Cross-checking Proportional STAR against BetterVoting's own fixtures¶

The strongest kind of agreement: BetterVoting's unit tests for Allocated Score, cast as real BetterVoting elections, and re-counted by an engine nobody at Equal Vote wrote.

Level: 301 · deep dive

→ the method: STAR-PR · the case this resolved: BV2130 · the paradox these clean counts made findable: Alabama

Why this exists¶

For a long time the library had exactly one BetterVoting-backed Proportional STAR case — BV2130, a 51-candidate, 102-ballot presidential board — and it disagreed with our engine on the last of seven seats. That is a bad place to be: with one contaminated data point you cannot tell whether the two implementations of Allocated Score differ, or whether something else does.

These two elections settle it. They are BetterVoting's own test fixtures for the method, taken from packages/backend/src/Tabulators/AllocatedScore.test.ts, cast as live public elections, and counted independently by Larry Hastings' starvote.

Case	BV election	Seats	BetterVoting elects	LH `allocated` elects
Fractional surplus	`kk2gxj` ↗	2	Allison, Doug	Allison, Doug	✅
Fewer voters than seats	`hk27tk` ↗	3	Allison, Bill, Carmen	Allison, Bill, Carmen	✅

Both exports report nAbstentions: 0 — every ballot counted, by both engines, on both sides. That matters, and the next section says why.

What this proved about BV2130¶

BV2130's seat-7 disagreement had two standing hypotheses: an implementation difference in Allocated Score, or a near-tie broken at random. These fixtures killed the first one. If the two implementations of the method disagreed, they would disagree here — on the method author's own tests. They don't.

That left the input, and the input was the answer: BetterVoting's export for BV2130 reports nTallyVotes: 100 against the ballot set's 102. Two ballots were discarded as abstentions (#1478), the Hare quota is voters ÷ seats, so a different ballot count means a different quota — 14.2857 against 14.5714 — applied in every round. The error compounds across six seats and flips the seventh.

So the engines agree; they were handed different elections. These two clean cases are what made that provable rather than suspected.

The fixtures, and what each is for¶

Fractional surplus (`kk2gxj`, 2 seats, 12 ballots)¶

Allison has eight top-level supporters, but with 12 voters and 2 seats a seat costs six. The whole quota therefore comes from inside her 5-star group, and no rule about which of eight identical ballots to spend would be defensible — so none is applied. Each of the eight keeps 1 − 6/8 = 0.25 of its weight.

That is fractional surplus handling, and this fixture is the reason it exists: voters who scored a winner identically are spent identically. Without it, four of those eight ballots would be fully consumed and four fully preserved, decided by nothing but list order.

--- Allocated Score Voting Method (2 winners) ---

[Allocated Score Voting]
 Tabulating 12 ballots to fill 2 seats.
Count × Allison,Bill,Carmen,Doug
    7 ×       5,   5,     1,   0
    3 ×       0,   0,     4,   5
    1 ×       5,   4,     4,   0
    1 ×       0,   0,     0,   3

[Allocated Score Voting: Round 1]
 The highest-scoring candidate wins a seat.
   Allison       -- 40 -- First place
   Bill          -- 39
   Carmen        -- 23
   Doug          -- 18
 Allison wins a seat.

[Allocated Score Voting: Round 1: Ballot allocation round]
 Allocating 6 ballots.

[Allocated Score Voting: Round 1: Ballot allocation round: Round 1]
 Allocating 8 ballots at score 5.
 This allocation overfills the quota.  Returning fractional surplus.
 Allocating only 75.00% of these ballots.
 Keeping these ballots, but multiplying their weights by 1/4.
 8 ballots reweighted from 1 to 1/4.

[Allocated Score Voting: Round 2]
 The highest-scoring candidate wins a seat.
   Doug          -- 18     -- First place
   Carmen        -- 14+3/4
   Bill          --  9+3/4
 Doug wins a seat.

[Allocated Score Voting: Winners — Allocated Score Voting Method (2 winners)]
 Allison
 Doug

Fewer voters than seats (`hk27tk`, 3 seats, 2 ballots)¶

Two voters, three seats. A degenerate election, and deliberately so: it exists to prove the tabulator does something sane when the quota (2 ÷ 3 ≈ 0.67) is smaller than a single ballot, rather than dividing by zero, looping, or seating nobody. Both engines fill all three seats.

Worth knowing that Allocated Score refuses seats = 1 outright — the method is defined for multi-winner races — so the degenerate end of its range is tested here rather than assumed.

--- Allocated Score Voting Method (3 winners) ---

[Allocated Score Voting]
 Tabulating 2 ballots to fill 3 seats.
Allison,Bill,Carmen,Doug
      5,   5,     0,   0
      5,   4,     3,   0

[Allocated Score Voting: Round 1]
 The highest-scoring candidate wins a seat.
   Allison       -- 10 -- First place
   Bill          --  9
   Carmen        --  3
   Doug          --  0
 Allison wins a seat.

[Allocated Score Voting: Round 1: Ballot allocation round]
 Allocating 2/3 ballots.

[Allocated Score Voting: Round 1: Ballot allocation round: Round 1]
 Allocating 2 ballots at score 5.
 This allocation overfills the quota.  Returning fractional surplus.
 Allocating only 33.33% of these ballots.
 Keeping these ballots, but multiplying their weights by 2/3.
 2 ballots reweighted from 1 to 2/3.

[Allocated Score Voting: Round 2]
 The highest-scoring candidate wins a seat.
   Bill          -- 6 -- First place
   Carmen        -- 2
   Doug          -- 0
 Bill wins a seat.

[Allocated Score Voting: Round 2: Ballot allocation round]
 Allocating 2/3 ballots.

[Allocated Score Voting: Round 2: Ballot allocation round: Round 1]
 Allocating 1 ballot at score 10/3.
 These ballots carry a remaining weight of 2/3.

[Allocated Score Voting: Round 3]
 Tabulating 1 remaining ballots.
Allison,Bill,Carmen,Doug
      5,   5,     0,   0
      5,   4,     3,   0

[Allocated Score Voting: Winners — Allocated Score Voting Method (3 winners)]
 Allison
 Bill
 Carmen

Why "their tests, our engine" is worth more than agreement on our own cases¶

A method's own test suite encodes what its authors meant, including the edge cases they thought to guard. Reproducing it in an independent implementation is a stronger claim than agreeing on cases we designed ourselves — we cannot accidentally test only the behaviours we happened to implement.

It also cuts the other way, and should be said: these fixtures are BetterVoting's, so they test what BetterVoting thought to test. Agreement here does not mean the two engines agree everywhere — only that they agree on the method's specified behaviour, including its documented edge cases. Where they might still part company is exactly what the Alabama paradox work explores.

Run them yourself¶

.venv/bin/python STARVote_LH_tabulation_engine/starvote_larry_hastings.py 03_STAR_PR/03_Criteria/bv_fixture_crosscheck/cases/bkk2gxj_fractional_surplus.yaml

Case	Seats	Files
Fractional surplus	2	page · yaml · frozen BV export
Fewer voters than seats	3	page · yaml · frozen BV export