No-show paradox (1 of 2) — 8 April fans stay home; RCV-IRV elects Bruno¶
▶ Live on BetterVoting: vote · results ↗ (election yyhr66 · test BV2174) — 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¶
There is no Condorcet winner — the head-to-head results form a cycle (X beats Y beats Z beats X). With no pairwise anchor the methods split: STAR=Bruno, RCV-IRV=Bruno, Ranked Robin=Celia (RR breaks the cycle by total margin). No rule is clearly 'right'; a genuinely hard election, not an indictment of any one method.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Bruno |
| RCV-IRV | Bruno |
| Ranked Robin (RCV-RR) | Celia |
| Approval | Celia |
| Range / Score | Celia |
| Condorcet | none (cycle) |
Flags: none
Source election: method_comparisons/participation_no_show/cases/bv2174_yyhr66_noshow_baseline.yaml · STAR tabulated mirror: bv2174_yyhr66_noshow_baseline_tabulated.txt
3 candidates, 54 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | April | Bruno | Celia |
|---|---|---|---|
| 16 | 5 | 2 | 0 |
| 18 | 0 | 5 | 2 |
| 20 | 2 | 0 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Celia 136, Bruno 122, April 120
Finalists (top two): Celia and Bruno
Automatic runoff: Celia 20 vs Bruno 34
STAR winner: Bruno
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Bruno | * Celia |
-----------------------------------------------
* Bruno > | --- |34 - 0 - 20 |
* Celia > | 20 - 0 - 34 | --- |
[Divergence from STAR]
STAR = Bruno
Choose-One (Plurality) = Celia (differs from STAR)
Approval = Celia (differs from STAR)
RCV-RR = Celia (differs from STAR)
[Runoff Reversal]
- Score Round Winner(s) = (Celia)
- Runoff Round Winner = (Bruno)
Candidate Celia earned the highest total score, but
Candidate Bruno 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 54 ballots.
Count × April,Bruno,Celia
20 × 2, 0, 5
18 × 0, 5, 2
16 × 5, 2, 0
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
April 16 0 0 20 0 18 | 120 2.2
Bruno 18 0 0 16 0 20 | 122 2.3
Celia 20 0 0 18 0 16 | 136 2.5
Scoring Round
The two highest-scoring candidates advance to the next round.
Celia -- 136 -- First place
Bruno -- 122 -- Second place
April -- 120
Celia and Bruno advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Bruno -- 34 -- First place
Celia -- 20
Equal Support -- 0
Bruno wins.
Voters with a preference: 54 of 54 (no Equal Support).
Bruno 34 (63%) vs Celia 20 (37%); majority = 28.
Winner — STAR Voting Method (single winner)
Bruno
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 54 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: April, Bruno, Celia
16 × April > Bruno (5, 2, 0)
18 × Bruno > Celia (0, 5, 2)
20 × Celia > April (2, 0, 5)
ROUND 1
Candidate Votes Status
----------- ------- --------
Celia 20 Hopeful
Bruno 18 Hopeful
April 16 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Bruno 34 Elected
Celia 20 Rejected
April 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Bruno
--- 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 (3 of 3): April, Bruno, Celia
Outside (0): —
More than one member ⇒ NO Condorcet winner: the top of the tournament is a
cycle, so the strongest "candidate" is a set, not a person. Which member of
the set should win is exactly what Minimax / Ranked Pairs / Schulze disagree
about — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.
RCV-IRV winner Bruno 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 54 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: April, Bruno, Celia
16 × April > Bruno > Celia (5, 2, 0)
18 × Bruno > Celia > April (0, 5, 2)
20 × Celia > April > Bruno (2, 0, 5)
Round-Robin — every pair, head-to-head (For – Against):
April beats Bruno 36 – 18
Celia beats April 38 – 16
Bruno beats Celia 34 – 20
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| April | Bruno | Celia |
------------------------------------------------------
April > | --- |36 - 0 - 18 |16 - 0 - 38 |
Bruno > | 18 - 0 - 36 | --- |34 - 0 - 20 |
Celia > | 38 - 0 - 16 |20 - 0 - 34 | --- |
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 Celia 1–1–0 1 +8 April
2 April 1–1–0 1 -4 Bruno
3 Bruno 1–1–0 1 -4 Celia
Winner — Ranked Robin (RCV-RR): Celia
*** 3 candidates tie for the most wins (April, Bruno, Celia) — a Condorcet cycle (no candidate beats all others). Resolved by total margin, then lot order. (This is where Minimax / Ranked Pairs / Schulze differ — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.)
--- 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 (3 of 3): April, Bruno, Celia
Outside (0): —
More than one member ⇒ NO Condorcet winner: the top of the tournament is a
cycle, so the strongest "candidate" is a set, not a person. Which member of
the set should win is exactly what Minimax / Ranked Pairs / Schulze disagree
about — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.
Ranked Robin (RCV-RR) winner Celia 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