No-show paradox (2 of 2) — the 8 April fans vote; RCV-IRV hands them their LAST choice¶
▶ Live on BetterVoting: vote · results ↗ (election 9dhv8y · test BV2175) — 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=April, RCV-IRV=Celia, Ranked Robin=April (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 | April |
| RCV-IRV | Celia |
| Ranked Robin (RCV-RR) | April |
| Approval | April |
| Range / Score | April |
| Condorcet | none (cycle) |
Flags: none
Source election: method_comparisons/participation_no_show/cases/bv2175_9dhv8y_noshow_showup.yaml · STAR tabulated mirror: bv2175_9dhv8y_noshow_showup_tabulated.txt
3 candidates, 62 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | April | Bruno | Celia |
|---|---|---|---|
| 24 | 5 | 2 | 0 |
| 18 | 0 | 5 | 2 |
| 20 | 2 | 0 | 5 |
STAR result (official)¶
Scoring round (sum of scores): April 160, Bruno 138, Celia 136
Finalists (top two): April and Bruno
Automatic runoff: April 44 vs Bruno 18
STAR winner: April
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * April | * Bruno |
-----------------------------------------------
* April > | --- |44 - 0 - 18 |
* Bruno > | 18 - 0 - 44 | --- |
[Divergence from STAR]
STAR = April
RCV-IRV = Celia (differs from STAR)
Note: no ballots had tied scores, so RCV-IRV vs STAR here is a genuine
method difference, not a tie-breaking artifact.
Note: Ranked Robin (RCV-RR) agrees with STAR, so RCV-IRV is the lone
outlier — the classic center-squeeze signature.
--- STAR Voting Method (single winner) ---
Tabulating 62 ballots.
Count × April,Bruno,Celia
24 × 5, 2, 0
20 × 2, 0, 5
18 × 0, 5, 2
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
April 24 0 0 20 0 18 | 160 2.6
Bruno 18 0 0 24 0 20 | 138 2.2
Celia 20 0 0 18 0 24 | 136 2.2
Scoring Round
The two highest-scoring candidates advance to the next round.
April -- 160 -- First place
Bruno -- 138 -- Second place
Celia -- 136
April and Bruno advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
April -- 44 -- First place
Bruno -- 18
Equal Support -- 0
April wins.
Voters with a preference: 62 of 62 (no Equal Support).
April 44 (71%) vs Bruno 18 (29%); majority = 32.
Winner — STAR Voting Method (single winner)
April
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 62 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
24 × April > Bruno (5, 2, 0)
18 × Bruno > Celia (0, 5, 2)
20 × Celia > April (2, 0, 5)
ROUND 1
Candidate Votes Status
----------- ------- --------
April 24 Hopeful
Celia 20 Hopeful
Bruno 18 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Celia 38 Elected
April 24 Rejected
Bruno 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Celia
--- 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 Celia 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 62 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: April, Bruno, Celia
24 × 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 44 – 18
Celia beats April 38 – 24
Bruno beats Celia 42 – 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 > | --- |44 - 0 - 18 |24 - 0 - 38 |
Bruno > | 18 - 0 - 44 | --- |42 - 0 - 20 |
Celia > | 38 - 0 - 24 |20 - 0 - 42 | --- |
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 April 1–1–0 1 +12 Bruno
2 Bruno 1–1–0 1 -4 Celia
3 Celia 1–1–0 1 -8 April
Winner — Ranked Robin (RCV-RR): April
*** 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 April 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