The seat nobody wanted — a field with no enthusiasm¶
▶ Live on BetterVoting: vote · results ↗ (election 8q3xcg · test BV2284) — an independent tabulator to check the winners below against.
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 Beth. Only Approval differs, electing Colin: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding Colin's breadth of acceptability over Beth's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Beth |
| RCV-IRV | Beth |
| Ranked Robin (RCV-RR) | Beth |
| Approval | Colin |
| Range / Score | Beth |
| Condorcet | Beth |
Flags: 17 tied-score ballot(s)
Source election: 01_STAR/01_Learn/reporting/cases/bv2284_8q3xcg_weak_mandate.yaml · STAR tabulated mirror: bv2284_8q3xcg_weak_mandate_tabulated.txt
4 candidates, 100 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Arlo | Beth | Colin | Dara |
|---|---|---|---|---|
| 1 | 0 | 0 | 5 | 0 |
| 3 | 1 | 0 | 0 | 1 |
| 5 | 0 | 1 | 2 | 0 |
| 3 | 1 | 1 | 0 | 1 |
| 2 | 1 | 0 | 0 | 2 |
| 8 | 2 | 0 | 0 | 0 |
| 3 | 2 | 0 | 0 | 1 |
| 2 | 0 | 0 | 4 | 0 |
| 5 | 1 | 2 | 0 | 0 |
| 17 | 0 | 1 | 0 | 0 |
| 6 | 0 | 2 | 0 | 0 |
| 3 | 1 | 0 | 0 | 0 |
| 3 | 1 | 5 | 0 | 0 |
| 8 | 0 | 0 | 0 | 0 |
| 6 | 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 4 | 0 |
| 2 | 1 | 0 | 2 | 0 |
| 2 | 0 | 1 | 5 | 0 |
| 1 | 5 | 0 | 0 | 0 |
| 4 | 0 | 0 | 0 | 2 |
| 2 | 1 | 4 | 0 | 0 |
| 3 | 2 | 1 | 0 | 0 |
| 1 | 0 | 1 | 0 | 2 |
| 2 | 0 | 0 | 0 | 5 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 2 | 1 | 0 | 1 |
| 2 | 1 | 1 | 2 | 0 |
| 1 | 1 | 0 | 0 | 4 |
| 1 | 0 | 1 | 4 | 0 |
| 1 | 0 | 0 | 2 | 0 |
STAR result (official)¶
Scoring round (sum of scores): Beth 88, Arlo 68, Colin 51, Dara 39
Finalists (top two): Beth and Arlo
Automatic runoff: Beth 43 vs Arlo 27 (30 equal/no-preference)
STAR winner: Beth
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Arlo | * Beth |
-----------------------------------------------
* Arlo > | --- |27 - 30 - 43 |
* Beth > | 43 - 30 - 27 | --- |
[Divergence from STAR]
STAR = Beth
Approval = Colin (differs from STAR)
--- STAR Voting Method (single winner) ---
Tabulating 100 ballots.
Count × Arlo,Beth,Colin,Dara
15 × 0, 1, -, 0
8 × 2, 0, -, 0
6 × 0, 2, -, 0
6 × 1, 1, -, 0
5 × 0, 1, 2, 0
5 × 1, 2, -, 0
5 × 0, 0, -, 0
4 × 0, 0, -, 2
3 × 1, 0, -, 1
3 × 1, 1, -, 1
3 × 2, 0, -, 1
3 × 1, 0, -, 0
3 × 1, 5, -, 0
3 × 0, 0, 0, 0
3 × 2, 1, -, 0
2 × 1, 0, -, 2
2 × 0, 0, 4, 0
2 × 0, 1, 0, 0
2 × 1, 0, 2, 0
2 × 0, 1, 5, 0
2 × 1, 4, -, 0
2 × 0, 0, -, 5
2 × 1, 1, 2, 0
1 × 0, 0, 5, 0
1 × 1, 1, 4, 0
1 × 5, 0, -, 0
1 × 0, 1, -, 2
1 × 0, 1, -, 1
1 × 2, 1, -, 1
1 × 1, 0, -, 4
1 × 0, 1, 4, 0
1 × 0, 0, 2, 0
('-' = left blank / abstained; '0' = scored zero — both count as 0 stars.)
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 Abs | Total Avg all Avg rated
Arlo 1 0 0 15 33 51 0 | 68 0.7 0.7
Beth 3 2 0 11 43 41 0 | 88 0.9 0.9
Colin 3 4 0 10 0 5 78 | 51 0.5 2.3
Dara 2 1 0 7 11 79 0 | 39 0.4 0.4
Avg all = Total / all ballots — a blank counts as 0, so this is the Total the Scoring Round ranks on, per ballot.
Avg rated = Total / the ballots that scored this candidate (Abs excluded) — support among voters who had an opinion.
Scoring Round
The two highest-scoring candidates advance to the next round.
Beth -- 88 -- First place
Arlo -- 68 -- Second place
Colin -- 51
Dara -- 39
Beth and Arlo advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Beth -- 43 -- First place
Arlo -- 27
Equal Support -- 30
Beth wins.
Voters with a preference: 70 of 100 (30 Equal Support).
Beth 43 (61%) vs Arlo 27 (39%); majority = 36.
Winner — STAR Voting Method (single winner)
Beth
RCV-IRV — round by round¶
--- 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: Arlo, Beth, Colin, Dara
1 × Colin (0, 0, 5, 0)
3 × Arlo > Dara (1, 0, 0, 1)
5 × Colin > Beth (0, 1, 2, 0)
3 × Arlo > Beth > Dara (1, 1, 0, 1)
2 × Dara > Arlo (1, 0, 0, 2)
8 × Arlo (2, 0, 0, 0)
3 × Arlo > Dara (2, 0, 0, 1)
2 × Colin (0, 0, 4, 0)
5 × Beth > Arlo (1, 2, 0, 0)
17 × Beth (0, 1, 0, 0)
6 × Beth (0, 2, 0, 0)
3 × Arlo (1, 0, 0, 0)
3 × Beth > Arlo (1, 5, 0, 0)
8 × (all unranked) (0, 0, 0, 0)
6 × Arlo > Beth (1, 1, 0, 0)
1 × Colin > Arlo > Beth (1, 1, 4, 0)
2 × Colin > Arlo (1, 0, 2, 0)
2 × Colin > Beth (0, 1, 5, 0)
1 × Arlo (5, 0, 0, 0)
4 × Dara (0, 0, 0, 2)
2 × Beth > Arlo (1, 4, 0, 0)
3 × Arlo > Beth (2, 1, 0, 0)
1 × Dara > Beth (0, 1, 0, 2)
2 × Dara (0, 0, 0, 5)
1 × Beth > Dara (0, 1, 0, 1)
1 × Arlo > Beth > Dara (2, 1, 0, 1)
2 × Colin > Arlo > Beth (1, 1, 2, 0)
1 × Dara > Arlo (1, 0, 0, 4)
1 × Colin > Beth (0, 1, 4, 0)
1 × Colin (0, 0, 2, 0)
ROUND 1
Candidate Votes Status
----------- ------- --------
Beth 34 Hopeful
Arlo 31 Hopeful
Colin 17 Rejected
Dara 10 Rejected
Blank Votes 8 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Beth 43 Elected
Arlo 39 Rejected
Colin 0 Rejected
Dara 0 Rejected
Blank Votes 18 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Beth
--- 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 4): Beth
Outside (3): Arlo, Colin, Dara
One member ⇒ Beth is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Beth 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 100 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Arlo, Beth, Colin, Dara
1 × Colin > Arlo=Beth=Dara (0, 0, 5, 0)
3 × Arlo=Dara > Beth=Colin (1, 0, 0, 1)
5 × Colin > Beth > Arlo=Dara (0, 1, 2, 0)
3 × Arlo=Beth=Dara > Colin (1, 1, 0, 1)
2 × Dara > Arlo > Beth=Colin (1, 0, 0, 2)
8 × Arlo > Beth=Colin=Dara (2, 0, 0, 0)
3 × Arlo > Dara > Beth=Colin (2, 0, 0, 1)
2 × Colin > Arlo=Beth=Dara (0, 0, 4, 0)
5 × Beth > Arlo > Colin=Dara (1, 2, 0, 0)
17 × Beth > Arlo=Colin=Dara (0, 1, 0, 0)
6 × Beth > Arlo=Colin=Dara (0, 2, 0, 0)
3 × Arlo > Beth=Colin=Dara (1, 0, 0, 0)
3 × Beth > Arlo > Colin=Dara (1, 5, 0, 0)
8 × Arlo=Beth=Colin=Dara (0, 0, 0, 0)
6 × Arlo=Beth > Colin=Dara (1, 1, 0, 0)
1 × Colin > Arlo=Beth > Dara (1, 1, 4, 0)
2 × Colin > Arlo > Beth=Dara (1, 0, 2, 0)
2 × Colin > Beth > Arlo=Dara (0, 1, 5, 0)
1 × Arlo > Beth=Colin=Dara (5, 0, 0, 0)
4 × Dara > Arlo=Beth=Colin (0, 0, 0, 2)
2 × Beth > Arlo > Colin=Dara (1, 4, 0, 0)
3 × Arlo > Beth > Colin=Dara (2, 1, 0, 0)
1 × Dara > Beth > Arlo=Colin (0, 1, 0, 2)
2 × Dara > Arlo=Beth=Colin (0, 0, 0, 5)
1 × Beth=Dara > Arlo=Colin (0, 1, 0, 1)
1 × Arlo > Beth=Dara > Colin (2, 1, 0, 1)
2 × Colin > Arlo=Beth > Dara (1, 1, 2, 0)
1 × Dara > Arlo > Beth=Colin (1, 0, 0, 4)
1 × Colin > Beth > Arlo=Dara (0, 1, 4, 0)
1 × Colin > Arlo=Beth=Dara (0, 0, 2, 0)
Round-Robin — every pair, head-to-head (For – Against):
Beth beats Arlo 43 – 27
Arlo beats Colin 44 – 17
Arlo beats Dara 40 – 11
Beth beats Colin 48 – 17
Beth beats Dara 53 – 16
Dara beats Colin 21 – 17
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Arlo | Beth | Colin | Dara |
--------------------------------------------------------------------
Arlo > | --- |27 - 30 - 43 |44 - 39 - 17 |40 - 49 - 11 |
Beth > | 43 - 30 - 27 | --- |48 - 35 - 17 |53 - 31 - 16 |
Colin > | 17 - 39 - 44 |17 - 35 - 48 | --- |17 - 62 - 21 |
Dara > | 11 - 49 - 40 |16 - 31 - 53 |21 - 62 - 17 | --- |
Win–loss record — Copeland score = wins + ½·ties (highest score wins; ties broken by the Ranked Robin degrees, then lot order):
# Candidate W–L–T Copeland Margin Beats
1 Beth 3–0–0 3 +84 Arlo, Dara, Colin
2 Arlo 2–1–0 2 +40 Dara, Colin
3 Dara 1–2–0 1 -62 Colin
4 Colin 0–3–0 0 -62 —
Winner — Ranked Robin (RCV-RR): Beth
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 4): Beth
Outside (3): Arlo, Colin, Dara
One member ⇒ Beth is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Beth 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