Bloc STAR — Honest Limits¶

One line: Bloc STAR inherits every limit single-winner STAR has, and adds four of its own: it gives a cohesive majority every seat, it can shut the score leader out entirely, a tie at one seat can change who wins a later one, and the sweep it enables rewards slate discipline. Say all of that out loud before recommending it — the sweep in particular is not a corner case, it is the method's design.

→ Companion critical pages, so every method gets the same treatment: STAR's limits · Approval's limits · Ranked Robin's limits. The method itself: Bloc STAR.

Level: 201 → 301 · deep dive

1. It is not proportional, and cannot be made so¶

A cohesive majority can take every seat: 55% of the electorate can hold a council 5–0 while 45% holds nothing. There is no threshold, no correction, and no tuning parameter — nothing in the count ever learns that a group has already been served. Worked in full, with the arithmetic, on the majority sweep.

Stated as a limit it sounds damning; stated as a design goal it is simply what "majoritarian" means. The failure mode isn't the sweep, it's using Bloc STAR for a body that was supposed to represent people. If a 45% minority holding zero seats would read as a broken election, the method was chosen wrong — go to STAR-PR or STV. That decision is made when the rules are written and cannot be repaired by the count.

In one class of jurisdiction that is not merely a design mistake but a legal exposure: where a racial or language minority is concentrated in one sector of a multi-seat district, an at-large majoritarian count is the mechanism §2 of the Voting Rights Act calls vote dilution, and the scored ballot does nothing to change the analysis. The law, the Gingles test, and what a scored ballot does and does not fix: at-large elections and the Voting Rights Act.

2. The score leader can win nothing¶

Every seat is decided by the runoff, so the candidate who leads every scoring round can lose every runoff and take no seat at all. BV1835 is the worked case: Ava leads by 63 points, reaches all four runoffs, loses all four 51–49, and finishes with nothing while the two rival camps split the seats 2–2.

This is runoff reversal — STAR's signature step, and defensible on its own terms — but the multi-winner version has a sting the single-winner one doesn't. In a one-seat race a reversal costs you the seat, which is the deal. Here it costs you all of them, and a body that wanted its compromise figure in the room has no rung anywhere in the method at which "led every round" earns anything. Full argument, both readings: the score leader can win no seat.

3. A tie propagates forward¶

Because Bloc STAR is sequential — elect, remove, re-run — the field for seat 2 depends on how seat 1 came out. So a tie broken at seat 1 doesn't just decide seat 1: it can change which candidate wins seat 2. Two engine-verified runs of five identical ballots, differing only in the published lot order, elect two different councils (lot A · lot B).

Every top-N at-large method — Bloc Approval, SNTV, Bloc Ranked Robin — confines a tie to the last seat. Bloc STAR is the one that lets it travel. Details and the BetterVoting reporting problem that hides it: ties, seat by seat.

4. It rewards slate discipline¶

Follow the incentive the sweep creates. A faction large enough to sweep only sweeps if it stays cohesive — so the rational move for an organized side is to publish a slate and ask supporters to score it uniformly high and everything else 0. That works, and it is available to organized groups in a way it is not available to unorganized voters. The cost of not doing it is Over 50% — what a landslide actually buys: three voters unanimous about one candidate elect them to seat 1 and then hand seat 2 to a candidate two of the three scored 0.

Two honest caveats on how far to push this claim:

It is milder than the plurality family's version. Under SNTV a side that runs one candidate too many can lose everything to vote splitting, which is why SNTV jurisdictions develop candidate-rationing machines. Bloc STAR has nothing to split — scoring one candidate never costs another — so the pressure is toward cohesion, not toward rationing. That is a real improvement, not a wash.
Bullet voting has a sharper edge here than in a single-winner race. Giving a rival a generous score can help them win a later seat, and there is no reweighting to soften it. The incentive to compress your scores toward 5s and 0s therefore repeats once per seat. Like every method (Gibbard), Bloc STAR can be gamed at the margins; what is specific here is that the margin recurs N times.

5. Everything single-winner STAR concedes, N times over¶

Bloc STAR is STAR, so all of STAR's honest limits apply unchanged — not Condorcet-compliant, not favorite-betrayal-proof, Later-No-Harm given up by design, a narrow residual of vote splitting. Nothing about filling several seats repairs any of them, and each one gets a fresh chance to bite at every seat.

One practical limit that is genuinely new: ballot length. An at-large race with fifteen candidates asks every voter for fifteen considered 0–5 judgments. That is a real cognitive cost, and it is the strongest argument for smaller districts even when you have decided you want a majoritarian body.

What it does not give up¶

Parity cuts both ways, so the concessions above should be read against what survives the move to multi-winner intact:

No vote splitting. Running a third candidate cannot cost your side a seat. On Food-Truck Row that is the difference between a 57-voter majority holding both seats and holding none.
It is still summable. Every quantity the count needs — per-candidate score totals, the full For / Equal Support / Against matrix, the five-star counts — is a fixed-size precinct table that adds. Removing a seated candidate doesn't change anyone else's totals, so seat 2 is read off the same summed tables as seat 1. Bloc STAR is precinct-auditable in a way STV is not; compare STAR's summability.
One ballot for every race. The same 0–5 ballot serves single-winner, bloc and proportional races, so a jurisdiction can change what a body is for without retraining its voters.