The Post-it RCV example (20 voters) — RCV-IRV: Purple wins the video's whiteboard count¶

Generated from bv2176_p8dp28_irv.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.

Method: RCV-IRV (Instant Runoff) · 1 seat · Expected winner: Purple

▶ Live on BetterVoting: vote · results ↗ (election p8dp28 · test BV2176).

Scenario¶

One of three races in the Post-it RCV example (BV2176, bvid p8dp28; BV-confirmed). The 20 ranked ballots from Equal Vote's video "Updated: How does RCV work? — With Post-its!" (https://youtu.be/Vte4nly_Neg), counted exactly as on the whiteboard. Round 1: Purple 7, Green 6, Blue 4, Pink 3 — Pink is eliminated (1 ballot goes to Green, 1 to Purple, and 1 bullet-vote Pink ballot exhausts). Round 2: Purple 8, Green 7, Blue 4 — Blue is eliminated (1 to Green, 1 to Purple, and the 2 Blue>Pink ballots exhaust, Pink being already gone). Final: Purple 9, Green 8 — Purple wins with 9 of the 17 still-active ballots. The sting the video builds to: Blue, the round-2 eliminee, beats Purple head-to-head 10-9 — a runoff RCV-IRV never held, but the STAR race on these voters' scores does (and Blue wins it).

Live results: https://bettervoting.com/p8dp28/results Companion races: bv2176_p8dp28_star.yaml, bv2176_p8dp28_ranked_robin.yaml. Overview page: bv2176_p8dp28_postit_rcv_example.md

Ballots¶

Each row is one voter's ranking, most-preferred first (N: prefix = N identical ballots).

Purple
Purple
Purple
Purple
Purple
Purple
Purple
Green>Blue>Pink
Green>Blue>Pink
Green>Blue>Pink
Green>Blue>Pink
Green>Blue>Pink
Green>Blue>Pink
Blue>Pink
Blue>Pink
Blue>Green>Pink
Blue>Purple
Pink>Green>Purple
Pink>Purple
Pink

What the engine says¶

Round-by-round Sankey diagram: each candidate's votes as a band, and where the votes of an eliminated candidate transferred to.

Where the votes went. Band thickness is votes; a band leaving an eliminated candidate lands on whoever that ballot ranked next, or on inactive if it ranked nobody who was left.

The count, step by step — the rounds and how the winner is reached:

--- RCV / Instant-Runoff Voting (single winner) ---
  The Post-it RCV example (20 voters) — RCV-IRV: Purple wins the video's whiteboard count
 Tabulating 20 ballots (ranked ballots).

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


Winner(s) — RCV / Instant-Runoff Voting (single winner)
  Purple

--- Transfers and inactive ballots (what the round tables leave out) ---
The tables above give each candidate's round total but not where a
transferred vote came FROM, nor how many ballots stopped counting.
Both are recomputed from the ballots, using the eliminations the
count above actually made.

ROUND 1 — 20 of 20 ballots still active; majority = 11
   Pink eliminated with 3:
      → (no continuing ranking)      1  ← these ballots go inactive
      → Green                     1
      → Purple                    1

ROUND 2 — 19 of 20 ballots still active (1 inactive); majority = 10
   Blue eliminated with 4:
      → (no continuing ranking)      2  ← these ballots go inactive
      → Green                     1
      → Purple                    1

FINAL ROUND — 17 of 20 ballots still active (3 inactive); majority = 9
   Purple                    9  (52.9% of the still-active)  ← elected
   Green                     8  (47.1% of the still-active)
   Never exhausted, never transferred:
      8 ballots held by Green carried a lower ranking that was never read
      (the count stopped here, so those preferences did nothing).

Inactive ballots at the final round: 3 of 20 (15.0%).
   Purple's 9 is a majority of the 17 still active but only 45.0% of all 20 cast —
   the 'majority' here is of a shrunken denominator. See
   06_Other/RCV_IRV/concepts/RCV_IRV_exhausted_ballots.md

Full audit — preference matrix, Condorcet, and score distribution¶

--- 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 (4 of 4): Green, Blue, Purple, Pink
   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.
   Note: the Copeland leaders (Green, Blue) are only part of the set — the
   win–loss table's top block understates how wide the contention is.
   RCV-IRV winner Purple is INSIDE the Smith set. ✓
      Not guaranteed — RCV-IRV is not Smith-efficient — but it holds here.
   More: 07_Concepts/topics/smith_set.md

Everything in one file: the _tabulated mirror (regenerated on every run; every analysis forced on).

Run it yourself:

python STARVote_LH_tabulation_engine/starvote_larry_hastings.py method_comparisons/postit_rcv_example/cases/bv2176_p8dp28_irv.yaml

The Post-it RCV example (20 voters) — RCV-IRV: Purple wins the video's whiteboard count¶

Scenario¶

Ballots¶

What the engine says¶

Full audit — preference matrix, Condorcet, and score distribution¶

See also¶