Lot S, phase 2 : le quorum dans le moteur (ADR 0013), vu rouge puis vert

Le quorum Q (votants = pour + contre) remplace le C additif : T' = max(T, Q),
la version passe si pour ≥ ⌈B^W + ratio(T')·T'⌉, ratio la courbe des cinq crans
(M, G calé à la participation de référence, inchangé). La règle d'Yvv du 03/11
(« Ils comptent comme non ») est seule dans threshold::judged_voters. Pour
l'écran : yes_needed (le total de pour qui passe avec les contre d'aujourd'hui)
et no_needed (le total de contre qui tient les pour d'aujourd'hui, 0 si le quorum
suffit) ; passe ⇔ pour ≥ yesNeeded ⇔ contre < noNeeded, éprouvé sur une grille.
well_rated : la part tient sur ceux qui sont venus. Scale porte les quorums par
cran, UnitState le quorum propre d'un article ; p0 reste 2·vote_floor/W.

Vu rouge : sans la règle (T' = T), 9 tests échouent ; avec l'autre lecture d'un
quorum (un minimum de votants, les absents non comptés), 8 échouent, dont « un
contre n'aide jamais ». Chiffres de contrôle (W 5 707, p0 = 100/W) tenus : 9, 39,
46 au quorum ; 7, 8, 9, 9, 10 à dix votants.

Le serveur suit au commit suivant.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

crates/ld-engine/src/compose.rs

@@ -19,7 +19,8 @@
 //! - what the document would read if the well-rated, or all, proposals passed
 //!   (`preview`);
 //! - which formula a proposal is judged by (`params_for`): the level of
-//!   inertia of its unit, on the scale of its group (`inertia::Scale`).
+//!   inertia of its unit and its quorum, on the scale of its document
+//!   (`inertia::Scale`).
 
 use crate::inertia::{InertiaLevel, Scale};
 use crate::threshold::{FormulaParams, Tally, ThresholdError, evaluate};
@@ -40,6 +41,10 @@ pub struct UnitState {
     pub id: String,
     pub position: f64,
     pub inertia: InertiaLevel,
+    /// Its own quorum, set by the author of its first version before the first vote
+    /// (ADR 0013); `None`: the quorum of its level.
+    #[serde(default)]
+    pub quorum: Option<u32>,
     pub in_force: Option<VersionText>,
 }
 
@@ -84,8 +89,11 @@ pub fn voting_level(unit: &UnitState, kind: ProposalKind) -> InertiaLevel {
     }
 }
 
+/// The formula a proposal is judged by: the level it is voted at, and the quorum of its
+/// unit — its own, or that level's (a change of inertia inherits both).
 pub fn params_for(unit: &UnitState, kind: ProposalKind, scale: &Scale) -> FormulaParams {
-    scale.params(voting_level(unit, kind))
+    let level = voting_level(unit, kind);
+    scale.params(level, scale.quorum(level, unit.quorum))
 }
 
 /// A proposal that changes nothing cannot enter into force.
@@ -264,6 +272,7 @@ mod tests {
             id: id.into(),
             position,
             inertia: InertiaLevel::DEFAULT,
+            quorum: None,
             in_force: in_force.map(|b| VersionText {
                 id: format!("{id}-v"),
                 title: id.into(),
@@ -286,8 +295,9 @@ mod tests {
         }
     }
 
-    /// Monnaie libre before any median: W 5745, C 50, the reference p0 = 2C/W.
+    /// Monnaie libre before any median: W 5745, the reference p0 = 2 × 50 / W, the quorums
-    const SCALE: Scale = Scale { electorate: 5745, floor: 50.0, participation: 100.0 / 5745.0 };
+    /// 12 · 12 · 50 · 50 · 50 (ADR 0013).
+    const SCALE: Scale = Scale { electorate: 5745, participation: 100.0 / 5745.0, quorums: [12, 12, 50, 50, 50] };
 
     fn level(k: u8) -> InertiaLevel {
         InertiaLevel::new(k).expect("1 to 5")
@@ -301,12 +311,18 @@ mod tests {
     }
 
     #[test]
-    fn the_floor_holds_then_releases() {
+    fn the_quorum_holds_then_releases() {
+        // Level 3, quorum 50: under it the voters missing count as against, 39 « pour » pass.
         let units = [unit("E3", 7.0, None)];
-        let few = [prop("p1", "E3", ProposalKind::Text, "connaître", 49, 0)];
+        let few = [prop("p1", "E3", ProposalKind::Text, "connaître", 38, 0)];
         assert!(adoptions(&units, &few, &SCALE).expect("valid").is_empty());
-        let enough = [prop("p1", "E3", ProposalKind::Text, "connaître", 50, 0)];
+        let enough = [prop("p1", "E3", ProposalKind::Text, "connaître", 39, 0)];
         assert_eq!(adoptions(&units, &enough, &SCALE).expect("valid"), vec!["p1".to_string()]);
+        // Its own quorum, lower, set by its author: the same curve on fewer voters.
+        let mut own = unit("E3", 7.0, None);
+        own.quorum = Some(12);
+        let lower = [prop("p1", "E3", ProposalKind::Text, "connaître", 11, 0)];
+        assert_eq!(adoptions(&[own], &lower, &SCALE).expect("valid"), vec!["p1".to_string()]);
     }
 
     #[test]
@@ -339,7 +355,10 @@ mod tests {
             assert_eq!(voting_level(&u, kind), level(4), "inherits the level of the article");
             assert_eq!(params_for(&u, kind, &SCALE), params_for(&u, ProposalKind::Text, &SCALE));
         }
-        assert_eq!(params_for(&u, ProposalKind::Text, &SCALE).majority_pct, 60.0);
+        let p = params_for(&u, ProposalKind::Text, &SCALE);
+        assert_eq!((p.majority_pct, p.quorum), (60.0, 50), "the level, and so its quorum");
+        u.quorum = Some(20);
+        assert_eq!(params_for(&u, ProposalKind::Inertia(level(1)), &SCALE).quorum, 20, "and the article's own");
     }
 
     #[test]
@@ -358,7 +377,7 @@ mod tests {
         // The seed a minima has no vote: the first rival that reaches its threshold wins.
         let rival = [prop("r", "E1", ProposalKind::Text, "unicité reformulée", 50, 0)];
         assert_eq!(adoptions(&units, &rival, &SCALE).expect("valid"), vec!["r".to_string()]);
-        // A version in force by vote, margin 60 − 58 = 2: a rival at 55 (margin 55 − 54 = 1) waits.
+        // A version in force by vote, margin 60 − 47 = 13: a rival at 55 (margin 55 − 43 = 12) waits.
         if let Some(v) = units[0].in_force.as_mut() {
             v.tally = Tally { for_votes: 60, against: 0 };
         }

crates/ld-engine/src/inertia.rs

@@ -5,20 +5,25 @@
 //! médiane aux votes du groupe » — the scale chosen is « calée sur la
 //! participation ».
 //!
-//! The formula stays the Ğ1 one (`threshold`); only M and G depend on the
+//! The formula stays the Ğ1 one (`threshold`); M, G and the quorum Q depend on
-//! level k:
+//! the level k:
 //!
 //! - M_k, the majority at full participation: 50, 50, 55, 60, 66 %;
-//! - s_k, the share of *for* votes asked **beyond C** at the group's usual
+//! - s_k, the share of *for* votes asked of the voters at the group's usual
 //!   participation p̃: 60, 67, 75, 83, 90 %;
 //! - G_k follows from `s_k = M_k + (1 − M_k)(1 − p̃^G_k)`:
-//!   `G_k = ln(1 − (s_k − M_k)/(1 − M_k)) / ln(p̃)`.
+//!   `G_k = ln(1 − (s_k − M_k)/(1 − M_k)) / ln(p̃)`;
+//! - Q_k, the quorum of the level, set by the document (Monnaie libre: 12, 12,
+//!   50, 50, 50; the test group: 1 everywhere — ADR 0013); an article may hold its
+//!   own, set by its author before the first vote (`Scale::quorum`).
 //!
 //! p̃ is the median number of voters on the group's proposals, over W
 //! (`Participation`). Until the group has voted on enough proposals, a
-//! reference `p0 = 2C/W` stands in. Both are kept within [1 %, 50 %]: ln(p̃)
+//! reference `p0 = 2Q₀/W` stands in, Q₀ the document's reference quorum (its
-//! stays negative and finite, so G is finite and positive, and the threshold
+//! `vote_floor`, never an article's quorum: an author who lowers his would move
-//! rises with the level and relaxes toward M as participation grows.
+//! the curve of everyone). Both are kept within [1 %, 50 %]: ln(p̃) stays
+//! negative and finite, so G is finite and positive, and the threshold rises
+//! with the level and relaxes toward M as participation grows.
 
 use crate::threshold::{Evaluation, FormulaParams, Tally, ThresholdError, evaluate};
 use serde::de::Error as _;
@@ -57,7 +62,7 @@ impl InertiaLevel {
         MAJORITY_PCT[self.index()]
     }
 
-    /// s_k, in percent: the share of *for* asked beyond C at the usual participation.
+    /// s_k, in percent: the share of *for* asked at the usual participation.
     pub fn share_pct(self) -> f64 {
         SHARE_PCT[self.index()]
     }
@@ -115,7 +120,7 @@ impl<'de> Deserialize<'de> for InertiaLevel {
 pub enum ParticipationSource {
     /// The median of the group's voted proposals.
     Median,
-    /// Too few voted proposals yet: `p0 = 2C/W`.
+    /// Too few voted proposals yet: `p0 = 2Q₀/W`, Q₀ the document's reference quorum.
     Reference,
 }
 
@@ -140,18 +145,19 @@ impl Participation {
     pub const LOWEST: f64 = 0.01;
     pub const HIGHEST: f64 = 0.5;
 
-    /// `2C/W`, before the bounds: the floor twice over, a participation the
+    /// `2Q₀/W`, before the bounds: the reference quorum of the document twice
-    /// group must reach anyway for C to leave room to the majority.
+    /// over (`documents.vote_floor`: 50 in Monnaie libre, 100 voters). It never
-    pub fn reference_ratio(electorate: u32, floor: f64) -> f64 {
+    /// rests on an article's quorum, which its author may lower (ADR 0013).
-        2.0 * floor.max(0.0) / f64::from(electorate.max(1))
+    pub fn reference_ratio(electorate: u32, reference_quorum: f64) -> f64 {
+        2.0 * reference_quorum.max(0.0) / f64::from(electorate.max(1))
     }
 
     /// p̃ from what was measured: the median when it rests on enough proposals,
     /// the reference otherwise; brought back within the bounds.
-    pub fn of(electorate: u32, floor: f64, median: Option<f64>, sample: u32) -> Self {
+    pub fn of(electorate: u32, reference_quorum: f64, median: Option<f64>, sample: u32) -> Self {
         let (raw, source) = match median {
             Some(m) if sample >= Self::MIN_SAMPLE => (m / f64::from(electorate.max(1)), ParticipationSource::Median),
-            _ => (Self::reference_ratio(electorate, floor), ParticipationSource::Reference),
+            _ => (Self::reference_ratio(electorate, reference_quorum), ParticipationSource::Reference),
         };
         let ratio = bounded(raw);
         Self { ratio, source, sample, median, bounded: ratio != raw }
@@ -190,35 +196,44 @@ pub fn gradient(level: InertiaLevel, participation: f64) -> f64 {
     (1.0 - (s - m) / (1.0 - m)).ln() / bounded(participation).ln()
 }
 
-/// What the votes of a group are judged by: its electorate W, its floor C and
+/// What the votes of a document are judged by: its electorate W, its usual
-/// its usual participation p̃.
+/// participation p̃ and the quorum of each level.
 #[derive(Clone, Copy, Debug, PartialEq, Serialize, Deserialize)]
 #[serde(rename_all = "camelCase")]
 pub struct Scale {
     pub electorate: u32,
-    pub floor: f64,
     /// p̃.
     pub participation: f64,
+    /// Q_k, the quorum of each level, 1 to 5: the default of an article at that level.
+    pub quorums: [u32; 5],
 }
 
 impl Scale {
-    /// The letters of the formula for a level.
+    /// The quorum an article is judged on: its own, set by its author before the first
-    pub fn params(&self, level: InertiaLevel) -> FormulaParams {
+    /// vote, else the one of its level (Yvv, 2026-11-02: « C suit le cran, mais c'est une
+    /// proposition par défaut, variable modifiable par l'auteur initial du texte »). A
+    /// change of inertia inherits the level of its article, and so its quorum.
+    pub fn quorum(&self, level: InertiaLevel, own: Option<u32>) -> u32 {
+        own.unwrap_or(self.quorums[level.index()])
+    }
+
+    /// The letters of the formula for a level, on a quorum.
+    pub fn params(&self, level: InertiaLevel, quorum: u32) -> FormulaParams {
         FormulaParams {
             majority_pct: level.majority_pct(),
             gradient: gradient(level, self.participation),
             base: FormulaParams::DEFAULT_BASE,
-            constant: self.floor,
+            quorum,
         }
     }
 
-    pub fn evaluate(&self, tally: Tally, level: InertiaLevel) -> Result<Evaluation, ThresholdError> {
+    pub fn evaluate(&self, tally: Tally, level: InertiaLevel, quorum: u32) -> Result<Evaluation, ThresholdError> {
-        evaluate(tally, self.electorate, &self.params(level))
+        evaluate(tally, self.electorate, &self.params(level, quorum))
     }
 
-    /// ⌈R⌉ for a level at `cast` votes.
+    /// ⌈R⌉ for a level and a quorum at `cast` votes.
-    pub fn required(&self, cast: u32, level: InertiaLevel) -> Result<u32, ThresholdError> {
+    pub fn required(&self, cast: u32, level: InertiaLevel, quorum: u32) -> Result<u32, ThresholdError> {
-        crate::threshold::wot_threshold(self.electorate, cast, &self.params(level))
+        crate::threshold::wot_threshold(self.electorate, cast, &self.params(level, quorum))
     }
 }
 
@@ -228,14 +243,22 @@ mod tests {
     use crate::threshold::required_ratio;
 
     const W: u32 = 7224;
-    const C: f64 = 50.0;
+    /// The reference quorum of Monnaie libre (`vote_floor`): p0 = 2 × 50 / W.
+    const Q0: f64 = 50.0;
+    /// The quorums of Monnaie libre by level (Yvv, 2026-11-02: « 12 · 12 · 50 · 50 · 50 »).
+    const QUORUMS: [u32; 5] = [12, 12, 50, 50, 50];
 
-    fn at_median(voters: u32) -> Scale {
+    fn level(k: u8) -> InertiaLevel {
-        Scale { electorate: W, floor: C, participation: f64::from(voters) / f64::from(W) }
+        InertiaLevel::new(k).expect("1 to 5")
     }
 
+    fn at_median(voters: u32) -> Scale {
+        Scale { electorate: W, participation: f64::from(voters) / f64::from(W), quorums: QUORUMS }
+    }
+
+    /// ⌈R⌉ at `cast` votes, each level on its own quorum.
     fn row(scale: &Scale, cast: u32) -> Vec<u32> {
-        InertiaLevel::ALL.iter().map(|k| scale.required(cast, *k).expect("valid")).collect()
+        InertiaLevel::ALL.iter().map(|k| scale.required(cast, *k, scale.quorum(*k, None)).expect("valid")).collect()
     }
 
     #[test]
@@ -265,30 +288,48 @@ mod tests {
         assert_eq!(serde_json::to_string(&InertiaLevel::HIGHEST).expect("json"), "5");
     }
 
+    #[test]
+    fn the_control_figures_of_the_quorum() {
+        // W 5 707, before any median: p0 = 2 × 50 / W = 100 / W (orch, 2026-11-03).
+        let w = 5707;
+        let scale = Scale { electorate: w, participation: Participation::of(w, Q0, None, 0).ratio, quorums: QUORUMS };
+        let yes = |k: u8, q: u32, against: u32| {
+            crate::threshold::yes_needed(against, w, &scale.params(level(k), q)).expect("valid")
+        };
+        // At the quorum: level 2, Q 12 → 9 « pour »; level 3, Q 50 → 39; level 5, Q 50 → 46.
+        assert_eq!((yes(2, 12, 0), yes(3, 50, 0), yes(5, 50, 0)), (9, 39, 46));
+        // 9 « pour » pass at level 2 with 3 « contre » at most (Yvv, 2026-11-03); with a 4th,
+        // 14 voters, 11 « pour » are asked (73,8 % of 14 is 10,2).
+        assert_eq!((yes(2, 12, 3), yes(2, 12, 4)), (9, 11));
+        // Ten voters, no quorum in the way: 7, 8, 9, 9 and 10 « pour », level 1 to 5.
+        let ten: Vec<u32> = InertiaLevel::ALL.iter().map(|k| scale.required(10, *k, 1).expect("valid")).collect();
+        assert_eq!(ten, [7, 8, 9, 9, 10]);
+    }
+
     #[test]
     fn the_values_shown_to_yvv() {
-        // W 7224, C 50, a median of 120 voters (the smith vote of 2024).
+        // W 7224, quorums 12 · 12 · 50 · 50 · 50, a median of 120 voters (the smith vote of 2024).
         let scale = at_median(120);
-        assert_eq!(row(&scale, 120), [92, 97, 103, 109, 113]);
+        assert_eq!(row(&scale, 120), [72, 81, 90, 100, 108]);
-        assert_eq!(row(&scale, 500), [306, 329, 362, 397, 432]);
+        assert_eq!(row(&scale, 500), [284, 310, 347, 386, 424]);
-        assert_eq!(row(&scale, 2000), [1091, 1145, 1271, 1404, 1549]);
+        assert_eq!(row(&scale, 2000), [1068, 1123, 1252, 1389, 1537]);
     }
 
     #[test]
     fn a_median_of_360_voters() {
         let scale = at_median(360);
-        assert_eq!(row(&scale, 120), [95, 101, 106, 112, 116]);
+        assert_eq!(row(&scale, 120), [76, 86, 96, 106, 113]);
-        assert_eq!(row(&scale, 360), [236, 258, 283, 308, 329]);
+        assert_eq!(row(&scale, 360), [216, 242, 270, 299, 324]);
-        assert_eq!(row(&scale, 500), [316, 345, 381, 416, 449]);
+        assert_eq!(row(&scale, 500), [296, 328, 367, 407, 443]);
-        assert_eq!(row(&scale, 2000), [1114, 1184, 1318, 1460, 1608]);
+        assert_eq!(row(&scale, 2000), [1092, 1164, 1301, 1446, 1598]);
     }
 
     #[test]
-    fn at_the_usual_participation_the_share_beyond_c_is_s_k() {
+    fn at_the_usual_participation_the_share_is_s_k() {
-        for (w, c, voters) in [(7224, 50.0, 120), (7224, 50.0, 360), (5745, 50.0, 300), (40, 1.0, 9), (2, 1.0, 1)] {
+        for (w, voters) in [(7224, 120), (7224, 360), (5745, 300), (40, 9), (2, 1)] {
-            let scale = Scale { electorate: w, floor: c, participation: f64::from(voters) / f64::from(w) };
+            let scale = Scale { electorate: w, participation: f64::from(voters) / f64::from(w), quorums: QUORUMS };
             for k in InertiaLevel::ALL {
-                let ratio = required_ratio(w, voters, &scale.params(k));
+                let ratio = required_ratio(w, voters, &scale.params(k, 0));
                 assert!((ratio - k.share_pct() / 100.0).abs() < 1e-12, "W {w}, k {}: {ratio}", k.get());
             }
         }
@@ -296,26 +337,33 @@ mod tests {
 
     #[test]
     fn a_threshold_landing_on_a_whole_number_stays_on_it() {
-        // Level 5 at the median: 90 % of the 70 votes beyond C is exactly 63.
+        // Level 5 at the median: 90 % of 120 voters is exactly 108.
-        assert_eq!(at_median(120).required(120, InertiaLevel::HIGHEST), Ok(113));
+        assert_eq!(at_median(120).required(120, InertiaLevel::HIGHEST, 50), Ok(108));
-        // Level 1: 60 % of 70 is exactly 42.
+        // Level 1: 60 % of 120 is exactly 72.
-        assert_eq!(at_median(120).required(120, InertiaLevel::LOWEST), Ok(92));
+        assert_eq!(at_median(120).required(120, InertiaLevel::LOWEST, 12), Ok(72));
     }
 
     #[test]
     fn the_threshold_rises_with_the_level() {
-        for (w, c) in [(7224, 50.0), (5745, 50.0), (40, 1.0), (2, 1.0), (1, 1.0)] {
+        for (w, q0, quorums) in [
+            (7224, Q0, QUORUMS),
+            (5745, Q0, QUORUMS),
+            (5745, Q0, [50; 5]),
+            (40, 1.0, [1; 5]),
+            (2, 1.0, [1; 5]),
+            (1, 1.0, [1; 5]),
+        ] {
             for voters in [1, 2, 9, 60, 120, 360, 3000] {
                 let scale = Scale {
                     electorate: w,
-                    floor: c,
+                    participation: Participation::of(w, q0, Some(f64::from(voters)), 9).ratio,
-                    participation: Participation::of(w, c, Some(f64::from(voters)), 9).ratio,
+                    quorums,
                 };
                 for cast in (0..=w.min(4000)).step_by(7).chain([w]) {
                     let r = row(&scale, cast);
                     assert!(r.windows(2).all(|p| p[0] <= p[1]), "W {w}, p̃ {voters}, T {cast}: {r:?}");
                     let ratios: Vec<f64> =
-                        InertiaLevel::ALL.iter().map(|k| required_ratio(w, cast, &scale.params(*k))).collect();
+                        InertiaLevel::ALL.iter().map(|k| required_ratio(w, cast, &scale.params(*k, 0))).collect();
                     if cast > 0 && cast < w {
                         assert!(
                             ratios.windows(2).all(|p| p[0] < p[1]),
@@ -332,7 +380,7 @@ mod tests {
         for voters in [120, 360] {
             let scale = at_median(voters);
             for k in InertiaLevel::ALL {
-                let p = scale.params(k);
+                let p = scale.params(k, 0);
                 let mut last = 1.0;
                 for cast in (1..=W).step_by(13).chain([W]) {
                     let ratio = required_ratio(W, cast, &p);
@@ -346,26 +394,44 @@ mod tests {
     }
 
     #[test]
-    fn c_stays_a_floor_one_vote_never_passes_in_monnaie_libre() {
+    fn under_the_quorum_one_vote_never_passes_in_monnaie_libre() {
         for voters in [1, 72, 120, 360, 3612] {
             let scale = Scale {
                 electorate: W,
-                floor: C,
+                participation: Participation::of(W, Q0, Some(f64::from(voters)), 9).ratio,
-                participation: Participation::of(W, C, Some(f64::from(voters)), 9).ratio,
+                quorums: QUORUMS,
             };
             for k in InertiaLevel::ALL {
-                let lone = scale.evaluate(Tally { for_votes: 1, against: 0 }, k).expect("valid");
+                let q = scale.quorum(k, None);
+                let lone = scale.evaluate(Tally { for_votes: 1, against: 0 }, k, q).expect("valid");
                 assert!(!lone.reached, "k {}", k.get());
-                assert_eq!(lone.required, 50);
+                // Under the quorum, the voters missing count as against: the bar of Q voters.
-                for cast in 1..=50 {
+                let at_q = scale.required(q, k, q).expect("valid");
-                    assert!(scale.required(cast, k).expect("valid") >= 50, "nothing passes under C for");
+                assert!(at_q >= 2, "one voice is never enough");
+                for cast in 0..=q {
+                    assert_eq!(scale.required(cast, k, q).expect("valid"), at_q, "under the quorum, k {}", k.get());
                 }
-                assert!(!scale.evaluate(Tally { for_votes: 49, against: 0 }, k).expect("valid").reached);
+                let short = Tally { for_votes: at_q - 1, against: 0 };
-                assert!(scale.evaluate(Tally { for_votes: 50, against: 0 }, k).expect("valid").reached);
+                assert!(!scale.evaluate(short, k, q).expect("valid").reached);
+                let enough = scale.evaluate(Tally { for_votes: at_q, against: 0 }, k, q).expect("valid");
+                assert!(enough.reached);
+                assert_eq!(enough.yes_needed, at_q);
             }
         }
     }
 
+    #[test]
+    fn an_article_s_own_quorum_stands_for_its_level() {
+        let scale = at_median(120);
+        assert_eq!(scale.quorum(InertiaLevel::DEFAULT, None), 50);
+        assert_eq!(scale.quorum(level(2), None), 12);
+        assert_eq!(scale.quorum(InertiaLevel::DEFAULT, Some(20)), 20);
+        // The curve stays the level's: only the quorum moves.
+        let own = scale.params(InertiaLevel::DEFAULT, 20);
+        let default = scale.params(InertiaLevel::DEFAULT, 50);
+        assert_eq!((own.majority_pct, own.gradient, own.quorum), (default.majority_pct, default.gradient, 20));
+    }
+
     #[test]
     fn the_median() {
         assert_eq!(median(&[]), None);
@@ -378,14 +444,14 @@ mod tests {
     #[test]
     fn the_reference_stands_in_until_five_proposals_are_voted_on() {
         // Monnaie libre: 2 × 50 / 7224 = 1.38 %, a hundred voters.
-        assert!((Participation::reference_ratio(W, C) - 100.0 / 7224.0).abs() < 1e-15);
+        assert!((Participation::reference_ratio(W, Q0) - 100.0 / 7224.0).abs() < 1e-15);
-        let early = Participation::of(W, C, Some(120.0), 4);
+        let early = Participation::of(W, Q0, Some(120.0), 4);
         assert_eq!(early.source, ParticipationSource::Reference);
         assert!((early.voters(W) - 100.0).abs() < 1e-9);
         assert_eq!((early.sample, early.median, early.bounded), (4, Some(120.0), false));
-        let none = Participation::of(W, C, None, 0);
+        let none = Participation::of(W, Q0, None, 0);
         assert_eq!(none.source, ParticipationSource::Reference);
-        let measured = Participation::of(W, C, Some(120.0), 5);
+        let measured = Participation::of(W, Q0, Some(120.0), 5);
         assert_eq!(measured.source, ParticipationSource::Median);
         assert!((measured.voters(W) - 120.0).abs() < 1e-9);
         assert!(!measured.bounded);
@@ -394,7 +460,7 @@ mod tests {
     #[test]
     fn participation_is_kept_within_one_and_fifty_percent() {
         // Two voters on 7224: brought up to 1 %.
-        let low = Participation::of(W, C, Some(2.0), 9);
+        let low = Participation::of(W, Q0, Some(2.0), 9);
         assert_eq!((low.ratio, low.bounded), (0.01, true));
         // A group where everyone votes: brought down to half.
         let all = Participation::of(12, 1.0, Some(12.0), 9);
@@ -418,12 +484,14 @@ mod tests {
     }
 
     #[test]
-    fn the_test_group_needs_everyone() {
+    fn the_test_group_at_a_quorum_of_one() {
-        // W = 2, C = 1: both must vote for, at every level.
+        // W = 2, quorum 1 everywhere (Yvv, 2026-11-02): one « pour » alone passes, at every
-        let scale = Scale { electorate: 2, floor: 1.0, participation: Participation::of(2, 1.0, None, 0).ratio };
+        // level; one « pour » and one « contre » never (half of all, under any M of the levels).
+        let scale = Scale { electorate: 2, participation: Participation::of(2, 1.0, None, 0).ratio, quorums: [1; 5] };
         for k in InertiaLevel::ALL {
-            assert!(!scale.evaluate(Tally { for_votes: 1, against: 0 }, k).expect("valid").reached);
+            assert!(scale.evaluate(Tally { for_votes: 1, against: 0 }, k, 1).expect("valid").reached);
-            assert!(scale.evaluate(Tally { for_votes: 2, against: 0 }, k).expect("valid").reached);
+            assert!(!scale.evaluate(Tally { for_votes: 1, against: 1 }, k, 1).expect("valid").reached);
+            assert!(scale.evaluate(Tally { for_votes: 2, against: 0 }, k, 1).expect("valid").reached);
         }
     }
 

crates/ld-engine/src/order.rs

@@ -274,13 +274,15 @@ mod tests {
         use crate::compose::{ProposalKind, ProposalState, UnitState, VersionText, adoptions};
         use crate::inertia::{InertiaLevel, Scale};
         use crate::threshold::Tally;
-        // Monnaie libre before any median: W 5745, C 50; the order of a section at level 2.
+        // Monnaie libre before any median: W 5745, p0 = 100 / W; the order of a section at
-        let scale = Scale { electorate: 5745, floor: 50.0, participation: 100.0 / 5745.0 };
+        // level 2, on the quorum of that level, 12 (ADR 0013).
+        let scale = Scale { electorate: 5745, participation: 100.0 / 5745.0, quorums: [12, 12, 50, 50, 50] };
         let section = ids(&["T1", "E1", "E2"]);
         let module = |tally: Tally| UnitState {
             id: "ordre.fondamental".into(),
             position: 0.0,
             inertia: InertiaLevel::new(2).expect("level"),
+            quorum: None,
             in_force: Some(VersionText { id: "seed".into(), title: String::new(), body: canonical(&section), tally }),
         };
         let proposal = |id: &str, order: &[&str], for_votes: u32| ProposalState {
@@ -294,12 +296,14 @@ mod tests {
             blocked: false,
         };
         let seed = [module(Tally::default())];
-        // Never under C voices for; the order in force at zero votes is a seed a minima: margin −C.
+        // Never under the bar of the quorum (9 « pour » of 12 voters); the order in force at zero
-        assert!(adoptions(&seed, &[proposal("p", &["E2", "E1", "T1"], 49)], &scale).expect("valid").is_empty());
+        // votes is a seed a minima: the margin of zero votes, −9.
-        assert_eq!(adoptions(&seed, &[proposal("p", &["E2", "E1", "T1"], 50)], &scale).expect("valid"), ["p"]);
+        assert!(adoptions(&seed, &[proposal("p", &["E2", "E1", "T1"], 8)], &scale).expect("valid").is_empty());
+        assert_eq!(adoptions(&seed, &[proposal("p", &["E2", "E1", "T1"], 9)], &scale).expect("valid"), ["p"]);
         // An order that is the one in force changes nothing, whatever its votes.
         assert!(adoptions(&seed, &[proposal("same", &["T1", "E1", "E2"], 80)], &scale).expect("valid").is_empty());
-        // Adopted by a vote, the order in force holds its margin: a weaker order waits, a stronger one passes.
+        // Adopted by a vote, the order in force holds its margin (70 − 48): a weaker order waits
+        // (60 − 42), a stronger one passes (90 − 61).
         let voted = [module(Tally { for_votes: 70, against: 0 })];
         assert!(adoptions(&voted, &[proposal("w", &["E2", "E1", "T1"], 60)], &scale).expect("valid").is_empty());
         assert_eq!(adoptions(&voted, &[proposal("s", &["E2", "E1", "T1"], 90)], &scale).expect("valid"), ["s"]);

crates/ld-engine/src/threshold.rs

@@ -1,21 +1,24 @@
-//! Inertial threshold for binary votes — the Ğ1 "g1vote" formula.
+//! Inertial threshold for binary votes — the Ğ1 "g1vote" formula, judged on a quorum.
 //!
 //! ```text
-//! R = C + B^W + (M + (1 − M)(1 − (T/W)^G)) · max(0, T − C)
+//! T' = max(T, Q)
+//! R  = B^W + (M + (1 − M)(1 − (T'/W)^G)) · T'
 //! ```
 //!
-//! R is the minimum number of *for* votes; a proposal is adopted when
+//! R is the minimum number of *for* votes; a version passes when `for ≥ ⌈R⌉`.
-//! `for ≥ ⌈R⌉`. W is the size of the electorate, T the votes cast (for +
+//! W is the size of the electorate, T the votes cast (for + against). At low
-//! against). At low participation the formula asks for near-unanimity, at full
+//! participation the formula asks for near-unanimity, at full participation the
-//! participation the simple majority M suffices. C is the minimal number of
+//! simple majority M suffices. Q is the **quorum** (ADR 0013, Yvv, 2026-11-02:
-//! *for* votes below which nothing passes — the guard of a permanent vote
+//! « ce n'est pas un nombre de vote pour a priori, c'est plutôt un quorum, à partir
-//! (Yvv, 2026-10-21: « Nombre minimal de votants »).
+//! de ce nombre, alors il faut la bonne proportion attendue par l'indice ») — and
+//! below it the voters missing count as against (`judged_voters`). It replaces the
+//! floor C of *for* votes added in front of the formula (ADR 0002, 0007).
 //!
-//! Parity: identical to `maquette/frontend/app/engine/threshold.ts` and the
+//! Parity with `maquette/frontend/app/engine/threshold.ts` at Q = 0 (the C = 0 of
-//! Python reference, with two deliberate guards — the participation ratio is
+//! the maquette), with two deliberate guards — the participation ratio is capped
-//! capped at 1, so a stale W can never lower the bar below M; and a count that
+//! at 1, so a stale W can never lower the bar below M; and a count that lands on a
-//! lands on a whole number stays on it (`settle`), so a rounding error never
+//! whole number stays on it (`settle`), so a rounding error never adds a vote.
-//! adds a vote. Which M and G a text is judged by: `inertia` (five levels).
+//! Which M, G and Q a text is judged by: `inertia` (five levels, their quorums).
 
 use serde::{Deserialize, Serialize};
 
@@ -28,8 +31,9 @@ pub struct FormulaParams {
     pub gradient: f64,
     /// B.
     pub base: f64,
-    /// C — minimal number of *for* votes.
+    /// Q — the quorum: the voters (for + against) from which the share of the inertia
-    pub constant: f64,
+    /// applies; below it, the voters missing count as against (`judged_voters`).
+    pub quorum: u32,
 }
 
 impl FormulaParams {
@@ -42,14 +46,26 @@ pub enum ThresholdError {
     MajorityOutOfRange,
 }
 
-/// The required ratio of *for* votes among the votes cast beyond C.
+/// T' — the voters a version is judged on. **The rule of the quorum, here alone.**
-pub fn required_ratio(electorate: u32, cast: u32, params: &FormulaParams) -> f64 {
+///
+/// Yvv, 2026-11-03, to « Sous le quorum, les votants qui manquent comptent-ils comme des
+/// « non » ? » : « Ils comptent comme non ». Below the quorum Q, the voters who did not
+/// come count as against: the share of the inertia is asked of max(T, Q) voters. At level
+/// 2, quorum 12, 9 « pour » pass with 3 « contre » at most; Yvv's own example, 60 % and
+/// Q = 10, takes 6 « pour ». So an « against » never helps a version pass — completing
+/// the quorum with a « non » adds nothing the missing voters did not already count.
+pub fn judged_voters(cast: u32, quorum: u32) -> u32 {
+    cast.max(quorum)
+}
+
+/// The share of *for* votes asked of `voters` voters (T' when judging a version).
+pub fn required_ratio(electorate: u32, voters: u32, params: &FormulaParams) -> f64 {
     let m = params.majority_pct / 100.0;
-    let participation = (f64::from(cast) / f64::from(electorate.max(1))).min(1.0);
+    let participation = (f64::from(voters) / f64::from(electorate.max(1))).min(1.0);
     m + (1.0 - m) * (1.0 - participation.powf(params.gradient))
 }
 
-/// ⌈R⌉ — the minimum number of *for* votes for adoption.
+/// ⌈R⌉ — the minimum number of *for* votes for adoption, at `cast` votes cast.
 pub fn wot_threshold(electorate: u32, cast: u32, params: &FormulaParams) -> Result<u32, ThresholdError> {
     if electorate == 0 {
         return Err(ThresholdError::EmptyElectorate);
@@ -57,20 +73,27 @@ pub fn wot_threshold(electorate: u32, cast: u32, params: &FormulaParams) -> Resu
     if !(0.0..=100.0).contains(&params.majority_pct) {
         return Err(ThresholdError::MajorityOutOfRange);
     }
-    let c = params.constant;
+    let voters = judged_voters(cast, params.quorum);
     let offset = params.base.powf(f64::from(electorate));
-    let raw = if cast == 0 {
+    let raw = if voters == 0 {
-        c + offset
+        offset
     } else {
-        c + offset + settle(required_ratio(electorate, cast, params) * (f64::from(cast) - c).max(0.0))
+        offset + settle(required_ratio(electorate, voters, params) * f64::from(voters))
     };
     // `raw` is finite and non-negative for any valid input; saturate rather than wrap.
     Ok(clamp_ceil(raw))
 }
 
+/// Does a version with this tally pass? At least one vote cast, and its *for* reach
+/// ⌈R⌉ on the voters it is judged on (`judged_voters`).
+pub fn passes(tally: Tally, electorate: u32, params: &FormulaParams) -> Result<bool, ThresholdError> {
+    let cast = tally.cast();
+    Ok(cast > 0 && tally.for_votes >= wot_threshold(electorate, cast, params)?)
+}
+
 /// A count of votes that lands on a whole number stays on it: a rounding error
 /// of the logarithms (a billionth of a vote) must never raise a threshold by
-/// one. At the usual participation, 90 % of the 70 votes beyond C is exactly 63.
+/// one. At the usual participation, 90 % of 70 votes is exactly 63.
 fn settle(votes: f64) -> f64 {
     let whole = votes.round();
     if (votes - whole).abs() < 1e-9 { whole } else { votes }
@@ -107,32 +130,82 @@ impl Tally {
 #[serde(rename_all = "camelCase")]
 pub struct Evaluation {
     pub cast: u32,
-    /// ⌈R⌉ at the current participation.
+    /// Q, the quorum it is judged on.
+    pub quorum: u32,
+    /// ⌈R⌉ at the current participation (on T' = max(T, Q) voters).
     pub required: u32,
-    /// `for ≥ ⌈R⌉` with at least one vote cast.
+    /// `passes`: `for ≥ ⌈R⌉` with at least one vote cast.
     pub reached: bool,
-    /// *for* votes still missing (0 once reached).
+    /// *for* votes still missing with the *against* of now: `yes_needed − for` (0 once reached).
     pub missing: u32,
-    /// The majority the inertia asks for at this participation.
+    /// The share of *for* the inertia asks of T' voters.
     pub required_ratio: f64,
-    /// « Bien cotée » : it holds the majority its inertia asks for, it only
+    /// « Bien cotée » : it holds the share its inertia asks of the T voters who came,
-    /// lacks voters (C ignored). Used by the "if the well-rated pass" preview.
+    /// it only lacks voters (the quorum ignored). Used by the "if the well-rated pass" preview.
     pub well_rated: bool,
+    /// The total of *for* that passes with the *against* cast now.
+    pub yes_needed: u32,
+    /// The total of *against* that holds the *for* cast now in check: 0 when the quorum
+    /// already holds them (they do not pass even without any *against*).
+    pub no_needed: u32,
+}
+
+/// The number of votes searched for never goes past this: the five levels always find
+/// theirs well before (`yes_needed`, `no_needed`).
+const SEARCH_LIMIT: u32 = u32::MAX / 4;
+
+/// The smallest `n` in `0..` for which `holds(n)`, `holds` being monotone (false, then
+/// true); `u32::MAX` if it never holds up to `SEARCH_LIMIT`.
+fn first(mut holds: impl FnMut(u32) -> Result<bool, ThresholdError>) -> Result<u32, ThresholdError> {
+    if holds(0)? {
+        return Ok(0);
+    }
+    let (mut lo, mut hi) = (0u32, 1u32);
+    while !holds(hi)? {
+        if hi >= SEARCH_LIMIT {
+            return Ok(u32::MAX);
+        }
+        lo = hi;
+        hi = hi.saturating_mul(2).min(SEARCH_LIMIT);
+    }
+    // holds(lo) is false, holds(hi) true.
+    while hi - lo > 1 {
+        let mid = lo + (hi - lo) / 2;
+        if holds(mid)? { hi = mid } else { lo = mid }
+    }
+    Ok(hi)
+}
+
+/// The total of *for* that passes with `against` votes against. A *for* more never
+/// hurts (`passes` is monotone): every total from this one on passes.
+pub fn yes_needed(against: u32, electorate: u32, params: &FormulaParams) -> Result<u32, ThresholdError> {
+    first(|y| passes(Tally { for_votes: y, against }, electorate, params))
+}
+
+/// The total of *against* that holds `for_votes` in check; 0 when they do not pass even
+/// without any *against* (the quorum holds them). An *against* more never helps: every
+/// total from this one on holds them.
+pub fn no_needed(for_votes: u32, electorate: u32, params: &FormulaParams) -> Result<u32, ThresholdError> {
+    first(|n| passes(Tally { for_votes, against: n }, electorate, params).map(|p| !p))
 }
 
 pub fn evaluate(tally: Tally, electorate: u32, params: &FormulaParams) -> Result<Evaluation, ThresholdError> {
     let cast = tally.cast();
     let required = wot_threshold(electorate, cast, params)?;
-    let without_floor = FormulaParams { constant: 0.0, ..*params };
+    let reached = passes(tally, electorate, params)?;
-    let required_without_floor = wot_threshold(electorate, cast, &without_floor)?;
+    let without_quorum = FormulaParams { quorum: 0, ..*params };
-    let reached = cast > 0 && tally.for_votes >= required;
+    let required_without_quorum = wot_threshold(electorate, cast, &without_quorum)?;
+    let yes = yes_needed(tally.against, electorate, params)?;
     Ok(Evaluation {
         cast,
+        quorum: params.quorum,
         required,
         reached,
-        missing: required.saturating_sub(tally.for_votes),
+        missing: if reached { 0 } else { yes.saturating_sub(tally.for_votes) },
-        required_ratio: required_ratio(electorate, cast, params),
+        required_ratio: required_ratio(electorate, judged_voters(cast, params.quorum), params),
-        well_rated: cast > 0 && tally.for_votes >= required_without_floor,
+        well_rated: cast > 0 && tally.for_votes >= required_without_quorum,
+        yes_needed: yes,
+        no_needed: no_needed(tally.for_votes, electorate, params)?,
     })
 }
 
@@ -141,19 +214,19 @@ mod tests {
     use super::*;
 
     fn g1vote(m: f64, g: f64) -> FormulaParams {
-        FormulaParams { majority_pct: m, gradient: g, base: 0.1, constant: 0.0 }
+        FormulaParams { majority_pct: m, gradient: g, base: 0.1, quorum: 0 }
     }
 
     /// The letters of the « standard » inertia before the five levels: M 50 %, G 0.2.
-    fn standard(constant: f64) -> FormulaParams {
+    fn standard(quorum: u32) -> FormulaParams {
-        FormulaParams { constant, ..g1vote(50.0, 0.2) }
+        FormulaParams { quorum, ..g1vote(50.0, 0.2) }
     }
 
     #[test]
     fn reference_case_of_the_smith_vote() {
         // Engagement forgeron v2.0.0: W 7224, 97 for, 23 against, M50 B.1 G.2 → 94.
-        // The formula's own reference, letters given: the five levels (ADR 0007)
+        // The formula's own reference, letters given, without a quorum (Q = 0, the C = 0
-        // choose M and G, the formula that turns them into a threshold is this one.
+        // of the maquette): the five levels choose M, G and Q (ADR 0007, 0013).
         let p = g1vote(50.0, 0.2);
         assert_eq!(wot_threshold(7224, 120, &p), Ok(94));
         let e = evaluate(Tally { for_votes: 97, against: 23 }, 7224, &p).expect("valid");
@@ -163,7 +236,7 @@ mod tests {
 
     #[test]
     fn parity_with_the_typescript_reference() {
-        // Values computed by maquette/frontend/app/engine/threshold.ts.
+        // Values computed by maquette/frontend/app/engine/threshold.ts (C = 0).
         let p = g1vote(50.0, 0.2);
         assert_eq!(wot_threshold(7224, 0, &p), Ok(0));
         assert_eq!(wot_threshold(7224, 1, &p), Ok(1));
@@ -174,42 +247,138 @@ mod tests {
     }
 
     #[test]
-    fn one_vote_passes_without_floor_and_never_with_it() {
+    fn yvv_s_example_sixty_percent_and_a_quorum_of_ten() {
-        // The trap of a permanent vote: a lone "for" meets the inertial bar.
+        // Yvv, 2026-11-02: « Si c'est 60% et c=10, alors il faut 6 voix pour et ça passe. »
-        let bare = standard(0.0);
+        // A share of 60 % whatever the participation (G = 0), a large web (B^W vanishes).
-        assert!(evaluate(Tally { for_votes: 1, against: 0 }, 5745, &bare).expect("valid").reached);
+        let p = FormulaParams { majority_pct: 60.0, gradient: 0.0, base: 0.1, quorum: 10 };
-        let guarded = standard(50.0);
+        // G = 0: (T/W)^0 = 1, the share is M, 60 %.
-        let e = evaluate(Tally { for_votes: 1, against: 0 }, 5745, &guarded).expect("valid");
+        assert!((required_ratio(7224, 10, &p) - 0.6).abs() < 1e-12);
-        assert!(!e.reached);
+        for against in 0..=4 {
-        assert_eq!(e.required, 50);
+            let t = Tally { for_votes: 6, against };
-        assert_eq!(e.missing, 49);
+            assert_eq!(passes(t, 7224, &p), Ok(true), "6 pour, {against} contre");
-        assert!(e.well_rated, "unanimous, it only lacks voters");
+        }
+        assert_eq!(passes(Tally { for_votes: 5, against: 0 }, 7224, &p), Ok(false), "5 of the 10 counted");
+        assert_eq!(wot_threshold(7224, 6, &p), Ok(6));
+        // Beyond the quorum, the share of all who came: 6 pour and 5 contre are 11 voters.
+        assert_eq!(passes(Tally { for_votes: 6, against: 5 }, 7224, &p), Ok(false));
+        assert_eq!(passes(Tally { for_votes: 7, against: 4 }, 7224, &p), Ok(true));
     }
 
     #[test]
-    fn floor_is_a_minimum_of_for_votes() {
+    fn under_the_quorum_the_voters_missing_count_as_against() {
-        let p = standard(50.0);
+        // Yvv, 2026-11-03: « Ils comptent comme non ». T' = max(T, Q).
-        // 50 unanimous votes reach it, 49 do not.
+        assert_eq!(
-        assert!(evaluate(Tally { for_votes: 50, against: 0 }, 5745, &p).expect("valid").reached);
+            (judged_voters(0, 12), judged_voters(9, 12), judged_voters(12, 12), judged_voters(30, 12)),
-        assert!(!evaluate(Tally { for_votes: 49, against: 0 }, 5745, &p).expect("valid").reached);
+            (12, 12, 12, 30)
-        // Beyond the floor the inertial majority applies to the rest.
+        );
-        let e = evaluate(Tally { for_votes: 55, against: 5 }, 5745, &p).expect("valid");
+        let p = standard(50);
-        assert!(!e.reached, "near-unanimity is asked of the votes beyond C");
+        // One « pour » alone is judged on 50 voters; so are 1 « pour » and 49 « contre ».
+        assert_eq!(wot_threshold(5745, 1, &p), wot_threshold(5745, 50, &p));
+        assert!(!passes(Tally { for_votes: 1, against: 0 }, 5745, &p).expect("valid"));
+    }
+
+    #[test]
+    fn an_against_never_helps_a_version_pass() {
+        // Without the rule, an « against » that completes the quorum could make a text pass.
+        for (m, g, q, w) in [(50.0, 0.1, 12, 5707), (55.0, 0.15, 50, 5707), (66.0, 0.3, 50, 5745), (50.0, 0.6, 1, 2)] {
+            let p = FormulaParams { majority_pct: m, gradient: g, base: 0.1, quorum: q };
+            for y in 0..80 {
+                let mut passed = passes(Tally { for_votes: y, against: 0 }, w, &p).expect("valid");
+                for n in 1..80 {
+                    let now = passes(Tally { for_votes: y, against: n }, w, &p).expect("valid");
+                    assert!(passed || !now, "M {m} Q {q} W {w}: {y} pour, {n} contre passes, {} contre did not", n - 1);
+                    passed = now;
+                }
+            }
+        }
+    }
+
+    #[test]
+    fn one_vote_never_passes_with_a_quorum_of_two_or_more() {
+        // The invariant of Monnaie libre (quorum 2 at least): one voice alone never passes.
+        for q in [2, 12, 50] {
+            for g in [0.05, 0.1, 0.3, 1.77] {
+                let p = FormulaParams { majority_pct: 50.0, gradient: g, base: 0.1, quorum: q };
+                let e = evaluate(Tally { for_votes: 1, against: 0 }, 5745, &p).expect("valid");
+                assert!(!e.reached, "Q {q}, G {g}");
+                assert!(e.well_rated, "unanimous, it only lacks voters");
+            }
+        }
+        // Without a quorum, the trap of a permanent vote: a lone « pour » meets the inertial bar.
+        assert!(evaluate(Tally { for_votes: 1, against: 0 }, 5745, &standard(0)).expect("valid").reached);
+    }
+
+    #[test]
+    fn yes_needed_and_no_needed_say_where_the_line_is() {
+        // At level 2 on the scale of Monnaie libre (G 0.10274, W 5707), quorum 12.
+        let p = FormulaParams { majority_pct: 50.0, gradient: 0.102_742, base: 0.1, quorum: 12 };
+        let e = evaluate(Tally::default(), 5707, &p).expect("valid");
+        assert_eq!((e.quorum, e.required, e.yes_needed, e.missing, e.no_needed), (12, 9, 9, 9, 0));
+        // 9 « pour »: they pass with 3 « contre » at most; the 4th holds them.
+        let e = evaluate(Tally { for_votes: 9, against: 0 }, 5707, &p).expect("valid");
+        assert!(e.reached);
+        assert_eq!((e.yes_needed, e.no_needed, e.missing), (9, 4, 0));
+        // With a 4th « contre », 14 voters at least: 11 « pour » are asked (10,2 rounded up).
+        let e = evaluate(Tally { for_votes: 9, against: 4 }, 5707, &p).expect("valid");
+        assert!(!e.reached);
+        assert_eq!(e.yes_needed, 11);
+        assert_eq!(e.missing, 2);
+        // 8 « pour »: the quorum already holds them, no « contre » is needed.
+        let e = evaluate(Tally { for_votes: 8, against: 0 }, 5707, &p).expect("valid");
+        assert_eq!((e.reached, e.no_needed, e.missing), (false, 0, 1));
+    }
+
+    #[test]
+    fn passes_means_yes_needed_reached_means_no_needed_not_reached() {
+        // On a grid: levels (M, G as at the reference participation and beyond), quorums,
+        // electorates, « pour », « contre ». passes ⇔ for ≥ yesNeeded(against) ⇔ against < noNeeded(for).
+        let levels = [(50.0, 0.055), (50.0, 0.103), (55.0, 0.145), (60.0, 0.212), (66.0, 0.303), (66.0, 1.77)];
+        for (m, g) in levels {
+            for q in [0, 1, 2, 12, 50] {
+                for w in [1, 2, 16, 40, 500, 5707] {
+                    let p = FormulaParams { majority_pct: m, gradient: g, base: 0.1, quorum: q };
+                    let yes: Vec<u32> = (0..70).map(|n| yes_needed(n, w, &p).expect("valid")).collect();
+                    for y in 0..70 {
+                        let no = no_needed(y, w, &p).expect("valid");
+                        for n in 0..70 {
+                            let t = Tally { for_votes: y, against: n };
+                            let ok = passes(t, w, &p).expect("valid");
+                            assert_eq!(ok, y >= yes[n as usize], "M {m} G {g} Q {q} W {w}: {y} pour {n} contre");
+                            assert_eq!(ok, n < no, "M {m} G {g} Q {q} W {w}: {y} pour {n} contre, noNeeded {no}");
+                        }
+                    }
+                }
+            }
+        }
+    }
+
+    #[test]
+    fn well_rated_holds_the_share_on_those_who_came() {
+        let p = standard(50);
+        // 30 « pour », 2 « contre »: the share holds on 32 voters, the quorum is not there.
+        let e = evaluate(Tally { for_votes: 30, against: 2 }, 5745, &p).expect("valid");
+        assert!(!e.reached && e.well_rated);
+        // 10 « pour », 10 « contre »: the share does not hold.
+        assert!(!evaluate(Tally { for_votes: 10, against: 10 }, 5745, &p).expect("valid").well_rated);
     }
 
     #[test]
     fn no_vote_is_never_reached() {
-        let p = g1vote(50.0, 0.1);
+        for q in [0, 1, 12] {
-        let e = evaluate(Tally::default(), 3, &p).expect("valid");
+            let p = FormulaParams { quorum: q, ..g1vote(50.0, 0.1) };
-        assert!(!e.reached);
+            let e = evaluate(Tally::default(), 3, &p).expect("valid");
-        assert!(!e.well_rated);
+            assert!(!e.reached);
+            assert!(!e.well_rated);
+        }
     }
 
     #[test]
-    fn small_group_needs_everyone() {
+    fn the_test_group_passes_with_one_voice_at_a_quorum_of_one() {
-        // Test group of two people, C = 1: both must vote for.
+        // Two people, quorum 1 (Yvv, 2026-11-02: the test group stays at 1 everywhere): one
-        let p = standard(1.0);
+        // « pour » of one voter holds any share; a « contre » beside it does not.
-        assert!(!evaluate(Tally { for_votes: 1, against: 0 }, 2, &p).expect("valid").reached);
+        let p = standard(1);
+        assert!(evaluate(Tally { for_votes: 1, against: 0 }, 2, &p).expect("valid").reached);
+        assert!(!evaluate(Tally { for_votes: 1, against: 1 }, 2, &p).expect("valid").reached);
         assert!(evaluate(Tally { for_votes: 2, against: 0 }, 2, &p).expect("valid").reached);
     }
 
@@ -225,12 +394,12 @@ mod tests {
 
     #[test]
     fn a_whole_number_of_votes_never_gains_one_by_rounding() {
-        // 101 members, everyone votes, M 55 %: 1 + 55 % of 100 = 56. In floating
+        // 100 members, everyone votes, M 55 %: 55 % of 100 = 55. In floating point 0.55 × 100
-        // point 0.55 × 100 is 55.000000000000007, which would ask for 57.
+        // is 55.000000000000007, which would ask for 56 (B^W = 10⁻¹⁰⁰ adds nothing).
-        let p = FormulaParams { majority_pct: 55.0, gradient: 0.3, base: 0.1, constant: 1.0 };
+        let p = FormulaParams { majority_pct: 55.0, gradient: 0.3, base: 0.1, quorum: 1 };
-        assert_eq!(wot_threshold(101, 101, &p), Ok(56));
+        assert_eq!(wot_threshold(100, 100, &p), Ok(55));
         // A genuine fraction still rounds up.
-        assert_eq!(wot_threshold(101, 100, &FormulaParams { constant: 0.0, ..p }), Ok(56));
+        assert_eq!(wot_threshold(101, 99, &FormulaParams { quorum: 0, ..p }), Ok(55));
     }
 
     #[test]
@@ -239,5 +408,6 @@ mod tests {
         assert_eq!(wot_threshold(0, 1, &p), Err(ThresholdError::EmptyElectorate));
         let bad = g1vote(120.0, 0.2);
         assert_eq!(wot_threshold(10, 1, &bad), Err(ThresholdError::MajorityOutOfRange));
+        assert_eq!(yes_needed(0, 0, &p), Err(ThresholdError::EmptyElectorate));
     }
 }