ADR-026 — Negative marking, per evaluation, with the total floored at 0¶

Status¶

Accepted (2026-09-25, issue #130, with @quiz/domain/mcqScore (negativeMarking), @quiz/domain/grade (attemptTotal, overridePointsRange), @quiz/domain/evaluationConfig (negativeMarkingOn, scoresNegatively) and the evaluation setting settings.negativeMarking). No migration.

Extended by ADR-036 (2026-09-29): the categorize type is a choice question too — placing a card is a choice among the columns — and negative marking scores it with its own rule (categorizeFraction). "Every choice question" below now means mcq and categorize (NEGATIVE_MARKING_TYPES).

Amended by ADR-052 (2026-09-30): a BONUS item is scored with the same negative rule, its final score floored at 0 (itemPoints); the student is told as on any other item; a correction by hand stays within [0, max] (scoresNegatively(type, on, bonus)). §3's attempt-level floor is unchanged: one attemptTotal, bonus items included.

Amended 2026-10-09: the Rollback section is removed (the runbook owns operational procedures).

Context¶

The first MCQ configuration (docs/spec/04 §4.4, v1) carried a penalty factor and an allowNegative flag per question. The v2 configuration replaced them with five named policies, every one floored at 0 — "a question is never worth less than not answering it" — and forced a single-answer question to all_or_nothing. The consequence, raised by a teacher in #130: guessing is always free. symmetric has a zero expectation for a random tick only before its floor; after it, a guess has a positive expectation, and a single-answer question cannot penalise a guess at all.

The teacher wants a mode where guessing costs points, so that students leave a question blank rather than tick at random — which is also what gives the "I won't answer" and "Clear" actions of #89 their meaning.

Decision¶

1. A setting of the evaluation, not a sixth policy¶

settings.negativeMarking: boolean (optional in the JSON column, absent = off). When it is on, EVERY choice question of the evaluation is scored with the negative rule, whatever its own policy or the evaluation's mcqPolicy says, single answer included. Mixing penalised and unpenalised questions in one sitting would leave the student guessing which is which; one evaluation, one rule, stated once in the waiting room and on each question.

It is structural like the rest of settings: frozen while the evaluation runs and once an attempt exists (configLock, F-EVAL-03). A poll refuses it (422 negative_marking_not_allowed) — a poll is tallied, not graded — and negativeMarkingOn reads it as off on a poll whatever the row says.

2. The rule¶

With C correct choices, W distractors, c and w of them ticked:

f = c/C - w/W        (W = 0: f = c/C), not floored, in [-1, 1]

For a single-answer question (C = 1, W = n - 1) this is +1 for the key and -1/(n - 1) for a distractor; for a multiple-answer one it is symmetric without its floor. No answer — nothing ticked, "I won't answer", cleared — is 0. Random guessing has an expected value of exactly 0, which mcqScore.test.ts checks by enumerating every key and every selection up to six choices. The fraction is multiplied by the item's points and rounded to the hundredth like every grade.

It travels to the grader as GradeContext.defaults.mcq.negativeMarking (gradeDefaults), so the grading pass, the per-attempt grading of a retake, the immediate feedback, the teacher preview and the regrade (F-GRADE-06) all apply it without a code path of their own. gradings.details records negativeMarking: true beside the question's resolved policy.

2b. A single-answer question takes one choice¶

Unfloored, c/C - w/W would pay a crafted single answer holding the key AND a distractor 1 - 1/(n - 1) — better than an honest guess. Two gates: the answer write refuses it (answerMisfit of the type, 422 answer_invalid, beside the schema check), and mcqFraction scores several selections on a single question as a wrong answer, -1/(n - 1) under negative marking and 0 otherwise, for a row written before the gate.

3. Negative points per question, a total floored at 0 in ONE function¶

Per-question points are stored and shown signed: the grade table, the CSV, the release snapshot, the grading panel, the student's feedback. The total of an attempt is attemptTotal(points) — the sum, rounded, floored at 0 — and it is the ONLY way the API sums points: the grade table (and therefore the CSV, the release snapshot, the statistics of grades), the student's feedback, the result cards, the student home, the teacher preview, and the tallies behind the kept attempt of a retake (ADR-025) and the score shown between attempts. The grade is computed from that floored total. The grading panel's running total of a student uses the same function. Outside negative marking every item scores in [0, max] and the floor changes nothing.

For the kept attempt, the consequence is deliberate: two attempts whose sums are -1 and -5 are both worth 0, and under best the tie goes to the latest, as for any tie. What counts is what the student is credited with, not how far below zero a sum went.

4. The student is told before answering¶

• the waiting room adds a fourth rule ("Wrong answers cost points", from LobbyView.negativeMarking);
• every choice question says it on the question itself: toStudent receives the same evaluation defaults (StudentView.defaults) and publishes ONE flag, negativeMarking: true, and nothing else of the scoring — the question's policy still never reaches a student. An exercise without a waiting room has only this line, which is why it is there.

5. Manual corrections¶

F-GRADE-05 overrides (and adjusted validations) take [0, max], or [-max, max] for a choice question of an evaluation with negative marking: the range the rule itself can reach. The routes now enforce the range (422 points_out_of_range); before, only the screen did. The panel reads the lower bound from the same domain function (overridePointsRange).

6. The CSV writes numbers as numbers¶

The formula guard of the CSV prefixed any field starting with - with a quote, which would have turned -1 into the text '-1. Numbers the export writes itself skip the guard; names and emails keep it.

Consequences¶

• Existing evaluations are unaffected: the field is absent, which reads as off, and no stored grading changes. No migration.
• The per-question success rate may be negative for a question under negative marking (the class's mean fraction). The API and the CSV carry the raw value; the screens (results by question, live dashboard) show it clamped to [0, 100 %] through displayedRate.
• docs/spec/04 §4.4 is rewritten to the v2 policies and this mode; the v1 penalty / allowNegative are gone for good (the v1 → v2 migration of packages/qt-mcq still drops them).

Alternatives considered¶

• A sixth question policy penalized. Rejected: the policy is resolved per question, so one evaluation could mix penalised and free questions, and the single-answer rule (always all or nothing) would need an exception in the resolution anyway. The issue itself asks for a per-evaluation mode.
• A penalty factor (v1's penalty). Rejected: the zero expectation is the whole point, and it holds for exactly one factor per question shape; a free factor is a knob nobody can reason about during an exam.
• Floor per question and not per evaluation. That is what the five policies already do; it is precisely what makes guessing free.
• Floor the total in each screen. Rejected: the grade table, the cards and the kept attempt would each need to remember it, and one forgotten place is a student reading two different totals.