Hillinger Table 4, rescaled — what 'cardinal' actually guarantees¶
Bucket — IRV_OUTLIER_RR_WITH_STAR: RCV-IRV is the outlier (center squeeze)
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 elects Ana — and so do Ranked Robin and Condorcet, because Ana is the head-to-head (pairwise) winner, beating every rival one-on-one. RCV-IRV instead elects Bruno: Ana collects fewer top (first-choice) votes, so IRV eliminates Ana early, and those ballots transfer to Bruno. This is the classic center squeeze — the broadly acceptable candidate is knocked out by round-by-round elimination even though a majority prefers them in a direct matchup. Two methods (STAR + RR) against one (RCV-IRV): IRV is the outlier.
Winners by method¶
| Method | Winner |
|---|---|
| STAR | Ana |
| RCV-IRV | Bruno |
| Ranked Robin (RCV-RR) | Ana |
| Approval | Ana |
| Range / Score | Ana |
| Condorcet | Ana |
Flags: none
Source election: method_comparisons/hillinger_evaluative_voting/cases/hillinger_t4_affine.yaml · STAR tabulated mirror: hillinger_t4_affine_tabulated.txt
3 candidates, 30 ballots.
The ballots¶
Each row is a group of identical score ballots (0 = no support, 5 = max).
| Count | Ana | Bruno | Chloe |
|---|---|---|---|
| 9 | 5 | 3 | 1 |
| 10 | 3 | 5 | 1 |
| 11 | 3 | 1 | 5 |
STAR result (official)¶
Scoring round (sum of scores): Ana 108, Bruno 88, Chloe 74
Finalists (top two): Ana and Bruno
Automatic runoff: Ana 20 vs Bruno 10
STAR winner: Ana
Full LH STAR engine report:
--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
* indicates Top 2 Finalist
| * Ana | * Bruno |
-----------------------------------------------
* Ana > | --- |20 - 0 - 10 |
* Bruno > | 10 - 0 - 20 | --- |
[Divergence from STAR]
STAR = Ana
Choose-One (Plurality) = Chloe (differs from STAR)
RCV-IRV = Bruno (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 30 ballots.
Count × Ana,Bruno,Chloe
11 × 3, 1, 5
10 × 3, 5, 1
9 × 5, 3, 1
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Ana 9 0 21 0 0 0 | 108 3.6
Bruno 10 0 9 0 11 0 | 88 2.9
Chloe 11 0 0 0 19 0 | 74 2.5
Scoring Round
The two highest-scoring candidates advance to the next round.
Ana -- 108 -- First place
Bruno -- 88 -- Second place
Chloe -- 74
Ana and Bruno advance.
Automatic Runoff Round
The candidate preferred in the most head-to-head matchups wins.
Ana -- 20 -- First place
Bruno -- 10
Equal Support -- 0
Ana wins.
Voters with a preference: 30 of 30 (no Equal Support).
Ana 20 (67%) vs Bruno 10 (33%); majority = 16.
Winner — STAR Voting Method (single winner)
Ana
RCV-IRV — round by round¶
--- RCV / Instant-Runoff Voting (single winner) ---
Tabulating 30 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: Ana, Bruno, Chloe
9 × Ana > Bruno > Chloe (5, 3, 1)
10 × Bruno > Ana > Chloe (3, 5, 1)
11 × Chloe > Ana > Bruno (3, 1, 5)
ROUND 1
Candidate Votes Status
----------- ------- --------
Chloe 11 Hopeful
Bruno 10 Hopeful
Ana 9 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Bruno 19 Elected
Chloe 11 Rejected
Ana 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 (1 of 3): Ana
Outside (2): Bruno, Chloe
One member ⇒ Ana is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Bruno is OUTSIDE the Smith set. ✗
Every member of the set (Ana) beats Bruno head-to-head, yet
RCV-IRV elected Bruno 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 30 ballots (score ballots).
Ballots:
the ranking Ranked Robin reads ("=" = tied); source scores follow in () per column: Ana, Bruno, Chloe
9 × Ana > Bruno > Chloe (5, 3, 1)
10 × Bruno > Ana > Chloe (3, 5, 1)
11 × Chloe > Ana > Bruno (3, 1, 5)
Round-Robin — every pair, head-to-head (For – Against):
Ana beats Bruno 20 – 10
Ana beats Chloe 19 – 11
Bruno beats Chloe 19 – 11
--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against (row vs column)
| Ana | Bruno | Chloe |
------------------------------------------------------
Ana > | --- |20 - 0 - 10 |19 - 0 - 11 |
Bruno > | 10 - 0 - 20 | --- |19 - 0 - 11 |
Chloe > | 11 - 0 - 19 |11 - 0 - 19 | --- |
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 Ana 2–0–0 2 +18 Bruno, Chloe
2 Bruno 1–1–0 1 -2 Chloe
3 Chloe 0–2–0 0 -16 —
Winner — Ranked Robin (RCV-RR): Ana
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): Ana
Outside (2): Bruno, Chloe
One member ⇒ Ana is the Condorcet winner, beating every rival head-to-head.
Ranked Robin (RCV-RR) winner Ana 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