Block Voting (3 seats): the majority ceiling — a unanimous candidate holds only 33%¶

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

Method: plurality · 3 seats · Expected winners: Alice, Bruno, Cleo

Official tie-break (lot) order: Alice > Bruno > Cleo > Dev > Esme — consulted only if every deterministic tiebreaker stays tied (how the ladder works).

Scenario¶

Why "the winner got less than half the votes" cannot be read as vote splitting in a MULTI-SEAT choose-one race — the arithmetic forbids it.

30 voters, 3 seats, 5 candidates. Each voter marks 3 names (Block Voting), so 90 votes are cast in total. Alice is on EVERY single ballot — literal unanimity, the most consensus a candidate can possibly have.

And Alice's share of votes cast is 30 / 90 = 33.3%.

With k marks per voter the total is k x voters, so no candidate can exceed 1/k of votes cast no matter how popular: 33% at 3 seats, 25% at 4, 9% at 11. A screening rule that flags every race whose leader is under 50% therefore flags 100% of multi-seat block-vote races — including unanimous ones. That is a denominator artifact, not evidence of a split.

This does NOT clear Block Voting. Its real defect is the opposite one: a bare majority sweeps every seat (see mmp_block_voting.yaml, 60/40 -> 3-0). The point is narrower and cuts both ways — the sub-majority test is blind here, missing the actual pathology while flagging consensus as a failure.

Ballots¶

Row 1 = candidate names; each later row is one voter's 0–5 scores (a N × prefix = N identical ballots).

Alice,Bruno,Cleo,Dev,Esme
12: 1,1,1,0,0
10: 1,1,0,1,0
8:  1,0,1,0,1

What the engine says¶

Full report from the _tabulated mirror (regenerated on every run; every analysis forced on):

--- Block Voting (plurality-at-large) — 3 winners ---
 Tabulating 30 ballots (3 votes/voter).

Votes (most votes fill the seats):
   Alice    30  <- Elected
   Bruno    22  <- Elected
   Cleo     20  <- Elected
   Dev      10
   Esme      8

Winners — Block Voting (plurality-at-large), 3 seats:
   1. Alice   (30 votes)
   2. Bruno   (22 votes)
   3. Cleo   (20 votes)

Run it yourself:

python STARVote_LH_tabulation_engine/starvote_larry_hastings.py method_comparisons/multi_member_plurality/cases/mmp_majority_ceiling.yaml

Block Voting (3 seats): the majority ceiling — a unanimous candidate holds only 33%¶

Scenario¶

Ballots¶

What the engine says¶

See also¶