STAR Is Summable — Add Up Precinct Totals¶
One line: a method is summable (precinct-summable) if you can get the final result by adding up independent precinct totals. STAR is summable, which makes it precinct-auditable and gives meaningful early/partial results.
→ Cross-method topic hub: Summability (STAR / Ranked Robin / IRV side by side). The method that is not summable is RCV-IRV — IRV's lack of summability. Glossary: summability.
Why STAR is summable¶
STAR's whole count reduces to sums:
- The scoring round is just each candidate's total stars — add the precinct totals together.
- The runoff uses the pairwise (For / Equal / Against) matrix: for every pair of candidates, how many ballots scored A over B, equal, or B over A. Those counts add across precincts too.
So each precinct can publish a small fixed-size table, and the statewide result is simply their sum. That makes STAR precinct-auditable, lets observers verify locally, and gives partial counts that actually mean something.
Worked example — two districts, subtotals that add up¶
The mirror of IRV's non-summable example. Same setup, opposite result — run summability_demo/ (three trees: Maple, Oak, Pine). The two districts even have different winners (Maple in A, Oak in B — district B is a runoff reversal), so the merge is genuinely non-trivial:
Score totals add:
| Maple | Oak | Pine | |
|---|---|---|---|
| District A | 10 | 9 | 6 |
| District B | 5 | 10 | 12 |
| Sum | 15 | 19 | 18 |
That sum is the combined election's score round (Oak 19, Pine 18, Maple 15 → Oak & Pine advance).
The pairwise matrix adds too — e.g. the decisive Oak-vs-Pine head-to-head:
District A: Oak 2 – Pine 1
District B: Oak 2 – Pine 1
Sum: Oak 4 – Pine 2 → Oak wins the runoff → Oak wins
Every number the statewide result needs — score totals and the For/Equal/Against matrix — is just the sum of the precinct tables. No recount, no pooling ballots, no central elimination order: each precinct publishes a fixed-size table (C scores + a C×C matrix) and anyone can add them and check the winner.
Verifiable, not just summable¶
Because the whole count is addition, STAR is hand-countable, runs on existing optical-scan equipment, and supports paper-ballot recounts and risk-limiting audits — a precinct can verify its own contribution. Independent confirmation that the engine's pairwise/runoff math (the summable artifact) is correct comes from the pref_voting cross-check — a second, independent engine agrees on every example.
External references (advocacy, but the summability math is standard): Is STAR Voting Precinct Summable? (starvoting.org) · STAR Voting security & audits · STAR Voting — Equal Vote Coalition.
The nuance — it's about the tabulation, not the ballot¶
Summability is a property of the count, not the ballot. A ranked ballot counted by a Condorcet method (Ranked Robin) is also summable, via the very same pairwise matrix. So "ranked ballots aren't summable" is wrong — it's IRV's elimination count specifically that isn't (see the IRV page). More on keeping the terms straight: Tips — Terminology: RCV vs IRV vs RCV-IRV (and friends).