Does it matter when voters don't use the whole 0–5 scale?¶

Level: 301 · deep dive

A measured answer, from real ballots. In Equal Vote's public US 2024 Presidential poll — 2,772 ballots, 8 candidates — 14.1% of STAR ballots never used both ends of the scale. This page reproduces that figure exactly, then tests whether it changed anything. It did not, and the reason is specific and checkable rather than reassuring.

▶ Live on BetterVoting: vote · results ↗ (election pres24)

▶ The full count: the generated case page ↗ (matrix, score distribution, every round) · _tabulated mirror ↗ (4,649 lines)

▶ The data: the 2,772 ballots as an engine case pres24_star_range_usage.yaml · rerun every figure on this page: analyze_range_usage.py

The number checks out — 14.1%, not a rounding of something else¶

Counting a blank as a zero (which is what the ballot instructions say and what the count does), a ballot "used the full range" if it gave someone a 5 and left someone at an effective 0:

	ballots	share
Used the full range	2,380	85.9%
Did not	392	14.1%

That reproduces the 86 / 14 split exactly. Worth noting why it reproduces: the naive version of this metric — looking for a literal 0 keystroke — gives 63.1%, because 43.5% of voters expressed their zero by leaving a candidate blank instead of clicking 0. Those two ballots are identical to the count. Any future scan of scale usage has to treat blank and 0 as the same thing, or it will invent a 23-point problem that doesn't exist.

What the 392 are actually missing: the top, not the bottom¶

This is the part that reframes the question.

Of the 392	ballots	share of the 392
Missing a 5 — nobody earned full marks	352	90%
Missing a bottom — everyone scored ≥ 1	40	10%

And the highest score they did give:

Top score on the ballot	0	1	2	3	4	5
ballots	3	13	11	75	250	40

The dominant behavior — 250 ballots, nearly two-thirds of the group — is "my favorite gets a 4." That is not a compressed or confused ballot. It is a voter grading on an absolute scale and declining to award full marks to anyone in the 2024 presidential field. The repo already has a name and a page for it: Compressed Middle, one of the thirteen legal voting styles, whose opening line is "nobody here is a 5." Only 3 ballots of the 2,772 scored nothing at all.

They are also not the low-effort ballots. Distinct score levels used per ballot:

	4+ levels used	mean levels
Not full range (392)	67.6%	3.80
Full range (2,380)	60.9%	3.90

The group flagged as a problem differentiates more candidates than the electorate at large. A bullet vote uses two levels and passes the full-range test; a 4-3-2-1 ballot uses four and fails it. "Used both endpoints" is not a measure of expressiveness, and it should not be reported as one.

Did it change the outcome? No — and not by luck¶

Four ways of asking, including two that are deliberately unfair to the compressed ballots:

Treatment of the 392	2nd finalist	Winner
As cast (baseline)	Cornell West	Kamala Harris
Stretched to a full 0–5 range	Cornell West	Kamala Harris
Discarded entirely	Cornell West	Kamala Harris
Every ballot normalized	Cornell West	Kamala Harris

The reason is structural, not lucky: the scoring-round leader is also the Condorcet winner — Harris beats all seven rivals head-to-head, by margins from 1,604–577 to 1,895–316. So whoever takes the second finalist slot, the runoff returns the same winner. Rescaling ballots can only reshuffle who comes second; it cannot reach the result. A bootstrap of 2,000 resamples returns Harris 2,000 / 2,000 times. And one more layer of the same point: the poll ran the same electorate through four ballots — Choose-One, RCV-IRV, Approval and STAR — and all four elected Harris. A result this robust is not one that a 14% change in scale usage could reach.

Where the real fragility is — and it isn't scale usage¶

Gemini's caveat, quoted in the thread, was that compression rarely matters "unless a race features an extremely narrow gap between the 2nd and 3rd place candidates." This poll is that race. West 4,262 vs Stein 4,197 — a 65-point gap, 1.5% of second place. The escape clause was satisfied and went unnoticed.

The conclusion survives anyway, for two reasons the caveat didn't reach:

The second slot is indeterminate from plain sampling noise, not from compression. In the bootstrap, West takes it 79% of the time and Stein 21%. That coin-flip exists whether or not anyone compressed anything.
Compression was not the thumb on the scale. Stretching those 392 ballots widens the 2nd–3rd gap from 65 to 78 — it makes second place more secure, not less. Compression here was roughly neutral across candidates, because the voters doing it were not concentrated in one camp.

So the honest verdict is stronger than "low to moderate concern": for this election the winner is provably invariant, and the one genuinely wobbly number is wobbly for a reason a full-scale prompt would not fix.

The metric that does measure lost power: Equal Support¶

A ballot's influence in the automatic runoff is binary — you either prefer one finalist or you don't. Scale usage is irrelevant there; Equal Support is the number that counts.

	expressed a runoff preference	Equal Support
Not full range (392)	81.9%	71
Full range (2,380)	78.2%	520

The flagged ballots carried more runoff weight than the average ballot. The 520 Equal Support ballots in the compliant group are mostly sincere — voters who rated both eventual finalists 0, having backed a candidate on the other side of the field. Nothing is wrong with those either, but it does mean the two metrics point in opposite directions: if you want to report one number about wasted voting power, report Equal Support, not scale usage.

On the suggested "are you sure?" prompt¶

The data supports the education framing over the validation framing, with one caution worth stating plainly:

A prompt nudging voters toward 0 and 5 is a nudge toward strategic maximization — awkward for a method whose central claim is that you never have to exaggerate. It also lands asymmetrically: it would alter the ballots of one identifiable 14% and nobody else's. Tolerable in a casual poll; in a certified public election, an administrator-side nudge that systematically moves one subgroup's ballots is the kind of thing that invites challenge.
The unambiguous case is different. A voter who left candidates blank and has no top score may have abandoned the form partway. Prompting on an incomplete ballot is a genuine error check; prompting on a complete but modest one second-guesses a sincere opinion.
A "your ballot as counted" review screen does the educational job without telling anyone what to think — it shows blanks resolving to 0, which is the misconception actually worth fixing (43.5% of these voters used blanks as zeros, and a scan that didn't know that mismeasured the poll by 23 points).

The count¶

Verified three ways: this repo's engine, BetterVoting's own tabulation, and the independent script above. All agree on every score, every five-star count, and every pairwise total.

Abridged for the lesson — this is an excerpt, not verbatim engine output

Scoring Round
   Kamala Harris (D)         -- 8250 -- First place
   Cornell West (I)          -- 4272 -- Second place
   Jill Stein (G)            -- 4207
   Chase Oliver (L)          -- 3817
   Donald J. Trump (R)       -- 3790
   Robert F. Kennedy Jr. (I) -- 3454
   Claudia De la Cruz (S)    -- 3415
   Randall Terry (C)         -- 1748
 Kamala Harris (D) and Cornell West (I) advance.

Automatic Runoff Round
   Kamala Harris (D)         -- 1604 -- First place
   Cornell West (I)          --  577
   Equal Support             --  591
 Kamala Harris (D) wins.
   Voters with a preference: 2181 of 2772 (591 Equal Support).
   Kamala Harris (D) 1604 (74%) vs Cornell West (I) 577 (26%); majority = 1091.

Want the whole count? The scoring round above is an excerpt. The full report — pairwise matrix, score distribution, every candidate's five-star count, all 2,772 ballots echoed — is on the generated case page, mirrored verbatim in pres24_star_range_usage_tabulated.txt.

One reconciliation note, so the two engines can be compared line by line. BetterVoting reports each candidate's score 10 points lower than the engine above — 8,240 vs 8,250, and the same −10 on all eight. The cause is benign, already documented in this repo, and now confirmed at scale: 7 ballots score every candidate identically (three all-0s, three all-3s, one all-1s), and BetterVoting treats a ballot with no preference at all as an abstention, excluding it from the score totals — the same divergence the abstain, blank & zero handling set isolates on small constructed cases (#884). This is that divergence appearing in 2,772 real ballots, where it moves every score by the same 10 points and decides nothing. Those 7 ballots contribute exactly 10 points to every candidate, so they cannot change any ranking, any pairwise comparison, or the winner. Excluding them, the two engines match to the point on all eight candidates and all eight five-star counts.

Reproduce it¶

The 13 MB export is deliberately not committed — one command regenerates it, and the ballots live here in engine form at 50 KB.

uv run STARVote_LH_tabulation_engine/tools_adam/fetch_bv_export.py pres24 -o /tmp/pres24.json

python3 01_STAR/04_Real_Elections/pres24_range_usage/analyze_range_usage.py /tmp/pres24.json

.venv/bin/python STARVote_LH_tabulation_engine/starvote_larry_hastings.py 01_STAR/04_Real_Elections/pres24_range_usage/cases/pres24_star_range_usage.yaml