The Post-it RCV example (20 voters) — the runoff RCV-IRV never held¶
▶ Live on BetterVoting: vote · results ↗ (election p8dp28, Test ID BV2176).
The 20-voter election from Equal Vote's video "Updated: How does RCV work? — With Post-its!" — the whiteboard demo that walks through an RCV-IRV count sticky note by sticky note, then asks the question the count itself never asks: was the eliminated candidate actually stronger head-to-head? Four candidates (Purple, Green, Blue, Pink), one electorate, three tabulations live on BetterVoting: RCV-IRV elects Purple, STAR (on the video's own 0–5 scores) elects Blue, and Ranked Robin exposes a Condorcet cycle whose 2–1 tie the two engines break differently — Green on BetterVoting, Blue in the LH engine. Same ballots, three defensible winners: the tabulation decides.
The ballots¶
The same 20 voters, ranked (the video's Post-its) and scored 0–5 (the video's STAR comparison):
| # voters | ranked ballot | scores (Purple, Green, Blue, Pink) |
|---|---|---|
| 7 | Purple | 5, 0, 0, 0 |
| 6 | Green > Blue > Pink | 0, 5, 4, 3 |
| 2 | Blue > Pink | 0, 0, 5, 4 |
| 1 | Blue > Green > Pink | 0, 4, 5, 3 |
| 1 | Blue > Purple | 4, 0, 5, 0 |
| 1 | Pink > Green > Purple | 3, 4, 0, 5 |
| 1 | Pink > Purple | 4, 0, 0, 5 |
| 1 | Pink | 0, 0, 0, 5 |
First choices: Purple 7, Green 6, Blue 4, Pink 3. Score totals: Purple 46, Blue 44, Pink 44, Green 38.
The video's count — and the video's question¶
RCV-IRV (the whiteboard walk-through): round 1 eliminates Pink (3 first choices; 1 ballot transfers to Green, 1 to Purple, 1 bullet-vote exhausts). Round 2 stands at Purple 8, Green 7, Blue 4 — Blue is eliminated (1 to Green, 1 to Purple, and both Blue>Pink ballots exhaust, Pink being already gone). Final: Purple 9, Green 8, with 3 of the 20 ballots exhausted — Purple wins with 9 of the 17 still-active ballots.
The video then flips the round-2 elimination: what if Green (7 votes) had gone out instead of Blue (4)? All six Green>Blue>Pink ballots land on Blue, and Blue wins 10–9. That hypothetical is not a fluke of transfer order — it is the actual head-to-head: on these 20 ballots Blue beats Purple 10–9. RCV-IRV eliminated Blue without ever holding that matchup.
STAR holds it automatically. Scoring round: Purple 46 advances; the 44–44 tie between Blue and Pink for the second finalist slot breaks by the official protocol's next rung — head-to-head, where Blue is preferred over Pink 10–3. The automatic runoff is then exactly the matchup the video asked about: Blue 10, Purple 9 (1 Equal Support) — Blue wins. It is also a Runoff Reversal: the score leader (Purple, 46) loses the majority check, STAR working as designed. BetterVoting concurs on every rung (tieBreakType: head_to_head on the scoring tie).
One electorate, three counts¶
| Race (BV) | Method | BV winner | LH winner | How |
|---|---|---|---|---|
| Post-its 20 voters — STAR | STAR | Blue | Blue | 46/38/44/44; second-finalist tie → head-to-head Blue 10–3 Pink; runoff Blue 10–9 (Runoff Reversal) |
| Post-its 20 voters — RCV-IRV | IRV | Purple | Purple | 7/6/4/3 → 8/7/4 → 9–8; 3 exhausted |
| Post-its 20 voters — Ranked Robin | RankedRobin (Copeland) | Green | Blue | 2-way Copeland tie at 2–1 — the two ladders part ways (below) |
The Ranked Robin race — one tie, two ladders, both deterministic¶
There is no Condorcet winner here: the pairwise picture is a genuine cycle (Purple beats Green 9–8, Green beats Blue 7–4, Blue beats Purple 10–9 — and Pink beats Purple 12–8). Green and Blue each go 2–1 (Copeland 2), and that tie is exactly where the two engines' tiebreak ladders diverge:
- BetterVoting (
RankedRobin.ts): exactly 2 tied → their own head-to-head. Green beats Blue 7–4 → Green, deterministically (BV-confirmed live). - LH (
run_ranked_robin): total margin. Blue +5 vs Green +4 → Blue, deterministically.
Both ladders are deterministic on this profile, so the race is freezable — making BV2176 the first live BetterVoting election to exhibit the documented ladder divergence (the previous worked example, the dead-heat case, is LH-only because BV's ladder falls through to random there). The independent pref_voting Copeland check reports the leader set {Blue, Green}: both engines tie-broke inside it, consistently with their published rules.
LH engine reports (View 2)¶
STAR — Blue (the runoff the video asked for)¶
[Divergence from STAR]
STAR = Blue
Choose-One (Plurality) = Purple (differs from STAR)
RCV-IRV = Purple (differs from STAR)
Approval = Pink (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.
Full round-by-round reports (generated for review):
RCV-IRV rounds: cases_tabulated/bv2176_p8dp28_star_RCV-IRV_tabulated.txt
[Runoff Reversal]
- Score Round Winner(s) = (Purple)
- Runoff Round Winner = (Blue)
Candidate Purple earned the highest total score, but
Candidate Blue 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) ---
[STAR Voting]
Tabulating 20 ballots.
Count × Purple,Green,Blue,Pink
7 × 5, 0, 0, 0
6 × 0, 5, 4, 3
2 × 0, 0, 5, 4
1 × 0, 4, 5, 3
1 × 4, 0, 5, 0
1 × 3, 4, 0, 5
1 × 4, 0, 0, 5
1 × 0, 0, 0, 5
[STAR Voting: Scoring Round]
The two highest-scoring candidates advance to the next round.
Purple -- 46 -- First place
Blue -- 44 -- Tied for second place
Pink -- 44 -- Tied for second place
Green -- 38
Purple advances, but there's a two-way tie for second.
[STAR Voting: Scoring Round: First tiebreaker]
The candidate preferred in the most head-to-head matchups advances.
Blue -- 10 -- Second place
Pink -- 3
Equal Support -- 7
Purple and Blue advance.
[STAR Voting: Automatic Runoff Round]
The candidate preferred in the most head-to-head matchups wins.
Blue -- 10 -- First place
Purple -- 9
Equal Support -- 1
Blue wins.
Runoff math:
20 ballots cast
− 1 Equal Support (no preference between the two finalists)
──
19 voters with a preference (majority = 10)
Blue 10 (53%) · Purple 9 (47%)
[STAR Voting: Winner — STAR Voting Method (single winner)]
Blue
RCV-IRV — Purple (the video's whiteboard rounds)¶
ROUND 1
Candidate Votes Status
----------- ------- --------
Purple 7 Hopeful
Green 6 Hopeful
Blue 4 Hopeful
Pink 3 Rejected
ROUND 2
Candidate Votes Status
----------- ------- --------
Purple 8 Hopeful
Green 7 Hopeful
Blue 4 Rejected
Pink 0 Rejected
Blank Votes 1 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Purple 9 Elected
Green 8 Rejected
Blue 0 Rejected
Pink 0 Rejected
Blank Votes 3 Rejected
Ranked Robin — the cycle, the 2–1 tie, and LH's margin rung¶
Round-Robin — every pair, head-to-head (For – Against):
Purple beats Green 9 – 8
Blue beats Purple 10 – 9
Pink beats Purple 12 – 8
Green beats Blue 7 – 4
Green beats Pink 7 – 5
Blue beats Pink 10 – 3
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 Blue 2–1–0 2 +5 Purple, Pink
2 Green 2–1–0 2 +4 Blue, Pink
3 Purple 1–2–0 1 -4 Green
4 Pink 1–2–0 1 -5 Purple
Winner — Ranked Robin (RCV-RR): Blue
*** 2 candidates tie for the most wins (Green, Blue) — tied on the tally, not a
cycle (some of them beat others head-to-head, but no loop closes). Resolved by
total margin, then lot order.
BetterVoting's live result for the same race: Green (Copeland 2, elected via the head-to-head rung of its ladder).
Files¶
| Race | YAML | _tabulated mirror |
|---|---|---|
| STAR (lead) | page · bv2176_p8dp28_star.yaml | txt |
| RCV-IRV | page · bv2176_p8dp28_irv.yaml | txt |
| Ranked Robin | page · bv2176_p8dp28_ranked_robin.yaml | txt |
Frozen BetterVoting export (Election + Ballots + Results): bv2176_p8dp28_bv_export.json — BV's stored winners match every LH prediction (STAR Blue, RCV-IRV Purple, Ranked Robin Green — the ladder divergence, on the record).
Related: the video · LH vs BV on Ranked Robin ties · cycle resolution · up: method_comparisons
BetterVoting result screenshots (View 1) can be dropped into img/ as img/p8dp28_<what>.png and linked here.