report.ipynb

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    "# Estimation du report des voix St Max 1er vers 2nd tour\n",
    "\n",
    "## Méthodologie\n",
    "* On a 15 bureaux différents, qui ont chacun des scores différents\n",
    "* On a les scores du 1er tour (Garello=G1, Molina=M1, etc. y compris nuls-nlancs et abstention)\n",
    "* On a les scores du second tour Garello (G2), Molina (M2), les nuls-blancs et l'abstention regroupés en A2\n",
    "* On différencie le vote Decanis D1, du reste des autres listes R1\n",
    "* On cherche à trouver la fonction F(score 1er tour) = score 2nd tour\n",
    "\n",
    "## Hypothèses\n",
    "* On considère que Garello et Molina ont gardé leurs électeurs, c'est-à-dire `G2 = G1 + ...` et `M2 = M1 + ...`\n",
    "* D1 se reporte dans G2 (D1G2), M2 (D1M2) et dans A2 (D1A2) de manière linéaire: D1G2 est une fraction fixe de D1.\n",
    "* R1 idem. On considère R1 comme une grandeur homogène comme étant les votants non-Garello, non-RN, non-Decanis.\n",
    "* `G2 = G1 + D1 * D1G2 + R1 * R1G2`, idem pour M2 avec D1M2 et R1G2\n",
    "* Si on a D1G2 et D1M2, on en déduit D1A2 puisque la somme des 3 fait 1 (100%)\n",
    "* On connaît G1 et G2 pour 15 bureaux, l'objectif est de trouver D1G2 et R1G2 qui minimise l'erreur entre le G2 calculé (G2c) et le G2 connu"
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    "# G1[n] correspond au bureau n, on met la G1[n] à 0\n",
    "G1 = [0, 172, 216, 170, 201, 227, 155, 183, 188, 148, 227, 204, 177, 166, 215, 222]\n",
    "D1 = [0, 106, 96,55,83,89,88,87,89,77,88,83,80,79,100,88]\n",
    "R1 = [0, 153, 143,114,148,148,108,145,116,134,154,178,138,110,148,143]\n",
    "G2 = [0, 291, 358,265,367,350,247,294,275,254,341,355,301,305,358,347]"
   ]
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   "execution_count": 2,
   "id": "be000e2b",
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    {
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     "text": [
      "   0%   90%   -35.0\n",
      "  10%   80%    44.2\n",
      "  20%   80%   -84.6\n",
      "  30%   70%    -5.4\n",
      "  40%   60%    73.8\n",
      "  50%   60%   -55.0\n",
      "  60%   50%    24.2\n",
      "  80%   40%   -25.4\n",
      "  90%   30%    53.8\n",
      " 100%   30%   -75.0\n"
     ]
    }
   ],
   "source": [
    "for d1g2 in range(11): # 1 .. 10 => 10% .. 100%\n",
    "    for r1g2 in range(11):\n",
    "        diff = 0.0\n",
    "        for bureau in range(1, 16):\n",
    "            g2c = G1[bureau] + D1[bureau] * d1g2/10 + R1[bureau] * r1g2/10\n",
    "            d = G2[bureau] - g2c\n",
    "            diff += d\n",
    "        if diff < 100 and diff > -100:\n",
    "            print(\"{:4}% {:4}% {:7.7}\".format(d1g2*10, r1g2*10, diff))"
   ]
  },
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   "id": "c86d2f30",
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   "source": [
    "On voit que pour minimiser la différence, chaque baisse de la part de D1 doit être compensé par la part de R1.\n",
    "On fait le même calcul pour Molina"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8efddef1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "   0%   60%    -5.0\n",
      "  10%   50%    74.2\n",
      "  20%   50%   -54.6\n",
      "  30%   40%    24.6\n",
      "  50%   30%   -25.0\n",
      "  60%   20%    54.2\n",
      "  70%   20%   -74.6\n",
      "  80%   10%     4.6\n",
      "  90%    0%    83.8\n",
      " 100%    0%   -45.0\n"
     ]
    }
   ],
   "source": [
    "M1 = [0, 151, 152,134,208,205,158,219,169,142,215,266,158,155,212,185]\n",
    "M2 = [0,262,251,180,262,296,263,308,255,222,305,339,244,205,294,286]\n",
    "for d1m2 in range(11):\n",
    "    for r1m2 in range(11):\n",
    "        diff = 0.0\n",
    "        for bureau in range(1, 16):\n",
    "            m2c = M1[bureau] + D1[bureau] * d1m2/10 + R1[bureau] * r1m2/10\n",
    "            d = M2[bureau] - m2c\n",
    "            diff += d\n",
    "        if diff < 100 and diff > -100:\n",
    "            print(\"{:4}% {:4}% {:7.7}\".format(d1m2*10, r1m2*10, diff))"
   ]
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   "source": [
    "On sait que `d1g2 + d1m2 + d1a2 = 100` (idem `r1*`), donc on peut faire varier d1a2 et utiliser `d1m2 = 100 - d1g2 - d1a2` pour calculer la diff globale des 2 boucles, et idem pour `r1*`.\n",
    "Comme la participation est presque la même et que les nuls-blancs augmentent de seulement 2%, on néglige la fuite vers l'absentation, d'où `d1a2 = 0% ou 10%`"
   ]
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  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bf86db3d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "De   Decanis            Réserve            Score\n",
      "vers Gar  Abs  Mol  |   Gar   Abs   Mol |  (meilleur qd petit)\n",
      "     0%   10%   90% |   80%   10%   10% |   392.4\n",
      "     0%    0%  100% |   90%   10%    0% |   377.8\n",
      "     0%   10%   90% |   90%    0%   10% |   397.0\n",
      "    10%    0%   90% |   80%   10%   10% |   371.4\n",
      "    10%   10%   80% |   80%   10%   10% |   375.4\n",
      "    20%   10%   70% |   70%   10%   20% |   377.8\n",
      "    30%    0%   70% |   70%   10%   20% |   376.2\n"
     ]
    }
   ],
   "source": [
    "print(\"De   {:18} {:18} {}\".format(\"Decanis\", \"Réserve\", \"Score\"))\n",
    "print(\"vers {:4} {:4} {:4} |   {:4}  {:4}  {:4}|  {}\".format(\"Gar\", \"Abs\", \"Mol\",\"Gar\", \"Abs\", \"Mol\", \"(meilleur qd petit)\"))\n",
    "for d1g2 in range(11): # 1 .. 10 => 10% .. 100%\n",
    "    for r1g2 in range(11):\n",
    "        for d1a2 in range(2):\n",
    "            d1m2 = 10 - d1g2 - d1a2\n",
    "            if d1m2 < 0:\n",
    "                continue\n",
    "            for r1a2 in range(2):\n",
    "                r1m2 = 10 - r1g2 - r1a2\n",
    "                if r1m2 < 0:\n",
    "                    continue\n",
    "                diff = 0.0\n",
    "                for bureau in range(1, 16):\n",
    "                    g2c = G1[bureau] + D1[bureau] * d1g2/10 + R1[bureau] * r1g2/10\n",
    "                    d = G2[bureau] - g2c\n",
    "                    diff += abs(d)\n",
    "                    m2c = M1[bureau] + D1[bureau] * d1m2/10 + R1[bureau] * r1m2/10\n",
    "                    d = M2[bureau] - m2c\n",
    "                    diff += abs(d)\n",
    "                if diff < 400:\n",
    "                    print(\"  {:4}% {:4}% {:4}% | {:4}% {:4}% {:4}% | {:7.7}\".format(\n",
    "                        d1g2*10, d1a2*10, d1m2*10, r1g2*10, r1a2*10, r1m2*10, diff))"
   ]
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   "execution_count": null,
   "id": "d9eeca84",
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