Edelman's 'Myth of the Condorcet Winner' 81 voters — the score count says Ben, the majorities say Ada¶
▶ Live on BetterVoting: vote · results ↗ (election gmfv4c · test BV2173) — 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 Ada. Only Approval differs, electing Ben: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding Ben's breadth of acceptability over Ada's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Ada |
| RCV-IRV | Ada |
| Ranked Robin (RCV-RR) | Ada |
| Approval | Ben |
| Range / Score | Ben |
| Condorcet | Ada |
Flags: none
Source election: method_comparisons/edelman_condorcet_myth/cases/bv2173_gmfv4c_edelman_saari_cancellation.yaml · STAR tabulated mirror: bv2173_gmfv4c_edelman_saari_cancellation_tabulated.txt
3 candidates, 81 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Ada | Ben | Cara |
|---|---|---|---|
| 30 | 5 | 2 | 0 |
| 1 | 5 | 0 | 2 |
| 29 | 2 | 5 | 0 |
| 10 | 0 | 5 | 2 |
| 10 | 2 | 0 | 5 |
| 1 | 0 | 2 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Ben 257, Ada 233, Cara 77
Finalists (top two): Ben and Ada
Automatic runoff: Ben 40 vs Ada 41
STAR winner: Ada
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Ada | * Ben |
-----------------------------------------------
* Ada > | --- |41 - 0 - 40 |
* Ben > | 40 - 0 - 41 | --- |
[Divergence from STAR]
STAR = Ada
Choose-One (Plurality) = Ben (differs from STAR)
Approval = Ben (differs from STAR)
[Runoff Reversal]
- Score Round Winner(s) = (Ben)
- Runoff Round Winner = (Ada)
Candidate Ben earned the highest total score, but
Candidate Ada 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 81 ballots.
Count × Ada,Ben,Cara
30 × 5, 2, 0
29 × 2, 5, 0
10 × 0, 5, 2
10 × 2, 0, 5
1 × 5, 0, 2
1 × 0, 2, 5
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Ada 31 0 0 39 0 11 | 233 2.9
Ben 39 0 0 31 0 11 | 257 3.2
Cara 11 0 0 11 0 59 | 77 1.0
Scoring Round
The two highest-scoring candidates advance to the next round.
Ben -- 257 -- First place
Ada -- 233 -- Second place
Cara -- 77
Ben and Ada advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Ada -- 41 -- First place
Ben -- 40
Equal Support -- 0
Ada wins.
Voters with a preference: 81 of 81 (no Equal Support).
Ada 41 (51%) vs Ben 40 (49%); majority = 41.
Winner — STAR Voting Method (single winner)
Ada
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 81 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: Ada, Ben, Cara
30 × Ada > Ben (5, 2, 0)
1 × Ada > Cara (5, 0, 2)
29 × Ben > Ada (2, 5, 0)
10 × Ben > Cara (0, 5, 2)
10 × Cara > Ada (2, 0, 5)
1 × Cara > Ben (0, 2, 5)
ROUND 1
Candidate Votes Status
----------- ------- --------
Ben 39 Hopeful
Ada 31 Hopeful
Cara 11 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Ada 41 Elected
Ben 40 Rejected
Cara 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Ada
--- 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): Ada
Outside (2): Ben, Cara
One member ⇒ Ada is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Ada 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 81 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Ada, Ben, Cara
30 × Ada > Ben > Cara (5, 2, 0)
1 × Ada > Cara > Ben (5, 0, 2)
29 × Ben > Ada > Cara (2, 5, 0)
10 × Ben > Cara > Ada (0, 5, 2)
10 × Cara > Ada > Ben (2, 0, 5)
1 × Cara > Ben > Ada (0, 2, 5)
Round-Robin — every pair, head-to-head (For – Against):
Ada beats Ben 41 – 40
Ada beats Cara 60 – 21
Ben beats Cara 69 – 12
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Ada | Ben | Cara |
-----------------------------------------------------
Ada > | --- |41 - 0 - 40 |60 - 0 - 21 |
Ben > | 40 - 0 - 41 | --- |69 - 0 - 12 |
Cara > | 21 - 0 - 60 |12 - 0 - 69 | --- |
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 Ada 2–0–0 2 +40 Ben, Cara
2 Ben 1–1–0 1 +56 Cara
3 Cara 0–2–0 0 -96 —
Winner — Ranked Robin (RCV-RR): Ada
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): Ada
Outside (2): Ben, Cara
One member ⇒ Ada is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Ada 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