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Over 50% — what a landslide actually buys

One line: a candidate can take 100% of the score and 100% of the runoff and it still buys exactly one seat — Bloc STAR spends that majority electing them, then starts the next seat over on the same ballots, where a candidate two of the three voters scored 0 can win on 13% of the points with no majority anywhere in sight.

→ the count itself: Bloc STAR · the opposite configuration, where a majority does take everything: the majority sweep · what a runoff percentage is a percentage of: Runoff percentages — two denominators

Level: 201 · for voters

The ceiling case — over 50% of everything

Start where there is nothing to argue about. Three voters, three candidates; every ballot gives A five stars, one voter gives B a single point, nobody scores C at all (full count → · yaml · live on BetterVoting ↗ — BV2263 xw23m9, where BV's tally agrees line for line):

--- STAR Voting Method (single winner) ---

[STAR Voting]
 Tabulating 3 ballots.
Count × A,B,C
    2 × 5,0,0
    1 × 5,1,0

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   A             -- 15 -- First place
   B             --  1 -- Second place
   C             --  0
 A and B advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   A             -- 3 -- First place
   B             -- 0
   Equal Support -- 0
 A wins.
   Runoff math:
     3  ballots cast
   − 0  Equal Support (no preference between the two finalists)
     ─
     3  voters with a preference  (majority = 2)
           A 3 (100%)  ·  B 0 (0%)

[STAR Voting: Winner — STAR Voting Method (single winner)]
 A

A wins on every denominator a STAR result has:

"Over 50%" of what? A how it's counted
the maximum possible score 15 / 15 = 100% 3 ballots × 5 stars
the ballots in the runoff 3 / 3 = 100% Equal Support left in the denominator
the voters with a preference 3 / 3 = 100% Equal Support removed — the number that decides the race

That is the whole reason this tiny election is worth keeping: it is the one case where those three numbers are the same, so it's the control you read every other result against. They come apart the moment a ballot rates the two finalists equally — see two denominators.

And note what did not happen: the count did not stop early. A held every point on every ballot and was still put through the automatic runoff, because the scoring round only ever picks finalists — it never elects anyone. There is no "wins outright in round 1" shortcut in STAR, the way a majority of first choices ends an RCV-IRV count in its first round. Two rounds, always. (Why the runoff is worth running even when it changes nothing: the automatic runoff.)

Now give the same electorate a second seat

BV1815 is the multi-seat twin — three ballots again, A dominant again, but two seats to fill (full count → · yaml):

--- Bloc STAR Voting Method (2 winners) ---

[Bloc STAR]
 Tabulating 3 ballots to fill 2 seats.
A,B,C
4,1,0
3,0,2
5,0,0

[Bloc STAR: Round 1: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   A             -- 12 -- First place
   C             --  2 -- Second place
   B             --  1
 A and C advance.

[Bloc STAR: Round 1: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   A             -- 3 -- First place
   C             -- 0
   Equal Support -- 0
 A wins.
   Runoff math:
     3  ballots cast
   − 0  Equal Support (no preference between the two finalists)
     ─
     3  voters with a preference  (majority = 2)
           A 3 (100%)  ·  C 0 (0%)

──────────────────────────────────────────────────

[Bloc STAR: Round 2: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   C             -- 2 -- First place
   B             -- 1 -- Second place
 C and B advance.

[Bloc STAR: Round 2: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   B             -- 1 -- Tied for first place
   C             -- 1 -- Tied for first place
   Equal Support -- 1
 There's a two-way tie for first.

[Bloc STAR: Round 2: Automatic Runoff Round: First tiebreaker]
 The highest-scoring candidate wins.
   C             -- 2 -- First place
   B             -- 1
 C wins.

[Bloc STAR: Winners — Bloc STAR Voting Method (2 winners)]
 A
 C

Seat 1 is the ceiling case again in all but the last decimal: A holds 12 of 15 points (80% of the maximum), is the top-scored candidate on every ballot, and wins the runoff 3–0. Seat 2 is a different election entirely — and this is what the same three denominators say about its winner:

"Over 50%" of what? C, at seat 2
the maximum possible score 2 / 15 = 13% one voter scored C at all; the other two left C on 0
the ballots in the runoff 1 / 3 = 33% one prefers C, one prefers B, one rates them equally
the voters with a preference 1 / 2 = 50% not more than half — a tie, not a majority

Nobody won that runoff. STAR's runoff guarantees the winner is preferred to the other finalist by more voters — and when that guarantee can't be met, the seat falls to the tie-break ladder, whose first rung is the score total: C's 2 beats B's 1. So the second seat on this board is held by a candidate a majority of the electorate gave zero points, seated by a rung rather than by a majority. Both engines agree on that — this is a real BetterVoting election (results ↗, id fk38pk), and BV reports the same winners with tieBreakType: "score".

It is also the clearest place to watch the denominators disagree in the wild. BetterVoting's results page paginates one card per seat, and on the seat-2 card all three runoff bars are labelled 33% while the dashed majority threshold line is drawn at 1 vote — level with the top of both candidate bars. On the seat-1 card, where nobody rated the finalists equally, the same line sits at 50% of the same axis and reads correctly. Both screenshots, side by side: BV1815. The mismatch is bettervoting#1471 and is presentation only — the count is right on both cards.

Why the majority doesn't carry over

Bloc STAR fills seats by running the whole count once per seat: elect, remove, re-run on the same unchanged ballots. The removal step is where the landslide is spent. A's twelve points and three head-to-head preferences elected A and then left the election with A; nothing about that first result is still on the table when seat 2 is counted. Round 2 is a fresh STAR election among whoever is left, and it is decided by the only thing the voters still disagree about.

Which is the honest version of the lesson: these three voters were unanimous about a candidate, not about a slate. Above A, their ballots have nothing in common — one prefers B, one prefers C, one rates both at zero. A group can be as cohesive as an electorate ever gets on the question "who should win?" and still be a three-way split on "who else?"

This is not a bug, and it is not the sweep either

Two failure modes get confused here, and they are opposites:

  • The majority sweep — a cohesive majority that runs several candidates can take every seat, leaving a large minority with nothing. That is Bloc STAR's defining property and the reason to think hard before choosing it.
  • This page — a majority that runs one candidate wins exactly that one seat, and hands the rest to whoever the leftovers favor. Same method, same majoritarian logic; the difference is entirely in how many candidates the majority put on the ballot.

Together they are one fact stated twice: Bloc STAR rewards slate discipline (honest limits). Winning big does not fill a board; running enough candidates does. If you want the second seat to reflect the second-largest group rather than the second-largest leftover, you want a proportional method — STAR-PR reweights the ballots that already won a seat so they count for less on the next one. That decision belongs before the ballots are printed: Electing more than one, simply.

See also

file: over_50_percent.md