Ice cream ladder — a STAR tie in both rounds, settled without the lot (BV2180, fp62p2)¶
▶ Live on BetterVoting: vote · results ↗ (election fp62p2 · test BV2180) — an independent tabulator to check the winners below against.
Bucket — APPROVAL_OR_MINOR: Only Approval differs
Generated by STARVote_LH_tabulation_engine/tools_adam/scripts/build_divergence_index.py — rebuilt from the election file; do not hand-edit.
What happens¶
STAR, RCV-IRV and Ranked Robin all agree on Strawberry. Only Approval differs, electing Chocolate: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding Chocolate's breadth of acceptability over Strawberry's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Strawberry |
| RCV-IRV | Strawberry |
| Ranked Robin (RCV-RR) | Strawberry |
| Approval | Chocolate |
| Range / Score | Strawberry |
| Condorcet | none (cycle) |
Flags: 2 tied-score ballot(s)
Source election: 01_STAR/03_Criteria/tie_break_ladder/cases/bv2180_fp62p2_ice_cream_ladder.yaml · STAR tabulated mirror: bv2180_fp62p2_ice_cream_ladder_tabulated.txt
6 candidates, 2 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Chocolate | Chocolate Chip | Fudge Brownie | Vanilla | Strawberry | Mango |
|---|---|---|---|---|---|---|
| 1 | 4 | 5 | 4 | 1 | 2 | 0 |
| 1 | 1 | 0 | 0 | 4 | 5 | 4 |
STAR result (official)¶
Scoring round (sum of scores): Strawberry 7, Chocolate 5, Chocolate Chip 5, Vanilla 5, Fudge Brownie 4, Mango 4
Finalists (top two): Strawberry and Chocolate
Automatic runoff: Strawberry 1 vs Chocolate 1
STAR winner: Chocolate
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
Note: Chocolate, Chocolate Chip and Vanilla tied at 5 in the Scoring
Round, and the five-star rung advanced Chocolate Chip. The *
marks who advanced, not who scored highest. Chocolate and
Vanilla are filtered out of this grid — see the Scoring Round
for how the tie was settled.
| * Chocolate Chip | * Strawberry |
-----------------------------------------------------------------
* Chocolate Chip > | --- | 1 - 0 - 1 |
* Strawberry > | 1 - 0 - 1 | --- |
[Divergence from STAR]
STAR = Strawberry
Choose-One (Plurality) = Chocolate Chip (differs from STAR)
Approval = Chocolate (differs from STAR)
--- STAR Voting Method (single winner) ---
Tabulating 2 ballots.
Chocolate,Chocolate Chip,Fudge Brownie,Vanilla,Strawberry,Mango
4, 5, 4, 1, 2, -
1, 0, 0, 4, 5, 4
('-' = left blank / abstained; '0' = scored zero — both count as 0 stars.)
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 Abs | Total Avg all Avg rated
Chocolate 0 1 0 0 1 0 0 | 5 2.5 2.5
Chocolate Chip 1 0 0 0 0 1 0 | 5 2.5 2.5
Fudge Brownie 0 1 0 0 0 1 0 | 4 2.0 2.0
Vanilla 0 1 0 0 1 0 0 | 5 2.5 2.5
Strawberry 1 0 0 1 0 0 0 | 7 3.5 3.5
Mango 0 1 0 0 0 0 1 | 4 2.0 4.0
Avg all = Total / all ballots — a blank counts as 0, so this is the Total the Scoring Round ranks on, per ballot.
Avg rated = Total / the ballots that scored this candidate (Abs excluded) — support among voters who had an opinion.
Scoring Round
The two highest-scoring candidates advance to the next round.
Strawberry -- 7 -- First place
Chocolate -- 5 -- Tied for second place
Chocolate Chip -- 5 -- Tied for second place
Vanilla -- 5 -- Tied for second place
Fudge Brownie -- 4
Mango -- 4
Strawberry advances, but there's a three-way tie for second.
Scoring Round: First tiebreaker
The candidate preferred in the most head-to-head matchups advances.
Chocolate -- 2 -- Tied for second place
Chocolate Chip -- 2 -- Tied for second place
Vanilla -- 2 -- Tied for second place
Equal Support -- 0
There's still a three-way tie for second.
Scoring Round: Second tiebreaker
The candidate with the most votes of score 5 advances.
Chocolate Chip -- 1 -- Second place
Chocolate -- 0
Vanilla -- 0
Strawberry and Chocolate Chip advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Chocolate Chip -- 1 -- Tied for first place
Strawberry -- 1 -- Tied for first place
Equal Support -- 0
There's a two-way tie for first.
Automatic Runoff Round: First tiebreaker
The highest-scoring candidate wins.
Strawberry -- 7 -- First place
Chocolate Chip -- 5
Strawberry wins.
Winner — STAR Voting Method (single winner)
Strawberry
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 2 ballots (converted from score ballots; 0 = unranked, equal scores broken by candidate priority).
Ballots:
the ranking RCV-IRV reads (0 = unranked, equal scores broken by priority);
the source score ballot follows in () per column: Chocolate, Chocolate Chip, Fudge Brownie, Vanilla, Strawberry, Mango
1 × Chocolate Chip > Chocolate > Fudge Brownie > Strawberry > Vanilla (4, 5, 4, 1, 2, 0)
1 × Strawberry > Vanilla > Mango > Chocolate (1, 0, 0, 4, 5, 4)
FINAL RESULT
Candidate Votes Status
-------------- ------- --------
Strawberry 1 Elected
Chocolate Chip 1 Rejected
Chocolate 0 Rejected
Vanilla 0 Rejected
Fudge Brownie 0 Rejected
Mango 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Strawberry
--- 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 (6 of 6): Strawberry, Chocolate, Chocolate Chip, Vanilla, Fudge Brownie, Mango
Outside (0): —
More than one member ⇒ NO Condorcet winner: the top of the tournament is a
group held open by draws, so the strongest "candidate" is a set, not a
person. Some members DO beat others, but no member beats them all — a draw
blocks the sweep. No loop closes either, so there is no cycle for Minimax /
Ranked Pairs / Schulze to resolve: which member wins is left to the
tiebreak, not to a cycle rule. See
05_Ranked_Robin/01_Learn/rr_tiebreak_lh_vs_bv.md.
Note: the Copeland leaders (Strawberry) are only part of the set — the
win–loss table's top block understates how wide the contention is.
RCV-IRV winner Strawberry is INSIDE the Smith set. ✓
Not guaranteed — RCV-IRV is not Smith-efficient — but it holds here.
Fine print: this set contains a pairwise DRAW, and a draw is enough to keep a
candidate in the Smith set but not in the tighter Schwartz set — so Schwartz
may be smaller here.
More: 07_Concepts/topics/smith_set.md
NOTE: a generated cross-method view of the STAR ballots, for comparison only — not the official STAR result.
Ranked Robin (RCV-RR) — every pair, head-to-head¶
--- Ranked Robin (RCV-RR / Copeland) Method (single winner) ---
Tabulating 2 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Chocolate, Chocolate Chip, Fudge Brownie, Vanilla, Strawberry, Mango
1 × Chocolate Chip > Chocolate=Fudge Brownie > Strawberry > Vanilla > Mango (4, 5, 4, 1, 2, 0)
1 × Strawberry > Vanilla=Mango > Chocolate > Chocolate Chip=Fudge Brownie (1, 0, 0, 4, 5, 4)
Round-Robin — every pair, head-to-head (For – Against):
Chocolate ties Chocolate Chip 1 – 1
Chocolate beats Fudge Brownie 1 – 0
Chocolate ties Vanilla 1 – 1
Chocolate ties Strawberry 1 – 1
Chocolate ties Mango 1 – 1
Chocolate Chip beats Fudge Brownie 1 – 0
Chocolate Chip ties Vanilla 1 – 1
Chocolate Chip ties Strawberry 1 – 1
Chocolate Chip ties Mango 1 – 1
Fudge Brownie ties Vanilla 1 – 1
Fudge Brownie ties Strawberry 1 – 1
Fudge Brownie ties Mango 1 – 1
Strawberry beats Vanilla 2 – 0
Vanilla beats Mango 1 – 0
Strawberry beats Mango 2 – 0
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Chocolate | Chocolate Chip | Fudge Brownie | Vanilla | Strawberry | Mango |
---------------------------------------------------------------------------------------------------------------------------------
Chocolate > | --- | 1 - 0 - 1 | 1 - 1 - 0 | 1 - 0 - 1 | 1 - 0 - 1 | 1 - 0 - 1 |
Chocolate Chip > | 1 - 0 - 1 | --- | 1 - 1 - 0 | 1 - 0 - 1 | 1 - 0 - 1 | 1 - 0 - 1 |
Fudge Brownie > | 0 - 1 - 1 | 0 - 1 - 1 | --- | 1 - 0 - 1 | 1 - 0 - 1 | 1 - 0 - 1 |
Vanilla > | 1 - 0 - 1 | 1 - 0 - 1 | 1 - 0 - 1 | --- | 0 - 0 - 2 | 1 - 1 - 0 |
Strawberry > | 1 - 0 - 1 | 1 - 0 - 1 | 1 - 0 - 1 | 2 - 0 - 0 | --- | 2 - 0 - 0 |
Mango > | 1 - 0 - 1 | 1 - 0 - 1 | 1 - 0 - 1 | 0 - 1 - 1 | 0 - 0 - 2 | --- |
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 Strawberry 2–0–3 3.5 +4 Vanilla, Mango
2 Chocolate 1–0–4 3 +1 Fudge Brownie
3 Chocolate Chip 1–0–4 3 +1 Fudge Brownie
4 Vanilla 1–1–3 2.5 -1 Mango
5 Fudge Brownie 0–2–3 1.5 -2 —
6 Mango 0–2–3 1.5 -3 —
Winner — Ranked Robin (RCV-RR): Strawberry
unbeaten, but draws Chocolate, Chocolate Chip, Fudge Brownie — a *weak* Condorcet winner, not a strict one (highest Copeland score, 3.5).
--- 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 (6 of 6): Strawberry, Chocolate, Chocolate Chip, Vanilla, Fudge Brownie, Mango
Outside (0): —
More than one member ⇒ NO Condorcet winner: the top of the tournament is a
group held open by draws, so the strongest "candidate" is a set, not a
person. Some members DO beat others, but no member beats them all — a draw
blocks the sweep. No loop closes either, so there is no cycle for Minimax /
Ranked Pairs / Schulze to resolve: which member wins is left to the
tiebreak, not to a cycle rule. See
05_Ranked_Robin/01_Learn/rr_tiebreak_lh_vs_bv.md.
Note: the Copeland leaders (Strawberry) are only part of the set — the
win–loss table's top block understates how wide the contention is.
Ranked Robin (RCV-RR) winner Strawberry 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.
Fine print: this set contains a pairwise DRAW, and a draw is enough to keep a
candidate in the Smith set but not in the tighter Schwartz set — so Schwartz
may be smaller here.
More: 07_Concepts/topics/smith_set.md