Hamlin & Hua §4.1 — the same marks read pairwise: 60 of 100 voters express no preference¶
Bucket — IRV_DIFFERS_ARTIFACT: RCV-IRV differs — tie-break artifact
Generated by STARVote_LH_tabulation_engine/tools_adam/scripts/build_divergence_index.py — rebuilt from the election file; do not hand-edit.
What happens¶
On these ballots RCV-IRV reports A rather than STAR's B, but this is an artifact of score→rank conversion, not a robust method difference: 100 of 100 ballots have tied non-zero scores, so their ranks are set by an arbitrary candidate-priority order; the RCV-IRV winner flips when that priority order is reversed. Ranked Robin and the Condorcet (pairwise) winner both agree with STAR (B). Do not use this case to criticize RCV-IRV — the disagreement is a coin-flip created by equal scores and would vanish under a different (equally arbitrary) tie-break.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | B |
| RCV-IRV | A |
| Ranked Robin (RCV-RR) | B |
| Approval | B |
| Range / Score | B |
| Condorcet | B |
Flags: 100 tied-score ballot(s); IRV winner flips under reversed priority (fragile tie); RR conversion-sensitive (weak=B, strict=A)
Source election: method_comparisons/approval_majority_criterion/cases/hh41_03_marks_read_pairwise.yaml · STAR tabulated mirror: hh41_03_marks_read_pairwise_tabulated.txt
3 candidates, 100 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | A | B | C |
|---|---|---|---|
| 60 | 5 | 5 | 0 |
| 40 | 0 | 5 | 5 |
STAR result (official)¶
Scoring round (sum of scores): B 500, A 300, C 200
Finalists (top two): B and A
Automatic runoff: B 40 vs A 0 (60 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
| * A | * B |
-----------------------------------------------
* A > | --- | 0 - 60 - 40 |
* B > | 40 - 60 - 0 | --- |
[Divergence from STAR]
STAR = B
Choose-One (Plurality) = A (differs from STAR)
RCV-IRV = A (differs from STAR)
Note: 100 of 100 ballots (100%) had equal non-zero scores, so their ranks
were decided by candidate priority order. The RCV-IRV result may be
an artifact of score-to-rank tie-breaking rather than a deep
difference.
Note: Ranked Robin (RCV-RR) agrees with STAR, so RCV-IRV is the lone
outlier — the classic center-squeeze signature.
--- STAR Voting Method (single winner) ---
Tabulating 100 ballots.
Count × A,B,C
60 × 5,5,0
40 × 0,5,5
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
A 60 0 0 0 0 40 | 300 3.0
B 100 0 0 0 0 0 | 500 5.0
C 40 0 0 0 0 60 | 200 2.0
Scoring Round
The two highest-scoring candidates advance to the next round.
B -- 500 -- First place
A -- 300 -- Second place
C -- 200
B and A advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
B -- 40 -- First place
A -- 0
Equal Support -- 60
B wins.
Voters with a preference: 40 of 100 (60 Equal Support).
B 40 (100%) vs A 0 (0%); majority = 21.
Winner — STAR Voting Method (single winner)
B
RCV-IRV — round by round¶
⚠️ This election has a fragile IRV tie (equal scores force an arbitrary tie-break). The round table below is only one realization; a different tie-break can change the winner. See the flag above.
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 100 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
60 × A > B (5, 5, 0)
40 × B > C (0, 5, 5)
FINAL RESULT
Candidate Votes Status
----------- ------- --------
A 60 Elected
B 40 Rejected
C 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
A
--- 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 3): B
Outside (2): A, C
One member ⇒ B is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner A is OUTSIDE the Smith set. ✗
Every member of the set (B) beats A head-to-head, yet
RCV-IRV elected A anyway. RCV-IRV is not Smith-efficient (nor
Condorcet-efficient) — this is the shape a center squeeze leaves behind.
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 100 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: A, B, C
60 × A=B > C (5, 5, 0)
40 × B=C > A (0, 5, 5)
Round-Robin — every pair, head-to-head (For – Against):
B beats A 40 – 0
A beats C 60 – 40
B beats C 60 – 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 |
--------------------------------------------------
A > | --- | 0 - 60 - 40 |60 - 0 - 40 |
B > | 40 - 60 - 0 | --- |60 - 40 - 0 |
C > | 40 - 0 - 60 | 0 - 40 - 60 | --- |
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 2–0–0 2 +100 A, C
2 A 1–1–0 1 -20 C
3 C 0–2–0 0 -80 —
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 3): B
Outside (2): A, C
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