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02_STAR_Bloc — Bloc STAR (multi-winner, majoritarian)

Score every candidate 0–5, exactly as in single-winner STAR. Then run that entire count once per seat.

A Bloc STAR ballot. Heading: Bloc STAR Voting. Above the race: This election will elect 3 winners. Instructions: give your favorite candidate five stars; give your last choice zero stars or leave them blank; equal scores are allowed; score other candidates as desired. A 0-5 grid with one row per candidate, marked Andre 5, Blake 0, Carmen 1, David 4, Ella 4. Below the grid: This election will use Bloc STAR Voting to elect 3 winners. In Bloc STAR Voting, the two highest scoring candidates are finalists and your vote goes to the finalist you prefer. The finalist preferred by the most voters wins. This process repeats until all seats have been filled.

The ballot — drawn here from the STAR Voting technical specifications §3.b–3.d rather than screenshotted, because BetterVoting's live one prints neither the right method name nor the sentence that explains multi-winner. Only two things on this page mark it as a multi-seat race: the seat count above the grid, and the last sentence below it. Nothing is rationed — three seats are up and you still score every candidate, once. Full treatment, beside its single-winner twin: the Bloc STAR ballot.

Filling several seats at once — a city council, a board, a committee — with the same expressive STAR ballot. Bloc STAR is the majoritarian multi-winner method: it asks "who does the majority most want?" for every seat. Its proportional cousin, STAR-PR, instead tries to give every faction its fair share. Which you want depends on the body you're electing — this folder teaches the majoritarian one and, just as importantly, when not to use it.

First, the bigger decision. Whether you want a majoritarian body at all — "the N best" — or a proportional one that mirrors the electorate, comes before choosing any method on this page: Electing more than one, simply.

New to STAR itself? Learn the single-winner method first — STAR — start here — because Bloc STAR is just that method, run once per seat.

The concept pages live in 01_Learn/ — the method, the majority sweep, the score leader who wins no seat, ties seat-by-seat, the at-large family, and the honest limits. This page is the folder's front door and the index of its runnable cases.

How Bloc STAR works

You score every candidate 0–5, exactly like single-winner STAR. To fill N seats, the count runs single-winner STAR N times:

  1. Seat 1: score everyone; the two highest advance to an automatic runoff; the runoff winner takes the seat.
  2. Remove that winner from every ballot.
  3. Seat 2: re-run the same STAR count on who's left. Repeat until all seats are filled.

Worked example (the baseline case, counted in full): 3 candidates, 2 seats. Score round: Alice 14, Bruno 12 are the top two; in the runoff Alice is preferred 2–1, so Alice takes seat 1. Remove Alice and re-run on the remaining two: Bruno takes seat 2.

The one thing to understand: majoritarian, not proportional

Because every seat is decided by the same electorate on the same ballots, a cohesive majority can win every seat. If 55% of voters share a slate, that slate can sweep the whole council 5–0, leaving the 45% with no representation at all.

That is a feature or a bug depending on what you're electing:

  • Use Bloc STAR when you want the body to reflect the majority as a unit — e.g. a slate of officers who must govern together, or any at-large seat where "the candidates most voters prefer" is the goal.
  • Don't use it when you want minorities represented — a legislature, a diverse committee. There, a majority sweep is exactly the wrong outcome, and you want Proportional STAR (STAR-PR) instead.

This tension is the whole reason proportional methods exist. Gentle intro to the trade-off (approval side, counting only): Electing a committee — making sure people have a voice. Concept hub: proportional representation.

Learning path

  1. The method — the elect-remove-rerun loop, what the removal step does and doesn't do: Bloc STAR. See the paper it runs on first if you'd rather start concrete: the Bloc STAR ballot — three seats change three lines of text and nothing about how you mark it. Its smallest runnable form is the baseline case (3 candidates, 2 seats), then a 2-seat committee election (4 candidates; the CURRICULUM 201.5 file).
  2. Watch a majority sweep — internalize why Bloc is majoritarian: The majority sweep. Worked at whiteboard scale in exercise 12 (60% takes both seats, then the same ten ballots counted proportionally), and against four other counts on one electorate in Food-Truck Row. Contrast: STAR-PR and Bloc Plurality / SNTV.
  3. The compromise candidate, shut out — the score leader can win no seat, worked on the first case here at a realistic electorate (100 voters, 4 seats): BV1835. Ava leads every scoring round by sixty-three points and takes nothing, losing all four runoffs 51–49. Read it for what the runoff step does: Bloc seats whoever is preferred, not whoever accumulates points. Note this is the opposite configuration to a sweep — two even camps splitting the seats 2–2.
  4. Edge cases & trust (201/301) — ties, seat by seat: how the STAR ladder runs once per seat, how a seat-1 coin toss can change who wins seat 2, and where BetterVoting's display diverges. The reference cases below are the receipts.
  5. The honest version — what Bloc STAR concedes, and how it sits among the other at-large methods.
  6. The criteria, as runnable elections (201/301) — 03_Criteria/: the properties single-winner STAR is usually asked about, checked for the multi-winner version rather than inherited. Participation — an honest joiner ends up with a worse council; seat order — the candidate who beats everyone head-to-head is seated second; the committee spoiler — a candidate who wins nothing changes who does. Five BetterVoting elections, BV and LH agreeing exactly, no tie-break anywhere.

Curriculum context: 201.5 — Multi-winner intro: Bloc STAR.

The reference cases

Every YAML carries expected_winners and is auto-checked by the test suite; BV-backed cases also keep a frozen _bv_export.json and a two-view .md. Many of these were built to expose or confirm a specific tie-breaking or reporting behavior in BetterVoting.

How to read the link cells. Every case is linked as an article first and a data file second: page / count is the readable write-up (scenario, ballots, the engine's full count) — start there; lesson is the hand-written two-view comparison (BetterVoting's result beside the independent LH count) that BV-backed cases also carry; yaml is the raw source you feed the engine to run it yourself.

Start here (teaching):

Case Seats What it shows Read · run
00 — pure baseline 2 The clean elect-remove-rerun loop, no tiebreak — read this first. page · yaml
01 — basic two-seat 2 4 candidates, 2 seats — the CURRICULUM 201.5 intro file. page · yaml
Shadow STAR — Lackner & Skowron 4 Bloc STAR on the academic running example used across the multi-winner literature. page · yaml
Lot path-dependence — A 2 A matched pair, LH-only. Identical ballots; only the published lot differs. Seat 1 is a perfect tie (score 15–15, five-star 3–3 — the rung is live and still can't separate them), so the lot decides it — and that choice changes who wins seat 2, not just the order. Lot [Nadia, Omar, Priya] → Nadia, Priya. page · yaml
Lot path-dependence — B 2 The same five ballots, lot reversed to [Omar, Nadia, Priya] → Omar, Nadia. Priya is on the council in A and absent from B. The demonstration behind ties, seat by seat. page · yaml
A race nobody can lose — the control 2 The seven ballots of BV2269 with one seat removed, so they count normally. Pair it with the three-seat file below: Celia wins nothing here and is a board member there, on the same ballots. page · yaml

Tie-breaking & BetterVoting reproductions (201/301):

BV id Scenario Seats Tie? BV status / issue Read · run
BV1815 3c/2s — seat 2 by score tiebreak 2 runoff (seat 2) Passed lesson · count · yaml
BV132 verify votes cast — flat ballots dropped 2 flat/no-pref Failed · #1073 lesson · count · yaml
BV131 Guido example — hidden lot-decided tie (seat 1) 2 lot (seat 1) "Passed" (but a coin toss; tieBreakType mislabeled none) lesson · count · yaml
BV129 3c/2w — seat 2 by score tiebreak 2 runoff (seat 2) count OK; "Failed" = method-name label #1086 (note) lesson · count · yaml
BV126 "ties every step" — yes Failed · #1052 pending
BV750 tie-breaking — all ballots identical (5,5,5) 2 lot (both seats) Failed — every ballot dropped (nTallyVotes 0) #1052 lesson · count · yaml
BV130 6c/3w — original (clean, no tie) 3 none tabulation OK; reporting fix (tabs → pages) star-server#731 lesson · count · yaml
BV130-r2 6c/3w — dead-rung lot tie (seat 1) 3 lot (seat 1) Passed (9ff9jk); lot-decided seat, tieBreakType reads none lesson · count · yaml
BV1525 5c/4w — Condorcet-loser ties for seat 1 (electowiki) 4 lot (seat 1) LH reproduces First–Fourth; STAR 2.0 random-tie non-reproducible lesson · count · yaml
BV2105 Favorite ice cream demo — a partial ballot filed as an abstention 2 — Failed (2025 baseline) · #1478 — not #1056, a different bug on the same election lesson · count · yaml
BV2105-r2 the same four ballots, re-cast a year later 2 — Failed again — still reproduces (2026-08-04); filed as #1478 lesson · count · yaml
BV1835 5c/4w, 100 voters — the score leader is the Condorcet loser and wins nothing (all four runoffs 51–49) 4 none Passed (8h3yrx); LH and BV agree exactly lesson · count · yaml
— (484mbm) 3c/2s — every rung ties (score, pairwise, five-star) on rotating ballots 2 lot (seat 1) LH reproduces BV once the perm is pinned; BV skips pairwise on 3-way ties and its top-level tieBreakType reads none lesson · count · yaml
BV2269 3c/3s — a race nobody can lose: as many seats as candidates 3 none The engines disagree on the premise: LH refuses the file (exit 1, no tally); BV accepts it, counts seats 1–2 normally and reports "Celia is the only candidate, and wins by default" for seat 3 lesson · count · yaml

file: README.md