STAR mono-raise-delete — part 2: raise X, delete Y-below-X, X loses¶
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 Z. Only Approval differs, electing X: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding X's breadth of acceptability over Z's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Z |
| RCV-IRV | Z |
| Ranked Robin (RCV-RR) | Z |
| Approval | X |
| Range / Score | X |
| Condorcet | Z |
Flags: none
Source election: method_comparisons/monotonicity/cases/mono_raise_delete_after.yaml · STAR tabulated mirror: mono_raise_delete_after_tabulated.txt
3 candidates, 30 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | X | Y | Z |
|---|---|---|---|
| 12 | 5 | 4 | 0 |
| 9 | 4 | 0 | 5 |
| 9 | 0 | 2 | 3 |
STAR result (official)¶
Scoring round (sum of scores): X 96, Z 72, Y 66
Finalists (top two): X and Z
Automatic runoff: X 12 vs Z 18
STAR winner: Z
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * X | * Z |
-----------------------------------------------
* X > | --- |12 - 0 - 18 |
* Z > | 18 - 0 - 12 | --- |
[Divergence from STAR]
STAR = Z
Approval = X (differs from STAR)
[Runoff Reversal]
- Score Round Winner(s) = (X)
- Runoff Round Winner = (Z)
Candidate X earned the highest total score, but
Candidate Z 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 30 ballots.
Count × X,Y,Z
12 × 5,4,0
9 × 4,0,5
9 × 0,2,3
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
X 12 9 0 0 0 9 | 96 3.2
Y 0 12 0 9 0 9 | 66 2.2
Z 9 0 9 0 0 12 | 72 2.4
Scoring Round
The two highest-scoring candidates advance to the next round.
X -- 96 -- First place
Z -- 72 -- Second place
Y -- 66
X and Z advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Z -- 18 -- First place
X -- 12
Equal Support -- 0
Z wins.
Voters with a preference: 30 of 30 (no Equal Support).
Z 18 (60%) vs X 12 (40%); majority = 16.
Winner — STAR Voting Method (single winner)
Z
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 30 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, 4, 0)
9 × Z > X (4, 0, 5)
9 × Z > Y (0, 2, 3)
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Z 18 Elected
X 12 Rejected
Y 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Z
--- 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): Z
Outside (2): X, Y
One member ⇒ Z is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Z 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 30 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: X, Y, Z
12 × X > Y > Z (5, 4, 0)
9 × Z > X > Y (4, 0, 5)
9 × Z > Y > X (0, 2, 3)
Round-Robin — every pair, head-to-head (For – Against):
X beats Y 21 – 9
Z beats X 18 – 12
Z beats Y 18 – 12
--- 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 > | --- |21 - 0 - 9 |12 - 0 - 18 |
Y > | 9 - 0 - 21 | --- |12 - 0 - 18 |
Z > | 18 - 0 - 12 |18 - 0 - 12 | --- |
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 Z 2–0–0 2 +12 X, Y
2 X 1–1–0 1 +6 Y
3 Y 0–2–0 0 -18 —
Winner — Ranked Robin (RCV-RR): Z
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): Z
Outside (2): X, Y
One member ⇒ Z is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Z 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