P3 manipulated — two voters bury their 4th choice and STAR elects their favourite¶
Bucket — CYCLE_OR_THREE_WAY: Cycle / three-way split
Generated by STARVote_LH_tabulation_engine/tools_adam/scripts/build_divergence_index.py — rebuilt from the election file; do not hand-edit.
What happens¶
There is no Condorcet winner — the head-to-head results form a cycle (X beats Y beats Z beats X). With no pairwise anchor the methods split: STAR=Edinburgh, RCV-IRV=Dublin, Ranked Robin=Edinburgh (RR breaks the cycle by total margin). No rule is clearly 'right'; a genuinely hard election, not an indictment of any one method.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Edinburgh |
| RCV-IRV | Dublin |
| Ranked Robin (RCV-RR) | Edinburgh |
| Approval | Bergen |
| Range / Score | Edinburgh |
| Condorcet | none (cycle) |
Flags: none
Source election: method_comparisons/manipulability_p3/cases/p3_manip_star.yaml · STAR tabulated mirror: p3_manip_star_tabulated.txt
5 candidates, 7 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Athens | Bergen | Cork | Dublin | Edinburgh |
|---|---|---|---|---|---|
| 2 | 3 | 0 | 4 | 0 | 5 |
| 3 | 0 | 3 | 2 | 5 | 4 |
| 2 | 5 | 4 | 3 | 2 | 0 |
STAR result (official)¶
Scoring round (sum of scores): Edinburgh 22, Cork 20, Dublin 19, Bergen 17, Athens 16
Finalists (top two): Edinburgh and Cork
Automatic runoff: Edinburgh 5 vs Cork 2
STAR winner: Edinburgh
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Cork | * Edinburgh |
--------------------------------------------------
* Cork > | --- | 2 - 0 - 5 |
* Edinburgh > | 5 - 0 - 2 | --- |
[Divergence from STAR]
STAR = Edinburgh
Choose-One (Plurality) = Dublin (differs from STAR)
RCV-IRV = Dublin (differs from STAR)
Approval = Bergen (differs from STAR)
Note: no ballots had tied scores, so RCV-IRV vs STAR here is a genuine
method difference, not a tie-breaking artifact.
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 7 ballots.
Count × Athens,Bergen,Cork,Dublin,Edinburgh
3 × 0, 3, 2, 5, 4
2 × 3, 0, 4, 0, 5
2 × 5, 4, 3, 2, 0
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Athens 2 0 2 0 0 3 | 16 2.3
Bergen 0 2 3 0 0 2 | 17 2.4
Cork 0 2 2 3 0 0 | 20 2.9
Dublin 3 0 0 2 0 2 | 19 2.7
Edinburgh 2 3 0 0 0 2 | 22 3.1
Scoring Round
The two highest-scoring candidates advance to the next round.
Edinburgh -- 22 -- First place
Cork -- 20 -- Second place
Dublin -- 19
Bergen -- 17
Athens -- 16
Edinburgh and Cork advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Edinburgh -- 5 -- First place
Cork -- 2
Equal Support -- 0
Edinburgh wins.
Voters with a preference: 7 of 7 (no Equal Support).
Edinburgh 5 (71%) vs Cork 2 (29%); majority = 4.
Winner — STAR Voting Method (single winner)
Edinburgh
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: Athens, Bergen, Cork, Dublin, Edinburgh
2 × Edinburgh > Cork > Athens (3, 0, 4, 0, 5)
3 × Dublin > Edinburgh > Bergen > Cork (0, 3, 2, 5, 4)
2 × Athens > Bergen > Cork > Dublin (5, 4, 3, 2, 0)
ROUND 1
Candidate Votes Status
----------- ------- --------
Dublin 3 Hopeful
Edinburgh 2 Hopeful
Athens 2 Rejected
Bergen 0 Rejected
Cork 0 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Dublin 5 Elected
Edinburgh 2 Rejected
Athens 0 Rejected
Bergen 0 Rejected
Cork 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Dublin
--- 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 (5 of 5): Edinburgh, Athens, Cork, Dublin, Bergen
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.
Note: the Copeland leaders (Edinburgh) are only part of the set — the
win–loss table's top block understates how wide the contention is.
RCV-IRV winner Dublin 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: Athens, Bergen, Cork, Dublin, Edinburgh
2 × Edinburgh > Cork > Athens > Bergen=Dublin (3, 0, 4, 0, 5)
3 × Dublin > Edinburgh > Bergen > Cork > Athens (0, 3, 2, 5, 4)
2 × Athens > Bergen > Cork > Dublin > Edinburgh (5, 4, 3, 2, 0)
Round-Robin — every pair, head-to-head (For – Against):
Athens beats Bergen 4 – 3
Cork beats Athens 5 – 2
Athens beats Dublin 4 – 3
Edinburgh beats Athens 5 – 2
Bergen beats Cork 5 – 2
Dublin beats Bergen 3 – 2
Edinburgh beats Bergen 5 – 2
Cork beats Dublin 4 – 3
Edinburgh beats Cork 5 – 2
Dublin beats Edinburgh 5 – 2
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Athens | Bergen | Cork | Dublin | Edinburgh |
---------------------------------------------------------------------------------
Athens > | --- | 4 - 0 - 3 | 2 - 0 - 5 | 4 - 0 - 3 | 2 - 0 - 5 |
Bergen > | 3 - 0 - 4 | --- | 5 - 0 - 2 | 2 - 2 - 3 | 2 - 0 - 5 |
Cork > | 5 - 0 - 2 | 2 - 0 - 5 | --- | 4 - 0 - 3 | 2 - 0 - 5 |
Dublin > | 3 - 0 - 4 | 3 - 2 - 2 | 3 - 0 - 4 | --- | 5 - 0 - 2 |
Edinburgh > | 5 - 0 - 2 | 5 - 0 - 2 | 5 - 0 - 2 | 2 - 0 - 5 | --- |
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 Edinburgh 3–1–0 3 +6 Cork, Athens, Bergen
2 Dublin 2–2–0 2 +2 Edinburgh, Bergen
3 Cork 2–2–0 2 -2 Dublin, Athens
4 Athens 2–2–0 2 -4 Dublin, Bergen
5 Bergen 1–3–0 1 -2 Cork
Winner — Ranked Robin (RCV-RR): Edinburgh
the most head-to-head wins (3).
--- 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 (5 of 5): Edinburgh, Athens, Cork, Dublin, Bergen
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.
Note: the Copeland leaders (Edinburgh) are only part of the set — the
win–loss table's top block understates how wide the contention is.
Ranked Robin (RCV-RR) winner Edinburgh 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