modification calcul mediane

backend/app/engine/median.py

@@ -5,12 +5,22 @@ Computes the element-wise median of (vinf, a, b, c, d, e) across all active vote
 This parametric median is chosen over geometric median because:
 - It's transparent and politically explainable
 - The result is itself a valid set of Bézier parameters
+
+Post-processing: the median is sanitized to guarantee monotonicity of tier 2.
+The condition for tier 2 to be non-decreasing is e <= 1/3.
+If the raw median violates this, e is clamped to E_MAX_MONOTONE.
 """
 
 import numpy as np
 from dataclasses import dataclass
 
 
+# Maximum value of e that guarantees tier-2 price monotonicity.
+# prix_m3_2 = p0 + (pmax-p0) * ((1-3e)t³ + 3e t²)
+# The cubic is monotone non-decreasing on [0,1] iff (1-3e) >= 0, i.e. e <= 1/3.
+E_MAX_MONOTONE = 1.0 / 3.0
+
+
 @dataclass
 class VoteParams:
     """The 6 citizen-adjustable parameters."""
@@ -22,23 +32,49 @@ class VoteParams:
     e: float
 
 
+def _is_tier2_monotone(e: float) -> bool:
+    """Check if tier-2 price curve is monotone non-decreasing."""
+    return e <= E_MAX_MONOTONE
+
+
+def sanitize_median(params: "VoteParams") -> "VoteParams":
+    """
+    Ensure the median curve is physically valid:
+    - Tier 2 must be monotone non-decreasing (penalizes high consumption)
+    - If e violates monotonicity, clamp it to E_MAX_MONOTONE
+    """
+    e = params.e
+    if not _is_tier2_monotone(e):
+        e = E_MAX_MONOTONE
+
+    return VoteParams(
+        vinf=params.vinf,
+        a=params.a,
+        b=params.b,
+        c=params.c,
+        d=params.d,
+        e=e,
+    )
+
+
 def compute_median(votes: list[VoteParams]) -> VoteParams | None:
     """
     Compute element-wise median of vote parameters.
 
     Returns None if no votes provided.
+    The result is sanitized for tier-2 monotonicity.
     """
     if not votes:
         return None
 
     vinfs = [v.vinf for v in votes]
-    a_s = [v.a for v in votes]
-    b_s = [v.b for v in votes]
-    c_s = [v.c for v in votes]
-    d_s = [v.d for v in votes]
-    e_s = [v.e for v in votes]
+    a_s   = [v.a    for v in votes]
+    b_s   = [v.b    for v in votes]
+    c_s   = [v.c    for v in votes]
+    d_s   = [v.d    for v in votes]
+    e_s   = [v.e    for v in votes]
 
-    return VoteParams(
+    raw = VoteParams(
         vinf=float(np.median(vinfs)),
         a=float(np.median(a_s)),
         b=float(np.median(b_s)),
@@ -46,3 +82,5 @@ def compute_median(votes: list[VoteParams]) -> VoteParams | None:
         d=float(np.median(d_s)),
         e=float(np.median(e_s)),
     )
+
+    return sanitize_median(raw)