#1035 — the runoff zero denominator: fix, tests, before/after¶

Fix written 2026-08-19. Branch fix/1035-runoff-zero-denominator off origin/main @ 454a38ae, commit 47d241a4. Local only — not pushed, no PR, nothing posted upstream.

Root cause was established and posted upstream on 2026-08-02 — see 1035-nan-root-cause-comment-posted.md. This page is the fix that follows from it. The browser baseline it has to beat is BV2264.

This is R2 from ../analysis/flat-scores-abstention/04-options.md — the prerequisite that has to land before anyone touches the abstention rule, because that rule is currently the only thing keeping this bug's trigger set narrow.

The defect¶

A STAR runoff's denominator is finalistVotes — the number of ballots that preferred one finalist over the other. It is zero whenever every counted ballot rates the two finalists equally, and that is not an exotic state: it needs no tie in the scoring round and no abstention. Three ballots of Ann 5 / Ben 5 / Cal 0 do it, and so does a mixed set like 5,5,1 / 4,4,0 / 3,3,2.

Crucially the ballots are counted — nTallyVotes = 3 — so Results.tsx:485's nTallyVotes == 0 short-circuit does not fire and the runoff widgets render against a zero denominator.

Two surfaces, two different symptoms, which is why the first prediction about this bug was half wrong:

Surface	Symptom before the fix
Runoff Table, "% Between Finalists"	`NaN%` on both finalist rows, and a total row asserting `100%` of nothing
Runoff pie chart	Blank circle. Recharts draws no sectors when every value is 0, so its label callback never runs and no `NaN` is ever printed — the chart is simply empty, with no explanation

The bar view was already safe: ResultsBarChart.tsx:53 does percentDenominator = Math.max(1, percentDenominator). So the guard exists in the codebase already, on one of the three views. The neighbouring noPreferencePercentage footnote is guarded too (STARResultSummaryWidget.tsx:54-56). The table and the pie were the two that were missed.

Every affected path, file:line¶

Line numbers before are on origin/main @ 454a38ae; after are on 47d241a4.

#	Path	Before	After	What happens there
1	`packages/frontend/src/components/Election/Results/STAR/STARDetailedResults.tsx`	`:69`	`:74`	`i == 2 ? '' : formatPercent(c.runoffVotes / finalistVotes)` — the `0/0`. Unchanged; now yields `—` because `formatPercent` guards
2	`packages/frontend/src/components/util.tsx`	`:89-92`	`:92-101`	`formatPercent` had no guard for a non-finite argument, so `NaN` reached `Math.round` and printed `NaN%`
3	`packages/frontend/src/components/Election/Results/STAR/STARDetailedResults.tsx`	`:71`	`:76`	The total row's `'% Between Finalists'` cell is a hard-coded `'100%'`. `formatPercent` never sees it, so guarding `formatPercent` alone leaves the table claiming 100% of a zero denominator
4	`packages/frontend/src/components/Election/Results/components/ResultsPieChart.tsx`	`:40`, `:14`	`:23`, `:72-81`	Recharts' `percent = value / total`. With `total = 0` it renders no `<Cell>`s, so `:40` never executes — the blank chart. Guarded now by an `isEmpty` check before the chart is built
5	`packages/frontend/src/components/Election/Results/STAR/STARResultSummaryWidget.tsx`	`:48-51`, `:80`	`:80`	Builds `pieData` from the two finalists only, so the pie's total is `finalistVotes`. Now passes the STAR-specific `emptyMessage`
6	`packages/frontend/src/i18n/en.yaml`	—	`:241-243`, `:309-311`	Two new keys: `results.chart_no_data`, `results.star.runoff_no_preference_chart`

Backend: nothing to fix. The tabulator emits counts, not percentages. Star.ts computes votesPreferredOver and never divides; the only percent() in packages/backend/src/Tabulators/ is AllocatedScore.ts:217, and its one zero-denominator path (weight_on_split == 0) was already guarded at :157 by the merged no-ballots fix. The zero denominator is created in the frontend, from two backend integers that are both correctly 0.

Paths deliberately not changed:

The bar view's majority marker still sits at 0 with the legend "majority threshold (½ of voters with preference)". That is arithmetically true (half of zero) and is not a NaN; whether it should be drawn at all when there are no voters with a preference belongs to #1471, which is about that marker's denominator generally.
The '% Runoff Votes' column (STARDetailedResults.tsx:68/:73) divides by nTallyVotes, which Results.tsx:524 guarantees is >= 1 before the STAR viewer mounts. It was never a NaN and is untouched.

The fix¶

Five files, 84 insertions. The whole of it:

formatPercent returns a placeholder for a non-finite input rather than NaN%. This is the one that covers path 1, and as a side effect it nets the other x/0 call sites nobody has reported yet — VoterProfileWidget.tsx:155 (numBullets/totalTopScored) and VoterErrorStatsWidget.tsx:83-93 (/totalVotes).
The total row is guarded explicitly, because it is a literal string that never passes through formatPercent.
ResultsPieChart renders a message instead of an empty circle when its slices sum to zero, in a box of the same 250px height so toggling bar↔pie does not shift the layout. New optional emptyMessage prop; the generic i18n fallback means the component's other caller (VoterIntentWidget.tsx:130) stops rendering a silent empty circle too.
STARResultSummaryWidget passes the STAR-specific wording.

Copy — needs review, and the test does not assert on it¶

Two strings were added to en.yaml. Neither is approved copy:

Key	Current text
`results.star.runoff_no_preference_chart`	No votes to chart — every counted ballot rated the two finalists equally.
`results.chart_no_data`	No votes to chart.

The placeholder in the table is an em dash, NO_DATA_PLACEHOLDER in util.tsx:92.

Per this repo's convention — assert on requirements, not on literal strings, when the copy is not approved — the requirement is: the runoff table must not print NaN, and the pie view must not render an empty circle with no explanation. Anything satisfying that passes. Three specific things a reviewer should decide:

— vs n/a vs an empty cell. A bare em dash reads fine sighted and says nothing to a screen reader. aria-label on the cell would fix that; ResultsTable has no such affordance today, so it was not added.
The pie message duplicates its own footnote. In the degenerate case the footnote below already reads "100.0% of voters expressed no preference between the two finalists." Saying it twice may be worse than saying it once — but the footnote is below the chart area, and an unexplained empty circle above it is the actual complaint.
Only en.yaml gained the keys. i18n.ts:24 sets fallbackLng: 'en', so es/pl/pt-BR fall back to English rather than showing the raw key.

Before and after¶

Produced by ../analysis/flat-scores-abstention/probe/nan-fix-verify.ts, run inside the branch worktree. formatPercent in the "after" column is the shipped function — the probe reads util.tsx at run time, extracts the function's source and evaluates it, so it cannot drift from the file. The tally is the real Star(). The two remaining expressions (the total-row cell and the pie's isEmpty) are one line each, transcribed verbatim.

A) Degenerate — three ballots `{A:5, B:5, C:0}` (the BV2264 election)¶

nTallyVotes = 3, nAbstentions = 0, finalists A and B, each preferred over the other 0 times, finalistVotes = 0.

Runoff Table, "% Between Finalists"

Row	Value	Before	After
A	`0/0`	`NaN%`	`—`
B	`0/0`	`NaN%`	`—`
Total	—	`100%`	`—`

Runoff Table, "% Runoff Votes" (denominator nTallyVotes = 3) — 0%, 0% before and after. Unchanged.

Runoff pie chart — total 0. Before: recharts draws no sectors, blank circle, no label, no explanation. After: the explanatory message replaces the chart.

Winner: A before and after. Scores A:15 B:15 C:0 before and after.

B) Degenerate — mixed scores, preferences cancel¶

{A:5,B:5,C:1} / {A:4,B:4,C:0} / {A:3,B:3,C:2}. Identical outcome to (A): NaN% → —, 100% total → —, blank pie → message. Winner A, scores A:12 B:12 C:3, unchanged. This is the set that shows the bug is not about a scoring-round tie.

C) Control — ordinary runoff¶

Five ballots, finalistVotes = 4, finalists B and A.

Row	Value	Before	After
B	`2/4`	`50%`	`50%`
A	`2/4`	`50%`	`50%`
Total	—	`100%`	`100%`

Pie renders, unchanged. Winner B, unchanged.

D) Control — lopsided runoff, exercises the `<1%` branch¶

201 ballots, finalistVotes = 201.

Row	Value	Before	After
A	`200/201`	`100%`	`100%`
C	`1/201`	`<1%`	`<1%`
Total	—	`100%`	`100%`

Pie renders, unchanged. Winner A, unchanged. This one matters because formatPercent's existing 0 < f && f < .01 special case is the branch most likely to be broken by a careless guard.

Test cases¶

T1 — backend unit test, added to the existing suite¶

Added to packages/backend/src/Tabulators/Star.test.ts:48, "Runoff with a zero denominator (#1035)".

Purpose — pin the condition, not the display: prove the frontend really is handed finalistVotes = 0 on a fully-counted ballot set, and lock the tally the fix must not move. It is also a tripwire for the abstention rule: if markAllEqualAsAbstention is ever changed, this ballot set moves in or out of the tally and the test says so.
Input — candidates Allison, Bill, Carmen; ballots [5,5,0] × 3.
Expected — nTallyVotes == 3; nAbstentions == 0; winner.votesPreferredOver[runnerUp] == 0; runnerUp.votesPreferredOver[winner] == 0; their sum (the denominator) == 0; both finalists score 15, Carmen 0; exactly one candidate elected.
Actual — PASS. npx jest src/Tabulators/ → 9 suites, 53 tests, all green (baseline before the change: 9 suites, 52 tests, all green).

What T1 does not do: it does not exercise the display guards. Those are frontend-only, and packages/frontend has no test harness at all — no jest config, no vitest, zero *.test.* files. Adding one would be a larger change than the fix. T2 is the substitute.

T2 — probe, the display expressions against real tabulator output¶

../analysis/flat-scores-abstention/probe/nan-fix-verify.ts.

Purpose — get a real before/after value for each render path without a React harness.
Input — the four ballot sets above, through the backend's real Star().
Expected — degenerate sets: no NaN anywhere, and the pie reports itself empty. Controls: every string identical before and after.
Actual — as expected; the tables above are its output. formatPercent's post-fix source, as extracted from util.tsx and executed:

(f) => {
  if(!Number.isFinite(f)) return "—";
  if(0 < f && f < .01) return '<1%';
  return `${Math.round(100*f)}%`
}

T3 — typecheck and lint¶

Purpose — the changed files still compile, and no new lint error is introduced.
Actual — npx tsc --noEmit in packages/frontend: clean, no output. npx eslint on the four changed frontend files reports 13 errors, all pre-existing (react/prop-types and ban-ts-comment in util.tsx, the untouched }: any) label callback in ResultsPieChart.tsx:33, an unused getEntry import in STARResultSummaryWidget.tsx:12). None sits on a changed line.

T4 — browser verification: NOT RUN¶

The BV2264 steps against a running build with this branch. Not done — see below.

No winner, tally or percentage changes¶

Stated explicitly because the neighbouring abstention argument (../analysis/flat-scores-abstention/) is contested precisely over outcome changes, and this fix must not be entangled with it.

Nothing in packages/backend changes except a test file. No tabulator source is touched. Winners, scores, pairwise counts, tie-breaks, nTallyVotes, nAbstentions and the JSON export are byte-identical.
formatPercent is identical for every finite input. The new line is if(!Number.isFinite(f)) return NO_DATA_PLACEHOLDER; ahead of the existing body — reachable only via NaN, Infinity or -Infinity, i.e. only from a zero denominator. Controls C and D confirm 50%, 100% and the <1% branch are untouched.
The total-row guard fires only on finalistVotes === 0. Strict equality on an integer sum of two counts.
The pie guard fires only when the slices sum to <= 0. Vote counts are non-negative, so that is exactly "all slices zero" — the case where recharts drew nothing anyway. No non-empty chart changes.
The bar chart is not touched at all.
The abstention rule is not touched. This fix neither widens nor narrows the trigger set; it makes the trigger set survivable, which is the whole point of doing it first.

What could not be verified¶

Marked as this repo's convention requires — these are gaps, not predictions dressed up as results.

Nothing was rendered in a browser. The rendered — in the table cell, the vertical centring of the message in the 250px box, its behaviour at 320px, and the bar↔pie toggle not shifting the layout are all read from source, not seen. BV2264's Expected after the fix section is the assertion to run; it wants the local stack on this branch (see the bv-dev skill). The one prior lesson here is directly on point: the first version of the root-cause comment predicted NaN% in the pie chart and a screenshot refuted it.
useTranslation() inside ResultsPieChart. The component previously had no i18n coupling. Both call sites sit well inside the app's i18n provider, so the hook is safe by inspection, but it has not been executed in a React tree.
The two new i18n keys have not been observed resolving. They parse (checked with js-yaml) and fallbackLng: 'en' covers the other three locales, but no rendered string was seen.
VoterIntentWidget's empty case is untested. The generic fallback now applies to it. Whether that widget can actually reach an all-zero state was not established — the change is a strict improvement over a blank circle either way, but it is a claim about a surface nobody has looked at.
No E2E run. testing/ has Playwright specs; none covers a results page, and none was run.
Not run against production data. The two degenerate ballot sets are synthetic, matching the reporter's tk476h and our 3d8qdr.

Provenance¶

Claim	How established
The condition is `finalistVotes == 0`, not a scoring-round tie	executed — `Star()` on both ballot sets, 2026-08-02 comment, re-executed here
`NaN%` in the runoff table; blank pie chart	verified in a browser 2026-08-02 — BV2264
Every affected file:line, before and after	read from source at `454a38ae` and `47d241a4`
The before/after strings in the tables above	executed — probe, with the shipped `formatPercent` extracted from `util.tsx` and evaluated
Winner / tally invariance	executed — the probe prints winner and scores per case; plus T1, plus "no backend source changed"
Bar chart already guarded; backend has no unguarded division	read from source — `ResultsBarChart.tsx:53`, `AllocatedScore.ts:157`
Tests green	executed — `npx jest src/Tabulators/`, 53/53
Anything about rendered appearance	not verified — see above

#1035 · root-cause comment · BV2264 · #1471 (the majority marker's denominator) · flat scores → abstention (why this is R2, and why it goes first) · #1484 (the other defect in this same runoff table — a backend sort key, fixed in runBlocTabulator; no file overlaps this fix, though it changes WHICH pair the table calls the finalists, and so which elections have a zero denominator)