Alaska 2022 US House general (reduced model) — IRV got it right: all four counts elect the Condorcet winner, Peltola¶
▶ Live on BetterVoting: vote · results ↗ (election m3hb6y · test BV2214) — 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 Peltola. Only Approval differs, electing Begich: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding Begich's breadth of acceptability over Peltola's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Peltola |
| RCV-IRV | Peltola |
| Ranked Robin (RCV-RR) | Peltola |
| Approval | Begich |
| Range / Score | Begich |
| Condorcet | Peltola |
Flags: none
Source election: method_comparisons/alaska_2022_general/cases/bv2214_m3hb6y_alaska_2022_general.yaml · STAR tabulated mirror: bv2214_m3hb6y_alaska_2022_general_tabulated.txt
3 candidates, 200 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Peltola | Begich | Palin |
|---|---|---|---|
| 50 | 5 | 0 | 0 |
| 42 | 5 | 4 | 0 |
| 6 | 5 | 0 | 4 |
| 11 | 0 | 5 | 0 |
| 33 | 0 | 5 | 4 |
| 6 | 4 | 5 | 0 |
| 17 | 0 | 0 | 5 |
| 32 | 0 | 4 | 5 |
| 3 | 4 | 0 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Begich 546, Peltola 526, Palin 416
Finalists (top two): Begich and Peltola
Automatic runoff: Begich 82 vs Peltola 101 (17 equal/no-preference)
STAR winner: Peltola
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Peltola | * Begich |
--------------------------------------------------------
* Peltola > | --- |101 - 17 - 82 |
* Begich > | 82 - 17 - 101 | --- |
[Divergence from STAR]
STAR = Peltola
Approval = Begich (differs from STAR)
[Runoff Reversal]
- Score Round Winner(s) = (Begich)
- Runoff Round Winner = (Peltola)
Candidate Begich earned the highest total score, but
Candidate Peltola 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 200 ballots.
Count × Peltola,Begich,Palin
50 × 5, 0, 0
42 × 5, 4, 0
33 × 0, 5, 4
32 × 0, 4, 5
17 × 0, 0, 5
11 × 0, 5, 0
6 × 5, 0, 4
6 × 4, 5, 0
3 × 4, 0, 5
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Peltola 98 9 0 0 0 93 | 526 2.6
Begich 50 74 0 0 0 76 | 546 2.7
Palin 52 39 0 0 0 109 | 416 2.1
Scoring Round
The two highest-scoring candidates advance to the next round.
Begich -- 546 -- First place
Peltola -- 526 -- Second place
Palin -- 416
Begich and Peltola advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Peltola -- 101 -- First place
Begich -- 82
Equal Support -- 17
Peltola wins.
Voters with a preference: 183 of 200 (17 Equal Support).
Peltola 101 (55%) vs Begich 82 (45%); majority = 92.
Winner — STAR Voting Method (single winner)
Peltola
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 200 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: Peltola, Begich, Palin
50 × Peltola (5, 0, 0)
42 × Peltola > Begich (5, 4, 0)
6 × Peltola > Palin (5, 0, 4)
11 × Begich (0, 5, 0)
33 × Begich > Palin (0, 5, 4)
6 × Begich > Peltola (4, 5, 0)
17 × Palin (0, 0, 5)
32 × Palin > Begich (0, 4, 5)
3 × Palin > Peltola (4, 0, 5)
ROUND 1
Candidate Votes Status
----------- ------- --------
Peltola 98 Hopeful
Palin 52 Hopeful
Begich 50 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Peltola 104 Elected
Palin 85 Rejected
Begich 0 Rejected
Blank Votes 11 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Peltola
--- 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): Peltola
Outside (2): Begich, Palin
One member ⇒ Peltola is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Peltola 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 200 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Peltola, Begich, Palin
50 × Peltola > Begich=Palin (5, 0, 0)
42 × Peltola > Begich > Palin (5, 4, 0)
6 × Peltola > Palin > Begich (5, 0, 4)
11 × Begich > Peltola=Palin (0, 5, 0)
33 × Begich > Palin > Peltola (0, 5, 4)
6 × Begich > Peltola > Palin (4, 5, 0)
17 × Palin > Peltola=Begich (0, 0, 5)
32 × Palin > Begich > Peltola (0, 4, 5)
3 × Palin > Peltola > Begich (4, 0, 5)
Round-Robin — every pair, head-to-head (For – Against):
Peltola beats Begich 101 – 82
Peltola beats Palin 104 – 85
Begich beats Palin 92 – 58
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Peltola | Begich | Palin |
-----------------------------------------------------------------
Peltola > | --- |101 - 17 - 82 |104 - 11 - 85 |
Begich > | 82 - 17 - 101 | --- | 92 - 50 - 58 |
Palin > | 85 - 11 - 104 | 58 - 50 - 92 | --- |
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 Peltola 2–0–0 2 +38 Begich, Palin
2 Begich 1–1–0 1 +15 Palin
3 Palin 0–2–0 0 -53 —
Winner — Ranked Robin (RCV-RR): Peltola
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): Peltola
Outside (2): Begich, Palin
One member ⇒ Peltola is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Peltola 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