Zero support — nobody scored anybody (STAR)¶
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=Ada, RCV-IRV=Dev, Ranked Robin=Ada (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 | Ada |
| RCV-IRV | Dev |
| Ranked Robin (RCV-RR) | Ada |
| Approval | Ada |
| Range / Score | Ada |
| Condorcet | none (cycle) |
Flags: none
Source election: method_comparisons/zero_support_election/cases/zero_support_star.yaml · STAR tabulated mirror: zero_support_star_tabulated.txt
5 candidates, 3 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Ada | Ben | Cleo | Dev | Elsa |
|---|---|---|---|---|---|
| 3 | 0 | 0 | 0 | 0 | 0 |
STAR result (official)¶
Scoring round (sum of scores): Ada 0, Ben 0, Cleo 0, Dev 0, Elsa 0
Finalists (top two): Ada and Ben
Automatic runoff: Ada 0 vs Ben 0 (3 equal/no-preference)
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
Note: Ada, Ben, Cleo, Dev and Elsa tied at 0 in the Scoring Round, and
the lot rung (the ballots could not separate them) advanced Ada
and Ben. The * marks who advanced, not who scored highest. Cleo,
Dev and Elsa are filtered out of this grid — see the Scoring
Round for how the tie was settled.
| * Ada | * Ben |
-----------------------------------------
* Ada > | --- |0 - 3 - 0 |
* Ben > | 0 - 3 - 0 | --- |
[Divergence from STAR]
STAR = Ada
RCV-IRV = Dev (differs from STAR)
Note: no ballot scored anybody above 0, so not one ballot ranks anyone and
RCV-IRV has nothing to count — its winner came from its own tiebreak
among candidates all holding 0 votes. This divergence is noise, not
a method difference.
--- STAR Voting Method (single winner) ---
Tabulating 3 ballots.
Count × Ada,Ben,Cleo,Dev,Elsa
3 × 0, 0, 0, 0, 0
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Ada 0 0 0 0 0 3 | 0 0.0
Ben 0 0 0 0 0 3 | 0 0.0
Cleo 0 0 0 0 0 3 | 0 0.0
Dev 0 0 0 0 0 3 | 0 0.0
Elsa 0 0 0 0 0 3 | 0 0.0
Scoring Round
The two highest-scoring candidates advance to the next round.
Ada -- 0 -- Tied for first place
Ben -- 0 -- Tied for first place
Cleo -- 0 -- Tied for first place
Dev -- 0 -- Tied for first place
Elsa -- 0 -- Tied for first place
There's a five-way tie for first.
Scoring Round: First tiebreaker
The two candidates preferred in the most head-to-head matchups advance.
Ada -- 0 -- Tied for first place
Ben -- 0 -- Tied for first place
Cleo -- 0 -- Tied for first place
Dev -- 0 -- Tied for first place
Elsa -- 0 -- Tied for first place
Equal Support -- 3
There's still a five-way tie for first.
Every head-to-head among the tied candidates is a draw, so none of them won a matchup.
Scoring Round: Second tiebreaker
The two candidates with the most votes of score 5 advance.
Ada -- 0 -- Tied for first place
Ben -- 0 -- Tied for first place
Cleo -- 0 -- Tied for first place
Dev -- 0 -- Tied for first place
Elsa -- 0 -- Tied for first place
There's still a five-way tie for first.
*(Ties are resolved by choosing the tied candidate with the highest-priority official lot number.)*
Lot-number priority order: ['Ada', 'Ben', 'Cleo', 'Dev', 'Elsa']
[Tiebreaker: Lot Number Priority]
Tie among: ['Ada', 'Ben', 'Cleo', 'Dev', 'Elsa']
Resolved: ['Ada', 'Ben'] (selected by lot-number priority).
[Lot-decided tie — rare]
⚠ The ballots did not break this tie, and had nothing to break
it with: not one ballot scored ANY of these candidates above 0,
so every rung was comparing zero with zero. The pre-published
LOT order chose among them — the result here was set by lot,
not by the votes. Nothing to verify in the rounds above; this
is a tie for lack of support, not a close race.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Ada -- 0 -- Tied for first place
Ben -- 0 -- Tied for first place
Equal Support -- 3
There's a two-way tie for first.
Automatic Runoff Round: First tiebreaker
The highest-scoring candidate wins.
Ada -- 0 -- Tied for first place
Ben -- 0 -- Tied for first place
There's still a two-way tie for first.
Automatic Runoff Round: Second tiebreaker
The candidate with the most votes of score 5 wins.
Ada -- 0 -- Tied for first place
Ben -- 0 -- Tied for first place
There's still a two-way tie for first.
[Tiebreaker: Lot Number Priority]
Tie among: ['Ada', 'Ben']
Resolved: ['Ada'] (selected by lot-number priority).
[Lot-decided tie — rare]
⚠ The ballots did not break this tie, and had nothing to break
it with: not one ballot scored ANY of these candidates above 0,
so every rung was comparing zero with zero. The pre-published
LOT order chose among them — the result here was set by lot,
not by the votes. Nothing to verify in the rounds above; this
is a tie for lack of support, not a close race.
Winner — STAR Voting Method (single winner)
Ada
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 3 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, Cleo, Dev, Elsa
3 × (all unranked) (0, 0, 0, 0, 0)
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Dev 0 Elected
Elsa 0 Rejected
Ada 0 Rejected
Ben 0 Rejected
Cleo 0 Rejected
Blank Votes 3 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Dev
--- 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 (5 of 5): Ada, Ben, Cleo, Dev, Elsa
Outside (0): —
More than one member ⇒ NO Condorcet winner: the top of the tournament is a
dead heat (its members DRAW each other head-to-head), so the strongest
"candidate" is a set, not a person. No member beats another, so there is no
loop for Minimax / Ranked Pairs / Schulze to disagree about — which member
wins is left to the tiebreak, not to a cycle rule. See
05_Ranked_Robin/01_Learn/rr_tiebreak_lh_vs_bv.md.
RCV-IRV winner Dev is INSIDE the Smith set. ✓
Not guaranteed — RCV-IRV is not Smith-efficient — but it holds here.
Fine print: this set contains a pairwise DRAW, and a draw is enough to keep a
candidate in the Smith set but not in the tighter Schwartz set — so Schwartz
may be smaller 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 3 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Ada, Ben, Cleo, Dev, Elsa
3 × Ada=Ben=Cleo=Dev=Elsa (0, 0, 0, 0, 0)
Round-Robin — every pair, head-to-head (For – Against):
Ada ties Ben 0 – 0
Ada ties Cleo 0 – 0
Ada ties Dev 0 – 0
Ada ties Elsa 0 – 0
Ben ties Cleo 0 – 0
Ben ties Dev 0 – 0
Ben ties Elsa 0 – 0
Cleo ties Dev 0 – 0
Cleo ties Elsa 0 – 0
Dev ties Elsa 0 – 0
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Ada | Ben | Cleo | Dev | Elsa |
------------------------------------------------------------------
Ada > | --- |0 - 3 - 0 |0 - 3 - 0 |0 - 3 - 0 |0 - 3 - 0 |
Ben > | 0 - 3 - 0 | --- |0 - 3 - 0 |0 - 3 - 0 |0 - 3 - 0 |
Cleo > | 0 - 3 - 0 |0 - 3 - 0 | --- |0 - 3 - 0 |0 - 3 - 0 |
Dev > | 0 - 3 - 0 |0 - 3 - 0 |0 - 3 - 0 | --- |0 - 3 - 0 |
Elsa > | 0 - 3 - 0 |0 - 3 - 0 |0 - 3 - 0 |0 - 3 - 0 | --- |
Win–loss record — Copeland score = wins + ½·ties (highest score wins; ties broken by the Ranked Robin degrees, then lot order):
# Candidate W–L–T Copeland Margin vs finalists Beats
1 Ada 0–0–4 2 +0 0 —
2 Ben 0–0–4 2 +0 0 —
3 Cleo 0–0–4 2 +0 0 —
4 Dev 0–0–4 2 +0 0 —
5 Elsa 0–0–4 2 +0 0 —
Winner — Ranked Robin (RCV-RR): Ada
*** 5 candidates tie on the highest Copeland score (2): Ada, Ben, Cleo, Dev, Elsa — a dead heat (they draw head-to-head, not a cycle). Neither the 1st nor the 2nd Degree tiebreaker separates them — resolved by lot order.
--- 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 (5 of 5): Ada, Ben, Cleo, Dev, Elsa
Outside (0): —
More than one member ⇒ NO Condorcet winner: the top of the tournament is a
dead heat (its members DRAW each other head-to-head), so the strongest
"candidate" is a set, not a person. No member beats another, so there is no
loop for Minimax / Ranked Pairs / Schulze to disagree about — which member
wins is left to the tiebreak, not to a cycle rule. See
05_Ranked_Robin/01_Learn/rr_tiebreak_lh_vs_bv.md.
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.
Fine print: this set contains a pairwise DRAW, and a draw is enough to keep a
candidate in the Smith set but not in the tighter Schwartz set — so Schwartz
may be smaller here.
More: 07_Concepts/topics/smith_set.md