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Unorthodox STAR — running the runoff on a scale wider than 0–5

Voting 301 · advanced / "what if" — the scale is a parameter, not a rule

STAR ballots are 0–5 everywhere you'll meet them — BetterVoting, the Equal Vote Coalition, every case in this repo. But nothing in the STAR algorithm requires it. The "5" is a design convention, and the underlying engine treats the scale as a plain parameter. This page is the "what if": run STAR on 0–9, 0–10, even 0–99, see that it works, understand what actually changes — and learn how to make LH do it.

This is deliberately non-standard. Don't ship a 0–10 STAR election and call it "STAR" without saying so — the point here is understanding, not a recommendation.

Why 0–5 in the first place?

The 0–5 range is a usability choice, not a mathematical one. It maps onto the five-star rating everyone already knows (movies, rideshares) plus an explicit 0, giving six levels — enough to express order and intensity without asking a voter to agonize over "is this a 7 or an 8 out of 100?" Equal Vote settled on it because it's expressive enough to matter and simple enough to fill out fast, with low ballot-error rates. It's a sweet spot, not a boundary.

And the sweet spot isn't only a voting-reform hunch. Wherever judgments get collected and averaged at scale — school and university grading, customer quality ratings, political opinion scales like the German Politbarometer — the discrete scale that gets chosen lands on roughly five or six values, which Hillinger reads as a practical ceiling on how finely people discriminate along a cardinal scale (the full roster, and where the figure comes from). Three independent domains converging on the same resolution is a better argument for 0–5 than familiarity alone. Worth knowing which way it cuts, though: the same section records that Hillinger himself would hand a general electorate a three-level ballot and reserve five levels for expert committees — so the convergence supports "about this many levels," not "exactly six."

One subtle consequence of six levels. With only six distinct scores (0, 1, 2, 3, 4, 5), a voter can put at most six candidates in a strictly different order. With seven or more candidates, some must share a score — so a 0–5 ballot can't encode every strict ordering that a ranked ballot can. This is the one narrow sense in which a ranked ballot out-expresses a 0–5 STAR ballot: Clelland (2023) puts it precisely — STAR offers a greater range of expression than IRV "unless there are more than 6 candidates." (Widen the scale and the threshold moves up: 0–9 strictly orders ten.) It rarely bites in practice — few single-winner races have seven serious contenders, and STAR trades this for what ranks can never capture, strength of support (and the runoff, being scale-agnostic, doesn't care about it at all).

What the scale changes — and what it doesn't

STAR has two rounds, and they react to the scale very differently:

  • The automatic runoff is scale-agnostic. The runoff asks one question per ballot: which finalist did you score higher? That's a preference, and a preference doesn't care whether the gap was 5-vs-4 or 50-vs-40. Widen the scale and the runoff step is untouched.
  • The scoring round is where granularity bites. Who the top two finalists are depends on total scores, and a wider scale gives intensity more room to move those totals. A candidate with a few passionate max-scores can climb past a broadly-but-mildly-liked rival when the max is 10 that they couldn't reach when the max was 5. So a wider scale can change who advances — and therefore, sometimes, who wins. That's exactly the effect worked in Scale granularity can flip the winner.

So "unorthodox STAR" isn't just cosmetic: it's a real knob that trades more expressiveness for more room to exaggerate and a less familiar ballot.

Worked example — STAR on a 0–10 ballot

Take the ten 0–10 ballots from the Range/Score worked comparison (Sullivan's Example 5.2) and run them through STAR instead of pure Range — Larry Hastings' engine at maximum_score=10:

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   C -- 70 -- First place
   A -- 61 -- Second place
   D -- 58
   B -- 47
 C and A advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   C             -- 6 -- First place
   A             -- 3
   No Preference -- 1
 C wins.

[STAR Voting: Winner]
 C

C leads the scoring round at 70, A is second at 61, and in the runoff C is preferred 6–3 (one voter scored them equally). Winner: C — the same candidate pure Range and median-Range pick on this electorate. The runoff simply confirmed the score leader; the wide scale changed none of that here. (For a case where scale does flip the outcome, see the granularity page linked above.)

How to make LH do it

The catch: this repo's teaching CLI (starvote_larry_hastings.py) deliberately rejects scores above 5 — a guardrail (validate_star_rows(..., max_score=5)) that keeps YAML demos on the 0–5 convention and catches typos. That cap is ours, not the engine's. Larry Hastings' underlying starvote library takes the scale as an argument, so you run the wide-scale election by calling it directly:

import starvote

ballots = [
    {"A": 10, "B": 0,  "C": 0,  "D": 0},
    {"A": 5,  "B": 7,  "C": 10, "D": 8},
    {"A": 0,  "B": 4,  "C": 10, "D": 8},
    {"A": 7,  "B": 7,  "C": 1,  "D": 10},
    {"A": 7,  "B": 9,  "C": 7,  "D": 4},
    {"A": 6,  "B": 6,  "C": 9,  "D": 4},
    {"A": 8,  "B": 3,  "C": 10, "D": 3},
    {"A": 0,  "B": 8,  "C": 5,  "D": 5},
    {"A": 8,  "B": 0,  "C": 10, "D": 6},
    {"A": 10, "B": 3,  "C": 8,  "D": 10},
]

winner = starvote.election(starvote.star, ballots, maximum_score=10)
# → ['C']

# add verbosity=1 for the round-by-round tabulation shown above:
starvote.election(starvote.star, ballots, maximum_score=10, verbosity=1)

That's the whole trick — maximum_score=N for any N. (If you'd rather drive it through the YAML CLI, you'd raise or remove the max_score=5 argument in validate_star_rows; but the library call above is cleaner for a one-off experiment and doesn't touch the guardrail everyone else relies on.) The same parameter is how the repo's divergence tools (tools_adam/find_divergence.py) already sweep across scales, and how the Range engine tabulates 0–10 ballots natively.

So should you widen the scale?

Rarely, and only on purpose. The honest ledger:

  • For a wider scale: more expressive; the median variant of Score becomes more meaningful; matches an existing 0–10 / 0–100 culture (some surveys, sports scoring).
  • Against: a less familiar ballot (higher error rates, slower to fill); more room for strategic min/max exaggeration, which pulls a score ballot back toward Approval; and it can shift who the finalists are in ways voters don't intuit (granularity effects). STAR's runoff blunts the strategy problem, but a wide scale hands some of that advantage back.

0–5 is where Equal Vote landed for good reasons. The value of this exercise isn't a better STAR — it's seeing exactly which part of STAR the scale touches (the finalists) and which part it can't (the runoff's majority test).

Where this fits

Cross-references: - STAR — start here · the scoring round · the automatic runoff - Range / Score voting · the fidelity ladder - Curriculum 301