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02_STAR_Bloc/03_Criteria — what Bloc STAR keeps, and what it drops

The formal side of Bloc STAR, always as runnable elections rather than assertions. Each set below isolates one criterion on the smallest electorate that shows it, and every one of them is a criterion the single-winner method is usually asked about — so the honest answer for the multi-winner version has to be checked, not inherited.

The prose companions live in 01_Learn/; this folder is where those claims get numbers. Levels follow the curriculum: 🟢 101 · 🟡 201 · 🔴 301.

Why the folder exists at all: Bloc STAR is single-winner STAR, run once per seat — so it is tempting to assume every STAR property carries over. Some do. Two of the three sets below are cases where one does not, and the reason is always the same mechanism: the removal step builds a fresh finalist pair for every seat, and a change that cannot touch the first pair can still change the second.

Set Level Elections What it shows
Participation 🔴 301 BV2264 j3hqvb · BV2265 th3pbp A voter joins, votes honestly, and gets a worse council by their own ballot — because their support lifted their favourite into the seat-2 runoff, where a candidate they scored 0 beat them.
Seat order 🟡 201 BV2266 k7pfqt The candidate who beats every rival head-to-head is seated second. "First seated" is not "most preferred," which matters wherever the top finisher gets the chair.
The committee spoiler 🔴 301 BV2267 my9jd9 · BV2268 6m3gxq Adding a candidate who wins no seat changes which candidates do — independence of irrelevant alternatives, at the level of the committee.

Every one of the five elections is live on BetterVoting and reproduced independently in the LH engine, and BV agrees with LH exactly in all five: same winners, same seat order, every ballot counted, and tieBreakType: none at every seat — nothing here rests on a lot. The ballots, the seat-by-seat count and the frozen export live with the case.

What is not here (yet)

Recorded so the gaps are visible rather than implied:

  • Monotonicity. Raising a seated candidate has not been made to cost them their seat: a strict search over ~377,000 tie-free profiles found no failure, and the two-seat case looks provable (a seat-2 winner had to beat the overall score leader head-to-head — the very opponent a raise would put in front of them at seat 1). Being settled; see the working note in _notes/.
  • Reinforcement, clones, and strategic min-maxing. Claimed in honest limits, not yet backed by a runnable case.
  • Proportionality axioms (JR / PJR / EJR). The formal statement of "Bloc STAR is not proportional," which the folder currently teaches by worked sweep instead.

file: README.md