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Participation — voting made this voter's council worse

One line: a voter turns up, scores the candidates honestly, and ends up with a council their own ballot rates lower than the one they would have got by staying home — because the support they gave their favourite pushed that favourite into the seat-2 runoff, where a candidate they scored 0 won it.

▶ Live on BetterVoting: BV2264 vote · results ↗ (election j3hqvb) — the council six voters elect · BV2265 vote · results ↗ (election th3pbp) — the same six plus the joiner.

→ The method: Bloc STAR · the concession list this belongs on: honest limits · the single-winner paradox page: no-show

Level: 301 · deep dive Two elections, same 4 candidates, 2 seats. The second is the first plus one ballot.

The two elections

Four candidates — Ada, Bruno, Cleo, Dov — for a two-seat board, scored 0–5.

Before: six voters

# Ada Bruno Cleo Dov
1 3 5 1 3
2 4 5 2 4
3 4 0 1 4
4 2 2 5 1
5 3 1 1 1
6 5 0 1 5

Seat 1 — scores Ada 21, Dov 18, Bruno 13, Cleo 11; Ada and Dov advance; runoff Ada 2 – Dov 0 (4 voters express no preference between them). Ada is seated.

Seat 2 — Ada is removed and the same ballots are re-counted: Dov 18, Bruno 13, Cleo 11; Dov and Bruno advance; runoff Bruno 3 – Dov 2 (1 Equal Support). Bruno is seated.

Council: Ada and Bruno.

After: the same six, plus one

A seventh voter arrives. Their honest ballot: Ada 3, Bruno 2, Cleo 5, Dov 0 — Cleo is their favourite, Dov the one candidate they cannot stand.

# Ada Bruno Cleo Dov
1–6 as above
7 3 2 5 0

Seat 1 — scores Ada 24, Dov 18, Cleo 16, Bruno 15; runoff Ada 3 – Dov 0 (4 Equal Support). Ada is seated, exactly as before.

Seat 2 — Ada removed: Dov 18, Cleo 16, Bruno 15. Cleo has passed Bruno by one point and takes the second finalist slot. Runoff Dov 4 – Cleo 2 (1 Equal Support). Dov is seated.

Council: Ada and Dov.

What just happened

By their own ballot, the new voter rates the two possible councils like this:

Ada + partner total
The council they would have got by staying home 3 Bruno 2 5
The council they got by voting 3 Dov 0 3

Their ballot changed exactly one thing that mattered: it lifted Cleo from 11 points to 16, which was enough to push Cleo past Bruno into the seat-2 runoff. Bruno — whom this voter scored 2, and who beat Dov in that runoff before — was no longer on the ballot at that stage. Dov, whom they scored 0, beat Cleo comfortably and took the seat.

Helping your favourite reach the runoff is what handed the seat to the candidate you scored zero. Nothing here is strategic and no ballot is insincere; the seventh voter simply voted.

Why it is worth a case

  • It is a participation failure — the no-show paradox — in cardinal, multi-winner form. The library's other no-show cases are all ranked-ballot ones (Burlington, Felsenthal Ex.4, the RCV-IRV pair), and in the Felsenthal pair STAR is the method that doesn't move. That reads as "STAR is fine here," and for one seat it largely is. For several seats it isn't.
  • The mechanism is specific to Bloc STAR, not inherited from STAR. Each seat rebuilds the finalist pair from what is left, so a ballot that cannot change seat 1 gets a second, independent chance to change seat 2 — and there is no reweighting step to absorb it. Compare STAR-PR, where support already spent on a seated winner is discounted.
  • The honest framing. Every deterministic voting method with more than two candidates can be embarrassed like this (Gibbard), and no rung of the tie-break ladder is involved here — this is the count working as designed. What the case establishes is the shape of Bloc STAR's failure, so it can be described accurately instead of denied or exaggerated.

Run them yourself

Both elections are live on BetterVoting and reproduced independently in the LH engine; BV and LH agree exactly, all seats decided with tieBreakType: none and every ballot counted (nTallyVotes 6 and 7).

Case Voters Council Read · run
BV2264 — the control 6 Ada, Bruno count · yaml · results ↗
BV2265 — the joiner votes 7 Ada, Dov count · yaml · results ↗

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

file: README.md