Borda SCC Ex.15 — STAR: C wins (and stays won when a loser exits)¶
▶ Live on BetterVoting: vote · results ↗ (election q3h4fk · test BV2161) — 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 C. Only Approval differs, electing B: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding B's breadth of acceptability over C's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | C |
| RCV-IRV | C |
| Ranked Robin (RCV-RR) | C |
| Approval | B |
| Range / Score | C |
| Condorcet | none (cycle) |
Flags: none
Source election: method_comparisons/felsenthal_paradoxes/cases/bv2161_q3h4fk_star.yaml · STAR tabulated mirror: bv2161_q3h4fk_star_tabulated.txt
3 candidates, 7 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | A | B | C |
|---|---|---|---|
| 2 | 5 | 1 | 3 |
| 2 | 3 | 5 | 1 |
| 3 | 1 | 3 | 5 |
STAR result (official)¶
Scoring round (sum of scores): C 23, B 21, A 19
Finalists (top two): C and B
Automatic runoff: C 5 vs B 2
STAR winner: C
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * B | * C |
-----------------------------------------
* B > | --- |2 - 0 - 5 |
* C > | 5 - 0 - 2 | --- |
[Divergence from STAR]
STAR = C
Approval = B (differs from STAR)
--- STAR Voting Method (single winner) ---
Tabulating 7 ballots.
Count × A,B,C
3 × 1,3,5
2 × 5,1,3
2 × 3,5,1
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
A 2 0 2 0 3 0 | 19 2.7
B 2 0 3 0 2 0 | 21 3.0
C 3 0 2 0 2 0 | 23 3.3
Scoring Round
The two highest-scoring candidates advance to the next round.
C -- 23 -- First place
B -- 21 -- Second place
A -- 19
C and B advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
C -- 5 -- First place
B -- 2
Equal Support -- 0
C wins.
Voters with a preference: 7 of 7 (no Equal Support).
C 5 (71%) vs B 2 (29%); majority = 4.
Winner — STAR Voting Method (single winner)
C
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 7 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
2 × A > C > B (5, 1, 3)
2 × B > A > C (3, 5, 1)
3 × C > B > A (1, 3, 5)
ROUND 1
Candidate Votes Status
----------- ------- --------
C 3 Hopeful
B 2 Hopeful
A 2 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
C 5 Elected
B 2 Rejected
A 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
C
--- 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 (3 of 3): A, B, C
Outside (0): —
More than one member ⇒ NO Condorcet winner: the top of the tournament is a
cycle, so the strongest "candidate" is a set, not a person. Which member of
the set should win is exactly what Minimax / Ranked Pairs / Schulze disagree
about — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.
RCV-IRV winner C 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 7 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: A, B, C
2 × A > C > B (5, 1, 3)
2 × B > A > C (3, 5, 1)
3 × C > B > A (1, 3, 5)
Round-Robin — every pair, head-to-head (For – Against):
B beats A 5 – 2
A beats C 4 – 3
C beats B 5 – 2
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| A | B | C |
-----------------------------------------
A > | --- |2 - 0 - 5 |4 - 0 - 3 |
B > | 5 - 0 - 2 | --- |2 - 0 - 5 |
C > | 3 - 0 - 4 |5 - 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 C 1–1–0 1 +2 B
2 B 1–1–0 1 +0 A
3 A 1–1–0 1 -2 C
Winner — Ranked Robin (RCV-RR): C
*** 3 candidates tie for the most wins (A, B, C) — a Condorcet cycle (no candidate beats all others). Resolved by total margin, then lot order. (This is where Minimax / Ranked Pairs / Schulze differ — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.)
--- 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 (3 of 3): A, B, C
Outside (0): —
More than one member ⇒ NO Condorcet winner: the top of the tournament is a
cycle, so the strongest "candidate" is a set, not a person. Which member of
the set should win is exactly what Minimax / Ranked Pairs / Schulze disagree
about — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.
Ranked Robin (RCV-RR) winner C 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