Preference vs Support — the center TOLERATED (wings score Blair 1)¶
▶ Live on BetterVoting: vote · results ↗ (election ywx39y · test BV2225) — an independent tabulator to check the winners below against.
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¶
The methods split: STAR=Alex, RCV-IRV=Alex, Ranked Robin=Blair; the Condorcet (pairwise) winner is Blair. A genuinely hard, divided electorate — useful for showing that the choice of method matters most exactly when voters are split.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Alex |
| RCV-IRV | Alex |
| Ranked Robin (RCV-RR) | Blair |
| Approval | Alex |
| Range / Score | Alex |
| Condorcet | Blair |
Flags: none
Source election: method_comparisons/preference_vs_support/cases/bv2225_ywx39y_center_tolerated.yaml · STAR tabulated mirror: bv2225_ywx39y_center_tolerated_tabulated.txt
3 candidates, 36 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Alex | Blair | Cole |
|---|---|---|---|
| 15 | 5 | 1 | 0 |
| 6 | 1 | 5 | 0 |
| 15 | 0 | 1 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Alex 81, Cole 75, Blair 60
Finalists (top two): Alex and Cole
Automatic runoff: Alex 21 vs Cole 15
STAR winner: Alex
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Alex | * Cole |
-----------------------------------------------
* Alex > | --- |21 - 0 - 15 |
* Cole > | 15 - 0 - 21 | --- |
[Divergence from STAR]
STAR = Alex
RCV-RR (Condorcet) = Blair (differs from STAR)
--- STAR Voting Method (single winner) ---
Tabulating 36 ballots.
Count × Alex,Blair,Cole
15 × 5, 1, 0
15 × 0, 1, 5
6 × 1, 5, 0
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Alex 15 0 0 0 6 15 | 81 2.3
Blair 6 0 0 0 30 0 | 60 1.7
Cole 15 0 0 0 0 21 | 75 2.1
Scoring Round
The two highest-scoring candidates advance to the next round.
Alex -- 81 -- First place
Cole -- 75 -- Second place
Blair -- 60
Alex and Cole advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Alex -- 21 -- First place
Cole -- 15
Equal Support -- 0
Alex wins.
Voters with a preference: 36 of 36 (no Equal Support).
Alex 21 (58%) vs Cole 15 (42%); majority = 19.
Winner — STAR Voting Method (single winner)
Alex
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 36 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: Alex, Blair, Cole
15 × Alex > Blair (5, 1, 0)
6 × Blair > Alex (1, 5, 0)
15 × Cole > Blair (0, 1, 5)
ROUND 1
Candidate Votes Status
----------- ------- --------
Alex 15 Hopeful
Cole 15 Hopeful
Blair 6 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Alex 21 Elected
Cole 15 Rejected
Blair 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Alex
--- 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): Blair
Outside (2): Alex, Cole
One member ⇒ Blair is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Alex is OUTSIDE the Smith set. ✗
Every member of the set (Blair) beats Alex head-to-head, yet
RCV-IRV elected Alex 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 36 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Alex, Blair, Cole
15 × Alex > Blair > Cole (5, 1, 0)
6 × Blair > Alex > Cole (1, 5, 0)
15 × Cole > Blair > Alex (0, 1, 5)
Round-Robin — every pair, head-to-head (For – Against):
Blair beats Alex 21 – 15
Alex beats Cole 21 – 15
Blair beats Cole 21 – 15
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Alex | Blair | Cole |
------------------------------------------------------
Alex > | --- |15 - 0 - 21 |21 - 0 - 15 |
Blair > | 21 - 0 - 15 | --- |21 - 0 - 15 |
Cole > | 15 - 0 - 21 |15 - 0 - 21 | --- |
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 Blair 2–0–0 2 +12 Alex, Cole
2 Alex 1–1–0 1 +0 Cole
3 Cole 0–2–0 0 -12 —
Winner — Ranked Robin (RCV-RR): Blair
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): Blair
Outside (2): Alex, Cole
One member ⇒ Blair is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Blair 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