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The committee spoiler — a candidate who wins nothing changes who does

One line: the same seven ballots elect Cyrus and Ari with three candidates on the ballot, and Cyrus and Bea once Dane is added — and Dane wins no seat. A candidate who cannot win still decides who sits in the second chair.

▶ Live on BetterVoting: BV2267 vote · results ↗ (election my9jd9) — three candidates · BV2268 vote · results ↗ (election 6m3gxq) — the same ballots with Dane added.

→ The method: Bloc STAR · the single-winner version: IIA & the cycle spoiler

Level: 301 · deep dive Two elections, 2 seats each, seven voters who never change their minds about anyone.

The two elections

Three candidates: Ari, Bea, Cyrus

# Ari Bea Cyrus
1 5 3 3
2 0 3 4
3 1 0 1
4 0 5 2
5 4 2 4
6 1 0 1
7 0 3 2

Seat 1 — scores Cyrus 17, Bea 16, Ari 11; runoff Cyrus 4 – Bea 2 (1 Equal Support). Cyrus is seated. Seat 2 — Cyrus removed: Bea 16, Ari 11; runoff Ari 4 – Bea 3. Ari is seated.

Council: Cyrus and Ari.

The same ballots, plus a fourth candidate: Dane

Every existing score is untouched; the voters simply also say what they think of Dane.

# Ari Bea Cyrus Dane
1 5 3 3 0
2 0 3 4 2
3 1 0 1 5
4 0 5 2 1
5 4 2 4 1
6 1 0 1 5
7 0 3 2 3

Seat 1 — scores Cyrus 17, Dane 17, Bea 16, Ari 11. Dane's arrival pushes Bea out of the finalist pair; runoff Cyrus 4 – Dane 3. Cyrus is seated — the same winner as before. Seat 2 — Cyrus removed: Dane 17, Bea 16, Ari 11. Dane and Bea advance; Ari, who won this seat a moment ago, is not even a finalist. Runoff Bea 4 – Dane 2 (1 Equal Support). Bea is seated.

Council: Cyrus and Bea. Dane wins nothing.

What it shows

Dane takes no seat in either round and loses both runoffs he reaches — yet his presence swaps Ari off the council for Bea. This is a failure of independence of irrelevant alternatives at the level of the committee: the set of winners depends on a candidate who is not one of them.

Two things make the Bloc version different from the single-winner one:

  • No Condorcet cycle is needed. The single-winner spoiler case has to arrange a genuine cycle before a non-winner can flip the result. Here the mechanism is plain arithmetic: each seat rebuilds the finalist pair from the candidates still standing, so an also-ran with a competitive score can occupy a finalist slot at seat 2 and crowd out the candidate who would have won it. Dane never has to be liked — he only has to score well enough to make the pair.
  • The spoiler gets N chances, not one. A candidate eliminated from contention for seat 1 is still on the ballot for seat 2, and every subsequent seat. The more seats, the more finalist pairs there are to disturb.

The practical reading, for anyone choosing rules rather than studying them: who else runs changes the composition of a Bloc STAR body, even when those candidates lose. That is true of nearly every method — it is worth knowing which shape it takes here, and knowing that it does not require anything exotic like a cycle to happen.

Run them yourself

Both are live on BetterVoting and reproduced independently in the LH engine; BV and LH agree exactly, nTallyVotes 7 on both, tieBreakType: none at every seat.

Case Candidates Council Read · run
BV2267 — the control 3 Cyrus, Ari count · yaml · results ↗
BV2268 — Dane runs 4 Cyrus, Bea count · yaml · results ↗

Frozen exports sit beside each yaml as …_bv_export.json.

file: README.md