Ice Cream — Flavor of the Year (the real recorded race)¶
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 ChocoAlm. Only Approval differs, electing ChocoDrk: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding ChocoDrk's breadth of acceptability over ChocoAlm's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | ChocoAlm |
| RCV-IRV | ChocoAlm |
| Ranked Robin (RCV-RR) | ChocoAlm |
| Approval | ChocoDrk |
| Range / Score | ChocoDrk |
| Condorcet | ChocoAlm |
Flags: none
Source election: 01_STAR/02_Examples/runoff_overturns_leader/cases/03_c7_b3_ice-cream-live.yaml · STAR tabulated mirror: 03_c7_b3_ice-cream-live_tabulated.txt
7 candidates, 3 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | ChocoDrk | ChocoAlm | ChocoHzn | VanillaClssc | VanillaFrnch | Mango | Peach |
|---|---|---|---|---|---|---|---|
| 1 | 4 | 5 | 3 | 0 | 1 | 2 | 0 |
| 1 | 0 | 3 | 0 | 0 | 0 | 0 | 0 |
| 1 | 5 | 0 | 0 | 0 | 0 | 0 | 0 |
STAR result (official)¶
Scoring round (sum of scores): ChocoDrk 9, ChocoAlm 8, ChocoHzn 3, Mango 2, VanillaFrnch 1, VanillaClssc 0, Peach 0
Finalists (top two): ChocoDrk and ChocoAlm
Automatic runoff: ChocoDrk 1 vs ChocoAlm 2
STAR winner: ChocoAlm
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * ChocoDrk | * ChocoAlm |
-----------------------------------------------
* ChocoDrk > | --- | 1 - 0 - 2 |
* ChocoAlm > | 2 - 0 - 1 | --- |
[Divergence from STAR]
STAR = ChocoAlm
Approval = ChocoDrk (differs from STAR)
[Runoff Reversal]
- Score Round Winner(s) = (ChocoDrk)
- Runoff Round Winner = (ChocoAlm)
Candidate ChocoDrk earned the highest total score, but
Candidate ChocoAlm won the automatic runoff — not a malfunction,
STAR working as designed: the runoff elects the finalist preferred
by the majority (of voters with a preference).
--- STAR Voting Method (single winner) ---
Tabulating 3 ballots.
ChocoDrk,ChocoAlm,ChocoHzn,VanillaClssc,VanillaFrnch,Mango,Peach
4, 5, 3, 0, 1, 2, 0
0, 3, 0, 0, 0, 0, 0
5, 0, 0, 0, 0, 0, 0
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
ChocoDrk 1 1 0 0 0 1 | 9 3.0
ChocoAlm 1 0 1 0 0 1 | 8 2.7
ChocoHzn 0 0 1 0 0 2 | 3 1.0
VanillaClssc 0 0 0 0 0 3 | 0 0.0
VanillaFrnch 0 0 0 0 1 2 | 1 0.3
Mango 0 0 0 1 0 2 | 2 0.7
Peach 0 0 0 0 0 3 | 0 0.0
Scoring Round
The two highest-scoring candidates advance to the next round.
ChocoDrk -- 9 -- First place
ChocoAlm -- 8 -- Second place
ChocoHzn -- 3
Mango -- 2
VanillaFrnch -- 1
Peach -- 0
VanillaClssc -- 0
ChocoDrk and ChocoAlm advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
ChocoAlm -- 2 -- First place
ChocoDrk -- 1
Equal Support -- 0
ChocoAlm wins.
Voters with a preference: 3 of 3 (no Equal Support).
ChocoAlm 2 (67%) vs ChocoDrk 1 (33%); majority = 2.
Winner — STAR Voting Method (single winner)
ChocoAlm
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 3 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: ChocoDrk, ChocoAlm, ChocoHzn, VanillaClssc, VanillaFrnch, Mango, Peach
1 × ChocoAlm > ChocoDrk > ChocoHzn > Mango > VanillaFrnch (4, 5, 3, 0, 1, 2, 0)
1 × ChocoAlm (0, 3, 0, 0, 0, 0, 0)
1 × ChocoDrk (5, 0, 0, 0, 0, 0, 0)
FINAL RESULT
Candidate Votes Status
------------ ------- --------
ChocoAlm 2 Elected
ChocoDrk 1 Rejected
ChocoHzn 0 Rejected
Mango 0 Rejected
VanillaFrnch 0 Rejected
VanillaClssc 0 Rejected
Peach 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
ChocoAlm
--- 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 7): ChocoAlm
Outside (6): ChocoDrk, ChocoHzn, VanillaClssc, VanillaFrnch, Mango, Peach
One member ⇒ ChocoAlm is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner ChocoAlm is INSIDE the Smith set. ✓
Not guaranteed — RCV-IRV is not Smith-efficient — but it holds 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 3 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: ChocoDrk, ChocoAlm, ChocoHzn, VanillaClssc, VanillaFrnch, Mango, Peach
1 × ChocoAlm > ChocoDrk > ChocoHzn > Mango > VanillaFrnch > VanillaClssc=Peach (4, 5, 3, 0, 1, 2, 0)
1 × ChocoAlm > ChocoDrk=ChocoHzn=VanillaClssc=VanillaFrnch=Mango=Peach (0, 3, 0, 0, 0, 0, 0)
1 × ChocoDrk > ChocoAlm=ChocoHzn=VanillaClssc=VanillaFrnch=Mango=Peach (5, 0, 0, 0, 0, 0, 0)
Round-Robin — every pair, head-to-head (For – Against):
ChocoAlm beats ChocoDrk 2 – 1
ChocoDrk beats ChocoHzn 2 – 0
ChocoDrk beats VanillaClssc 2 – 0
ChocoDrk beats VanillaFrnch 2 – 0
ChocoDrk beats Mango 2 – 0
ChocoDrk beats Peach 2 – 0
ChocoAlm beats ChocoHzn 2 – 0
ChocoAlm beats VanillaClssc 2 – 0
ChocoAlm beats VanillaFrnch 2 – 0
ChocoAlm beats Mango 2 – 0
ChocoAlm beats Peach 2 – 0
ChocoHzn beats VanillaClssc 1 – 0
ChocoHzn beats VanillaFrnch 1 – 0
ChocoHzn beats Mango 1 – 0
ChocoHzn beats Peach 1 – 0
VanillaFrnch beats VanillaClssc 1 – 0
Mango beats VanillaClssc 1 – 0
VanillaClssc ties Peach 0 – 0
Mango beats VanillaFrnch 1 – 0
VanillaFrnch beats Peach 1 – 0
Mango beats Peach 1 – 0
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| ChocoDrk | ChocoAlm | ChocoHzn | VanillaClssc | VanillaFrnch | Mango | Peach |
-----------------------------------------------------------------------------------------------------------------------------------
ChocoDrk > | --- | 1 - 0 - 2 | 2 - 1 - 0 | 2 - 1 - 0 | 2 - 1 - 0 | 2 - 1 - 0 | 2 - 1 - 0 |
ChocoAlm > | 2 - 0 - 1 | --- | 2 - 1 - 0 | 2 - 1 - 0 | 2 - 1 - 0 | 2 - 1 - 0 | 2 - 1 - 0 |
ChocoHzn > | 0 - 1 - 2 | 0 - 1 - 2 | --- | 1 - 2 - 0 | 1 - 2 - 0 | 1 - 2 - 0 | 1 - 2 - 0 |
VanillaClssc > | 0 - 1 - 2 | 0 - 1 - 2 | 0 - 2 - 1 | --- | 0 - 2 - 1 | 0 - 2 - 1 | 0 - 3 - 0 |
VanillaFrnch > | 0 - 1 - 2 | 0 - 1 - 2 | 0 - 2 - 1 | 1 - 2 - 0 | --- | 0 - 2 - 1 | 1 - 2 - 0 |
Mango > | 0 - 1 - 2 | 0 - 1 - 2 | 0 - 2 - 1 | 1 - 2 - 0 | 1 - 2 - 0 | --- | 1 - 2 - 0 |
Peach > | 0 - 1 - 2 | 0 - 1 - 2 | 0 - 2 - 1 | 0 - 3 - 0 | 0 - 2 - 1 | 0 - 2 - 1 | --- |
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 ChocoAlm 6–0–0 6 +11 ChocoDrk, ChocoHzn, Mango, VanillaFrnch, VanillaClssc, Peach
2 ChocoDrk 5–1–0 5 +9 ChocoHzn, Mango, VanillaFrnch, VanillaClssc, Peach
3 ChocoHzn 4–2–0 4 +0 Mango, VanillaFrnch, VanillaClssc, Peach
4 Mango 3–3–0 3 -2 VanillaFrnch, VanillaClssc, Peach
5 VanillaFrnch 2–4–0 2 -4 VanillaClssc, Peach
6 VanillaClssc 0–5–1 0.5 -7 —
7 Peach 0–5–1 0.5 -7 —
Winner — Ranked Robin (RCV-RR): ChocoAlm
beats every opponent head-to-head — the Condorcet winner.
--- 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 7): ChocoAlm
Outside (6): ChocoDrk, ChocoHzn, VanillaClssc, VanillaFrnch, Mango, Peach
One member ⇒ ChocoAlm is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner ChocoAlm 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