – 9
Finn beats Dev 13 – 12
Emma beats Ada 18 – 7
Gus beats Ada 13 – 9
Ada ties Hugo 9 – 9
Ada ties Iris 9 – 9
Finn beats Ada 16 – 9
Gus beats Emma 13 – 12
Emma beats Hugo 17 – 8
Emma beats Iris 17 – 8
Finn beats Emma 13 – 12
Gus beats Hugo 8 – 5
Gus beats Iris 9 – 4
Gus beats Finn 9 – 7
Hugo beats Iris 7 – 2
Hugo ties Finn 8 – 8
Iris ties Finn 8 – 8
--- 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 | Gus | Hugo | Iris | Finn |
-----------------------------------------------------------------------------------------------------------------------------------------
Ben > | --- | 9 - 9 - 7 | 9 - 9 - 7 | 7 - 13 - 5 | 9 - 0 - 16 |12 - 0 - 13 |12 - 4 - 9 |12 - 4 - 9 |11 - 0 - 14 |
Cleo > | 7 - 9 - 9 | --- |10 - 9 - 6 |10 - 9 - 6 |10 - 0 - 15 |12 - 0 - 13 |16 - 0 - 9 |16 - 0 - 9 |12 - 0 - 13 |
Dev > | 7 - 9 - 9 | 6 - 9 - 10 | --- |10 - 9 - 6 |10 - 0 - 15 |12 - 0 - 13 |16 - 0 - 9 |16 - 0 - 9 |12 - 0 - 13 |
Ada > | 5 - 13 - 7 | 6 - 9 - 10 | 6 - 9 - 10 | --- | 7 - 0 - 18 | 9 - 3 - 13 | 9 - 7 - 9 | 9 - 7 - 9 | 9 - 0 - 16 |
Emma > | 16 - 0 - 9 |15 - 0 - 10 |15 - 0 - 10 |18 - 0 - 7 | --- |12 - 0 - 13 |17 - 0 - 8 |17 - 0 - 8 |12 - 0 - 13 |
Gus > | 13 - 0 - 12 |13 - 0 - 12 |13 - 0 - 12 |13 - 3 - 9 |13 - 0 - 12 | --- | 8 - 12 - 5 | 9 - 12 - 4 | 9 - 9 - 7 |
Hugo > | 9 - 4 - 12 | 9 - 0 - 16 | 9 - 0 - 16 | 9 - 7 - 9 | 8 - 0 - 17 | 5 - 12 - 8 | --- | 7 - 16 - 2 | 8 - 9 - 8 |
Iris > | 9 - 4 - 12 | 9 - 0 - 16 | 9 - 0 - 16 | 9 - 7 - 9 | 8 - 0 - 17 | 4 - 12 - 9 | 2 - 16 - 7 | --- | 8 - 9 - 8 |
Finn > | 14 - 0 - 11 |13 - 0 - 12 |13 - 0 - 12 |16 - 0 - 9 |13 - 0 - 12 | 7 - 9 - 9 | 8 - 9 - 8 | 8 - 9 - 8 | --- |
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 Gus 8–0–0 8 +18 Emma, Finn, Ben, Cleo, Dev, Hugo, Ada, Iris
2 Emma 6–2–0 6 +44 Ben, Cleo, Dev, Hugo, Ada, Iris
3 Finn 5–1–2 6 +11 Emma, Ben, Cleo, Dev, Ada
4 Ben 5–3–0 5 +1 Cleo, Dev, Hugo, Ada, Iris
5 Cleo 4–4–0 4 +13 Dev, Hugo, Ada, Iris
6 Dev 3–5–0 3 +5 Hugo, Ada, Iris
7 Hugo 1–5–2 2 -24 Iris
8 Ada 0–6–2 1 -32 —
9 Iris 0–6–2 1 -36 —
Winner — Ranked Robin (RCV-RR): Gus
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): Gus
Outside (8): Ben, Cleo, Dev, Ada, Emma, Hugo, Iris, Finn
One member ⇒ Gus is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Gus 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_top5.yaml
See also¶
- Condorcet efficiency (topic hub)
- Ties & tie-breaking (topic hub)
- The tie-breaking ladder (full chain)
- Vote splitting (worked set)
- Glossary · all cases by method
More cases in this set: ballot_expressiveness_c9_irv_top5 · bv2280_37yf8x_irv_full · bv2280_37yf8x_rr_full · bv2280_37yf8x_star