Condorcet's 1788 rebuttal to Borda — STAR elects the Condorcet winner¶
▶ Live on BetterVoting: vote · results ↗ (election khcwm4 · test BV2250) — 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 Peter. Only Approval differs, electing Paul: Approval counts every score of 3–5 as one equal 'approve' and ignores intensity, rewarding Paul's breadth of acceptability over Peter's stronger but more concentrated support. A threshold story about Approval, not a STAR-vs-IRV teaching case.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Peter |
| RCV-IRV | Peter |
| Ranked Robin (RCV-RR) | Peter |
| Approval | Paul |
| Range / Score | Paul |
| Condorcet | Peter |
Flags: none
Source election: method_comparisons/borda_condorcet_1788/cases/condorcet_1788_star.yaml · STAR tabulated mirror: condorcet_1788_star_tabulated.txt
3 candidates, 11 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Peter | Paul | James |
|---|---|---|---|
| 4 | 5 | 3 | 0 |
| 3 | 0 | 5 | 3 |
| 2 | 3 | 5 | 0 |
| 2 | 3 | 0 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Paul 37, Peter 32, James 19
Finalists (top two): Paul and Peter
Automatic runoff: Paul 5 vs Peter 6
STAR winner: Peter
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Peter | * Paul |
-----------------------------------------
* Peter > | --- |6 - 0 - 5 |
* Paul > | 5 - 0 - 6 | --- |
[Divergence from STAR]
STAR = Peter
Choose-One (Plurality) = Paul (differs from STAR)
Approval = Paul (differs from STAR)
[Runoff Reversal]
- Score Round Winner(s) = (Paul)
- Runoff Round Winner = (Peter)
Candidate Paul earned the highest total score, but
Candidate Peter 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 11 ballots.
Count × Peter,Paul,James
4 × 5, 3, 0
3 × 0, 5, 3
2 × 3, 5, 0
2 × 3, 0, 5
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Peter 4 0 4 0 0 3 | 32 2.9
Paul 5 0 4 0 0 2 | 37 3.4
James 2 0 3 0 0 6 | 19 1.7
Scoring Round
The two highest-scoring candidates advance to the next round.
Paul -- 37 -- First place
Peter -- 32 -- Second place
James -- 19
Paul and Peter advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Peter -- 6 -- First place
Paul -- 5
Equal Support -- 0
Peter wins.
Voters with a preference: 11 of 11 (no Equal Support).
Peter 6 (55%) vs Paul 5 (45%); majority = 6.
Winner — STAR Voting Method (single winner)
Peter
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 11 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: Peter, Paul, James
4 × Peter > Paul (5, 3, 0)
3 × Paul > James (0, 5, 3)
2 × Paul > Peter (3, 5, 0)
2 × James > Peter (3, 0, 5)
ROUND 1
Candidate Votes Status
----------- ------- --------
Paul 5 Hopeful
Peter 4 Hopeful
James 2 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Peter 6 Elected
Paul 5 Rejected
James 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Peter
--- 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): Peter
Outside (2): Paul, James
One member ⇒ Peter is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Peter 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 11 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Peter, Paul, James
4 × Peter > Paul > James (5, 3, 0)
3 × Paul > James > Peter (0, 5, 3)
2 × Paul > Peter > James (3, 5, 0)
2 × James > Peter > Paul (3, 0, 5)
Round-Robin — every pair, head-to-head (For – Against):
Peter beats Paul 6 – 5
Peter beats James 6 – 5
Paul beats James 9 – 2
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Peter | Paul | James |
---------------------------------------------
Peter > | --- |6 - 0 - 5 |6 - 0 - 5 |
Paul > | 5 - 0 - 6 | --- |9 - 0 - 2 |
James > | 5 - 0 - 6 |2 - 0 - 9 | --- |
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 Peter 2–0–0 2 +2 Paul, James
2 Paul 1–1–0 1 +6 James
3 James 0–2–0 0 -8 —
Winner — Ranked Robin (RCV-RR): Peter
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): Peter
Outside (2): Paul, James
One member ⇒ Peter is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Peter 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