Voting styles — five more ways to fill out one 5-star ballot¶
Bucket — IRV_DIFFERS_ARTIFACT: RCV-IRV differs — tie-break artifact
Generated by STARVote_LH_tabulation_engine/tools_adam/scripts/build_divergence_index.py — rebuilt from the election file; do not hand-edit.
What happens¶
On these ballots RCV-IRV reports Alice rather than STAR's Clara, but this is an artifact of score→rank conversion, not a robust method difference: 4 of 5 ballots have tied non-zero scores, so their ranks are set by an arbitrary candidate-priority order; the RCV-IRV winner flips when that priority order is reversed. Ranked Robin and the Condorcet (pairwise) winner both agree with STAR (Clara). Do not use this case to criticize RCV-IRV — the disagreement is a coin-flip created by equal scores and would vanish under a different (equally arbitrary) tie-break.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Clara |
| RCV-IRV | Alice |
| Ranked Robin (RCV-RR) | Clara |
| Approval | Clara |
| Range / Score | Clara |
| Condorcet | Clara |
Flags: 4 tied-score ballot(s); IRV winner flips under reversed priority (fragile tie); RR conversion-sensitive (weak=Clara, strict=Alice)
Source election: 01_STAR/02_Examples/cases/03d_c5_b5_style-gallery-five-more.yaml · STAR tabulated mirror: 03d_c5_b5_style-gallery-five-more_tabulated.txt
5 candidates, 5 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Alice | Bruno | Clara | Diego | Erin |
|---|---|---|---|---|---|
| 1 | 5 | 0 | 5 | 0 | 0 |
| 1 | 5 | 1 | 5 | 2 | 0 |
| 1 | 0 | 0 | 5 | 3 | 0 |
| 1 | 2 | 2 | 3 | 2 | 3 |
| 1 | 3 | 3 | 3 | 3 | 3 |
STAR result (official)¶
Scoring round (sum of scores): Clara 21, Alice 15, Diego 10, Bruno 6, Erin 6
Finalists (top two): Clara and Alice
Automatic runoff: Clara 2 vs Alice 0 (3 equal/no-preference)
STAR winner: Clara
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Alice | * Clara |
-----------------------------------------
* Alice > | --- |0 - 3 - 2 |
* Clara > | 2 - 3 - 0 | --- |
[Divergence from STAR]
STAR = Clara
Choose-One (Plurality) = Alice (differs from STAR)
RCV-IRV = Alice (differs from STAR)
Note: 4 of 5 ballots (80%) had equal non-zero scores, so their ranks were
decided by candidate priority order. The RCV-IRV result may be an
artifact of score-to-rank tie-breaking rather than a deep
difference.
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 5 ballots.
Alice,Bruno,Clara,Diego,Erin
5, 0, 5, 0, 0
5, 1, 5, 2, 0
-, -, 5, 3, -
2, 2, 3, 2, 3
3, 3, 3, 3, 3
('-' = left blank / abstained; '0' = scored zero — both count as 0 stars.)
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 Abs | Total Avg all Avg rated
Alice 2 0 1 1 0 0 1 | 15 3.0 3.8
Bruno 0 0 1 1 1 1 1 | 6 1.2 1.5
Clara 3 0 2 0 0 0 0 | 21 4.2 4.2
Diego 0 0 2 2 0 1 0 | 10 2.0 2.0
Erin 0 0 2 0 0 2 1 | 6 1.2 1.5
Avg all = Total / all ballots — a blank counts as 0, so this is the Total the Scoring Round ranks on, per ballot.
Avg rated = Total / the ballots that scored this candidate (Abs excluded) — support among voters who had an opinion.
Scoring Round
The two highest-scoring candidates advance to the next round.
Clara -- 21 -- First place
Alice -- 15 -- Second place
Diego -- 10
Bruno -- 6
Erin -- 6
Clara and Alice advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Clara -- 2 -- First place
Alice -- 0
Equal Support -- 3
Clara wins.
Voters with a preference: 2 of 5 (3 Equal Support).
Clara 2 (100%) vs Alice 0 (0%); majority = 2.
Winner — STAR Voting Method (single winner)
Clara
RCV-IRV — round by round¶
⚠️ This election has a fragile IRV tie (equal scores force an arbitrary tie-break). The round table below is only one realization; a different tie-break can change the winner. See the flag above.
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 5 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: Alice, Bruno, Clara, Diego, Erin
1 × Alice > Clara (5, 0, 5, 0, 0)
1 × Alice > Clara > Diego > Bruno (5, 1, 5, 2, 0)
1 × Clara > Diego (0, 0, 5, 3, 0)
1 × Clara > Erin > Alice > Bruno > Diego (2, 2, 3, 2, 3)
1 × Alice > Bruno > Clara > Diego > Erin (3, 3, 3, 3, 3)
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Alice 3 Elected
Clara 2 Rejected
Diego 0 Rejected
Bruno 0 Rejected
Erin 0 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Alice
--- 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 5): Clara
Outside (4): Alice, Bruno, Diego, Erin
One member ⇒ Clara is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Alice is OUTSIDE the Smith set. ✗
Every member of the set (Clara) beats Alice head-to-head, yet
RCV-IRV elected Alice anyway. RCV-IRV is not Smith-efficient (nor
Condorcet-efficient) — this is the shape a center squeeze leaves behind.
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 5 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Alice, Bruno, Clara, Diego, Erin
1 × Alice=Clara > Bruno=Diego=Erin (5, 0, 5, 0, 0)
1 × Alice=Clara > Diego > Bruno > Erin (5, 1, 5, 2, 0)
1 × Clara > Diego > Alice=Bruno=Erin (0, 0, 5, 3, 0)
1 × Clara=Erin > Alice=Bruno=Diego (2, 2, 3, 2, 3)
1 × Alice=Bruno=Clara=Diego=Erin (3, 3, 3, 3, 3)
Round-Robin — every pair, head-to-head (For – Against):
Alice beats Bruno 2 – 0
Clara beats Alice 2 – 0
Alice beats Diego 2 – 1
Alice beats Erin 2 – 1
Clara beats Bruno 4 – 0
Diego beats Bruno 2 – 0
Bruno ties Erin 1 – 1
Clara beats Diego 4 – 0
Clara beats Erin 3 – 0
Diego beats Erin 2 – 1
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Alice | Bruno | Clara | Diego | Erin |
-------------------------------------------------------------------
Alice > | --- |2 - 3 - 0 |0 - 3 - 2 |2 - 2 - 1 |2 - 2 - 1 |
Bruno > | 0 - 3 - 2 | --- |0 - 1 - 4 |0 - 3 - 2 |1 - 3 - 1 |
Clara > | 2 - 3 - 0 |4 - 1 - 0 | --- |4 - 1 - 0 |3 - 2 - 0 |
Diego > | 1 - 2 - 2 |2 - 3 - 0 |0 - 1 - 4 | --- |2 - 2 - 1 |
Erin > | 1 - 2 - 2 |1 - 3 - 1 |0 - 2 - 3 |1 - 2 - 2 | --- |
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 Clara 4–0–0 4 +13 Alice, Diego, Erin, Bruno
2 Alice 3–1–0 3 +2 Diego, Erin, Bruno
3 Diego 2–2–0 2 -2 Erin, Bruno
4 Erin 0–3–1 0.5 -5 —
5 Bruno 0–3–1 0.5 -8 —
Winner — Ranked Robin (RCV-RR): Clara
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 5): Clara
Outside (4): Alice, Bruno, Diego, Erin
One member ⇒ Clara is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Clara 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