Monotonicity — STAR counterpart (BEFORE — X wins)¶
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=X, RCV-IRV=X, Ranked Robin=Y (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 | X |
| RCV-IRV | X |
| Ranked Robin (RCV-RR) | Y |
| Approval | Y |
| Range / Score | Y |
| Condorcet | none (cycle) |
Flags: none
Source election: method_comparisons/monotonicity/cases/monotonicity_star_before.yaml · STAR tabulated mirror: monotonicity_star_before_tabulated.txt
3 candidates, 34 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | X | Y | Z |
|---|---|---|---|
| 12 | 5 | 3 | 0 |
| 12 | 0 | 5 | 3 |
| 10 | 3 | 0 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Y 96, X 90, Z 86
Finalists (top two): Y and X
Automatic runoff: Y 12 vs X 22
STAR winner: X
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * X | * Y |
-----------------------------------------------
* X > | --- |22 - 0 - 12 |
* Y > | 12 - 0 - 22 | --- |
[Divergence from STAR]
STAR = X
Approval = Y (differs from STAR)
RCV-RR = Y (differs from STAR)
[Runoff Reversal]
- Score Round Winner(s) = (Y)
- Runoff Round Winner = (X)
Candidate Y earned the highest total score, but
Candidate X 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 34 ballots.
Count × X,Y,Z
12 × 5,3,0
12 × 0,5,3
10 × 3,0,5
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
X 12 0 10 0 0 12 | 90 2.6
Y 12 0 12 0 0 10 | 96 2.8
Z 10 0 12 0 0 12 | 86 2.5
Scoring Round
The two highest-scoring candidates advance to the next round.
Y -- 96 -- First place
X -- 90 -- Second place
Z -- 86
Y and X advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
X -- 22 -- First place
Y -- 12
Equal Support -- 0
X wins.
Voters with a preference: 34 of 34 (no Equal Support).
X 22 (65%) vs Y 12 (35%); majority = 18.
Winner — STAR Voting Method (single winner)
X
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 34 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: X, Y, Z
12 × X > Y (5, 3, 0)
12 × Y > Z (0, 5, 3)
10 × Z > X (3, 0, 5)
ROUND 1
Candidate Votes Status
----------- ------- --------
Y 12 Hopeful
X 12 Hopeful
Z 10 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
X 22 Elected
Y 12 Rejected
Z 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
X
--- 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): X, Y, Z
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 X 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 34 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: X, Y, Z
12 × X > Y > Z (5, 3, 0)
12 × Y > Z > X (0, 5, 3)
10 × Z > X > Y (3, 0, 5)
Round-Robin — every pair, head-to-head (For – Against):
X beats Y 22 – 12
Z beats X 22 – 12
Y beats Z 24 – 10
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| X | Y | Z |
--------------------------------------------------
X > | --- |22 - 0 - 12 |12 - 0 - 22 |
Y > | 12 - 0 - 22 | --- |24 - 0 - 10 |
Z > | 22 - 0 - 12 |10 - 0 - 24 | --- |
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 Y 1–1–0 1 +4 Z
2 X 1–1–0 1 +0 Y
3 Z 1–1–0 1 -4 X
Winner — Ranked Robin (RCV-RR): Y
*** 3 candidates tie for the most wins (X, Y, Z) — 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): X, Y, Z
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 Y 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