The eight ambiguous CSV lines, disambiguated (BV issue #778 ex1)¶
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 B. Only Approval differs, electing A: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding A's breadth of acceptability over B's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | B |
| RCV-IRV | B |
| Ranked Robin (RCV-RR) | B |
| Approval | A |
| Range / Score | B |
| Condorcet | B |
Flags: 1 tied-score ballot(s)
Source election: 01_STAR/02_Examples/cases/csv_ambiguity_ex1_c4_b8.yaml · STAR tabulated mirror: csv_ambiguity_ex1_c4_b8_tabulated.txt
4 candidates, 8 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | A | B | C | D |
|---|---|---|---|---|
| 3 | 0 | 1 | 0 | 0 |
| 4 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 1 |
STAR result (official)¶
Scoring round (sum of scores): B 3, C 1, D 1, A 0
Finalists (top two): B and C
Automatic runoff: B 3 vs C 1 (4 equal/no-preference)
STAR winner: B
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
Note: C and D tied at 1 in the Scoring Round, and the lot rung (the
ballots could not separate them) advanced C. The * marks who
advanced, not who scored highest. D is filtered out of this grid
— see the Scoring Round for how the tie was settled.
| * B | * C |
-----------------------------------------
* B > | --- |3 - 4 - 1 |
* C > | 1 - 4 - 3 | --- |
[Divergence from STAR]
STAR = B
Approval = A (differs from STAR)
--- STAR Voting Method (single winner) ---
Tabulating 8 ballots. Note: 2 of 8 ballots are marked as abstentions.
A,B,C,D
0,1,0,0
~,~,~,~
0,1,0,&
0,0,1,1
?,?,?,?
0,1,0,-
0,0,0,0
0,-,0,-
('-' = 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
A 0 0 0 0 0 6 2 | 0 0.0 0.0
B 0 0 0 0 3 2 3 | 3 0.4 0.6
C 0 0 0 0 1 5 2 | 1 0.1 0.2
D 0 0 0 0 1 2 5 | 1 0.1 0.3
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.
B -- 3 -- First place
C -- 1 -- Tied for second place
D -- 1 -- Tied for second place
A -- 0
B advances, but there's a two-way tie for second.
Scoring Round: First tiebreaker
The candidate preferred in the most head-to-head matchups advances.
C -- 0 -- Tied for second place
D -- 0 -- Tied for second place
Equal Support -- 8
There's still a two-way tie for second.
Scoring Round: Second tiebreaker
The candidate with the most votes of score 5 advances.
C -- 0 -- Tied for second place
D -- 0 -- Tied for second place
There's still a two-way tie for second.
*(Ties are resolved by choosing the tied candidate with the highest-priority official lot number.)*
Lot-number priority order: ['A', 'B', 'C', 'D']
[Tiebreaker: Lot Number Priority]
Tie among: ['C', 'D']
Resolved: ['C'] (selected by lot-number priority).
[Lot-decided tie — rare]
⚠ The ballots did not break this tie: the deterministic rungs
(pairwise / score, then five-star) all came back equal, so the
pre-published LOT order chose among the tied candidates — the
result here was set by lot, not by the votes. Usually the
"dead rung": no tied candidate held a score-5 vote (five-star
counts fives, not fours). Verify the tied candidates' 5-counts.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
B -- 3 -- First place
C -- 1
Equal Support -- 4
B wins.
Voters with a preference: 4 of 8 (4 Equal Support).
B 3 (75%) vs C 1 (25%); majority = 3.
Winner — STAR Voting Method (single winner)
B
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 8 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: A, B, C, D
3 × B (0, 1, 0, 0)
4 × (all unranked) (0, 0, 0, 0)
1 × C > D (0, 0, 1, 1)
FINAL RESULT
Candidate Votes Status
----------- ------- --------
B 3 Elected
C 1 Rejected
D 0 Rejected
A 0 Rejected
Blank Votes 4 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
B
--- 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.
RCV-IRV winner B 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 8 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: A, B, C, D
3 × B > A=C=D (0, 1, 0, 0)
4 × A=B=C=D (0, 0, 0, 0)
1 × C=D > A=B (0, 0, 1, 1)
Round-Robin — every pair, head-to-head (For – Against):
B beats A 3 – 0
C beats A 1 – 0
D beats A 1 – 0
B beats C 3 – 1
B beats D 3 – 1
C ties D 0 – 0
--- 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 > | --- |0 - 5 - 3 |0 - 7 - 1 |0 - 7 - 1 |
B > | 3 - 5 - 0 | --- |3 - 4 - 1 |3 - 4 - 1 |
C > | 1 - 7 - 0 |1 - 4 - 3 | --- |0 - 8 - 0 |
D > | 1 - 7 - 0 |1 - 4 - 3 |0 - 8 - 0 | --- |
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 +7 C, D, A
2 C 1–1–1 1.5 -1 A
3 D 1–1–1 1.5 -1 A
4 A 0–3–0 0 -5 —
Winner — Ranked Robin (RCV-RR): B
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 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