01-StableVoting.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stable Voting\n",
    "\n",
    "Implementation of Simple Stable Voting and Stable Voting from the paper [Stable Voting](https://arxiv.org/abs/2108.00542) by W. Holliday and E. Pacuit.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import the Profile class\n",
    "from pref_voting.profiles import *\n",
    "from pref_voting.voting_method import *\n",
    "# import the voting methods\n",
    "from pref_voting.voting_methods import *\n",
    "\n",
    "from pref_voting.generate_profiles import *\n",
    "import math"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simple Stable Voting \n",
    "\n",
    "Simple Stable Voting selects a winner as follows:\n",
    "\n",
    "1. If only one candidate $a$ appears on all ballots, then $a$ wins.\n",
    "2. Otherwise list all head-to-head matches of the form $a$ vs. $b$ in order from the largest to smallest margin of $a$ vs. $b$. Find the first match $a$ vs. $b$ in the list such that $a$ wins according to Simple Stable Voting *after $b$ is removed from all ballots*; this $a$ is the winner for the original set of ballots.  \n",
    "\n",
    "Note that if there are two (or more) earliest matches $a$ vs. $b$ and $a'$ vs. $b'$ in the list with the same margins such that $a$ wins after $b$ is removed from the ballots, and $a'$ wins after $b'$ is removed from the ballots, then $a$ and $a'$ are tied Simple Stable Voting winners for the original set of ballots.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This code is available in pref_voting.margin_methods.py but is included here for reference. \n",
    "\n",
    "# Simple Stable Voting \n",
    "def _simple_stable_voting(curr_cands, \n",
    "                          sorted_matches,\n",
    "                          mem_sv_winners): \n",
    "    '''\n",
    "    Determine the Simple Stable Voting winners while keeping track \n",
    "    of the winners in any subprofiles checked during computation. \n",
    "    '''\n",
    "    \n",
    "    sv_winners = list()\n",
    "        \n",
    "    if len(curr_cands) == 1: \n",
    "        mem_sv_winners[tuple(curr_cands)] = curr_cands\n",
    "        return curr_cands, mem_sv_winners\n",
    "    \n",
    "    margin_witnessing_win = -math.inf\n",
    "\n",
    "    for a, b, s in sorted_matches:\n",
    "        if s < margin_witnessing_win: \n",
    "            break\n",
    "        if a not in sv_winners: \n",
    "            cands_minus_b = [c for c in curr_cands if c != b]\n",
    "            cands_minus_b_key = tuple(sorted(cands_minus_b))\n",
    "            if cands_minus_b_key not in mem_sv_winners.keys(): \n",
    "                ws, mem_sv_winners = _simple_stable_voting(curr_cands = cands_minus_b,\n",
    "                                                           sorted_matches = [(a, c, s) for a, c, s in sorted_matches \n",
    "                                                                             if a != b and c != b],\n",
    "                                                           mem_sv_winners = mem_sv_winners)\n",
    "                mem_sv_winners[cands_minus_b_key] = ws\n",
    "            else: \n",
    "                ws = mem_sv_winners[cands_minus_b_key]\n",
    "            if a in ws:\n",
    "                sv_winners.append(a)\n",
    "                margin_witnessing_win = s\n",
    "                \n",
    "    return sv_winners, mem_sv_winners\n",
    "\n",
    "          \n",
    "@vm(name = \"Simple Stable Voting\")\n",
    "def simple_stable_voting(edata, curr_cands = None, strength_function = None):  \n",
    "\n",
    "    curr_cands = edata.candidates if curr_cands is None else curr_cands\n",
    "    strength_function = edata.margin if strength_function is None else strength_function  \n",
    "\n",
    "    matches = [(a, b, strength_function(a, b)) for a in curr_cands for b in curr_cands if a != b]\n",
    "    sorted_matches = sorted(matches, reverse=True, key=lambda m_w_weight: m_w_weight[2])\n",
    "    \n",
    "    return sorted(_simple_stable_voting(curr_cands = curr_cands,  \n",
    "                                        sorted_matches = sorted_matches,\n",
    "                                        mem_sv_winners = {})[0])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stable Voting\n",
    "\n",
    "Stable Voting is defined analogously to Simple Stable Voting:\n",
    "\n",
    "1. If there is only one undefeated candidate  $a$, then $a$ wins.\n",
    "2. Otherwise list all head-to-head matches of the form $a$ vs. $b$ in order from the largest to smallest margin of $a$ vs. $b$, where $a$ is undefeated. Find the first match $a$ vs. $b$ in the list such that $a$ wins according to  Stable Voting *after $b$ is removed from all ballots*; this $a$ is the winner for the original set of ballots.  \n",
    "\n",
    "We say that $b$ *does not defeat* $a$ if we can make a list of candidates starting with $a$ and ending with $b$ such that the margin of each candidate vs. the next candidate in the list is at least the margin of $b$ vs. $a$; if there is no such list, then $b$ defeats $a$; and $a$ is undefeated if there is no $b$ that defeats $a$ (this notion of defeat is defended at length in [Axioms for Defeat in Democratic Elections](https://arxiv.org/abs/2008.08451)). \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_undefeated_candidates(edata, curr_cands = None):   \n",
    "    \"\"\"\n",
    "    A path from candidate a to candidate b is a list of candidates starting with a and ending with b \n",
    "    such that each candidate in the list has a nonzero margin vs. the next candidate in the list. \n",
    "    The strength of a path is the minimum margin between consecutive candidates in the path \n",
    "    The strength of the pair of candidates (a,b) is strength of the strongest path from a to b.   \n",
    "    We find these strengths using the Floyd-Warshall Algorithm.   \n",
    "    \n",
    "    A candidate c is undefeated if for all candidates d that are majority preferred to c, \n",
    "    the strength of the strongest path from c to d is at least the margin of d over c. \n",
    "    \n",
    "    Note that this is an implementation of the Split Cycle voting method. \n",
    "    \"\"\"\n",
    "    curr_cands = curr_cands if curr_cands is not None else edata.candidates\n",
    "    mg = [[-np.inf for _ in curr_cands] for _ in curr_cands]\n",
    "    for c1_idx,c1 in enumerate(curr_cands):\n",
    "        for c2_idx,c2 in enumerate(curr_cands):\n",
    "            if edata.margin(c1,c2) > 0:\n",
    "                mg[c1_idx][c2_idx] = edata.margin(c1, c2)   \n",
    "\n",
    "    # initial strength to mg\n",
    "    strength = list(map(lambda i : list(map(lambda j : j , i)) , mg))\n",
    "    \n",
    "    for i_idx, i in enumerate(curr_cands):         \n",
    "        for j_idx, j in enumerate(curr_cands): \n",
    "            if i != j:\n",
    "                for k_idx, k in enumerate(curr_cands): \n",
    "                    if i!= k and j != k:\n",
    "                        strength[j_idx][k_idx] = max(strength[j_idx][k_idx], min(strength[j_idx][i_idx], strength[i_idx][k_idx]))\n",
    "    undefeated = {i:True for i in curr_cands}\n",
    "    for i_idx, i in enumerate(curr_cands): \n",
    "        for j_idx,j in enumerate(curr_cands):\n",
    "            if i != j:\n",
    "                if mg[j_idx][i_idx] > strength[i_idx][j_idx]: # the main difference with Beat Path\n",
    "                    undefeated[i] = False\n",
    "                    \n",
    "    return sorted([c for c in curr_cands if undefeated[c]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "def _stable_voting(edata, \n",
    "                   curr_cands,\n",
    "                   strength_function,\n",
    "                   sorted_matches,\n",
    "                   mem_sv_winners): \n",
    "    '''\n",
    "    Determine the Stable Voting winners for the profile while keeping track of the winners in any subprofiles checked during computation. \n",
    "    '''\n",
    "    \n",
    "    sv_winners = list()\n",
    "    \n",
    "    undefeated_candidates = find_undefeated_candidates(edata, curr_cands = curr_cands)\n",
    "        \n",
    "    if len(curr_cands) == 1: \n",
    "        mem_sv_winners[tuple(curr_cands)] = curr_cands\n",
    "        return curr_cands, mem_sv_winners\n",
    "    \n",
    "    margin_witnessing_win = -math.inf\n",
    "\n",
    "    for a, b, s in sorted_matches:\n",
    "        if s < margin_witnessing_win: \n",
    "            break\n",
    "        if a in undefeated_candidates and a not in sv_winners: \n",
    "            cands_minus_b = [c for c in curr_cands if c != b]\n",
    "            cands_minus_b_key = tuple(sorted(cands_minus_b))\n",
    "            if cands_minus_b_key not in mem_sv_winners.keys(): \n",
    "                ws, mem_sv_winners = _stable_voting(edata,\n",
    "                                                    curr_cands = cands_minus_b,\n",
    "                                                    strength_function = strength_function,\n",
    "                                                    sorted_matches = [(a, c, s) for a, c, s in sorted_matches \n",
    "                                                                      if a != b and c != b],\n",
    "                                                    mem_sv_winners = mem_sv_winners)\n",
    "                mem_sv_winners[cands_minus_b_key] = ws\n",
    "            else: \n",
    "                ws = mem_sv_winners[cands_minus_b_key]\n",
    "            if a in ws:\n",
    "                sv_winners.append(a)\n",
    "                margin_witnessing_win = s\n",
    "                \n",
    "    return sv_winners, mem_sv_winners\n",
    "\n",
    "        \n",
    "@vm(name = \"Stable Voting\")\n",
    "def stable_voting(edata, curr_cands = None, strength_function = None): \n",
    "\n",
    "    curr_cands = edata.candidates if curr_cands is None else curr_cands\n",
    "    strength_function = edata.margin if strength_function is None else strength_function  \n",
    "\n",
    "    matches = [(a, b, strength_function(a, b)) for a in curr_cands for b in curr_cands if a != b]\n",
    "    sorted_matches = sorted(matches, reverse=True, key=lambda m_w_weight: m_w_weight[2])\n",
    "\n",
    "    return sorted(_stable_voting(edata, \n",
    "                                 curr_cands = curr_cands, \n",
    "                                 strength_function = strength_function,\n",
    "                                 sorted_matches = sorted_matches,\n",
    "                                 mem_sv_winners = {})[0])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stable Voting\n",
    "\n",
    "The following examples (not included in the paper) illustrate (Simple) Stable Voting.  For the examples in the paper see the notebook StableVotingExamples.ipynb. "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example A\n",
    "\n",
    "The following is an example with a Condorcet winner ($B$) where the Instant Runoff winner ($A$) and the Plurality winners ($A$ and $C$) are different than the SV winner ($B$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---+---+---+\n",
      "| 2 | 1 | 2 |\n",
      "+---+---+---+\n",
      "| A | B | C |\n",
      "| B | A | B |\n",
      "| C | C | A |\n",
      "+---+---+---+\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Instant Runoff winner is {A}\n",
      "Plurality winners are {A, C}\n",
      "Stable Voting winner is {B}\n",
      "Simple Stable Voting winner is {B}\n",
      "Condorcet winner is {B}\n"
     ]
    }
   ],
   "source": [
    "A = 0\n",
    "B = 1 \n",
    "C = 2\n",
    "\n",
    "cmap = {A: \"A\", B: \"B\", C: \"C\" }\n",
    "prof = Profile(\n",
    "    [\n",
    "        (A, B, C),\n",
    "        (B, A, C), \n",
    "        (C, B, A)\n",
    "    ], \n",
    "    rcounts = [2, 1, 2], \n",
    "    cmap=cmap\n",
    ")\n",
    "\n",
    "prof.display()\n",
    "\n",
    "prof.display_margin_graph()\n",
    "instant_runoff.display(prof)\n",
    "plurality.display(prof)\n",
    "stable_voting.display(prof)\n",
    "simple_stable_voting.display(prof)\n",
    "condorcet.display(prof)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example B\n",
    "\n",
    "The following is an example without a Condorcet winner where the Instant Runoff winner ($D$) and the Plurality winners ($C$ and $D$),  and the Beat Path and Ranked Pairs winners ($B$, $C$ and $D$) are all different than the SV winner ($B$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---+---+---+---+\n",
      "| 2 | 1 | 1 | 1 |\n",
      "+---+---+---+---+\n",
      "| C | D | D | B |\n",
      "| B | A | B | D |\n",
      "| A | C | A | A |\n",
      "| D | B | C | C |\n",
      "+---+---+---+---+\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Instant Runoff winner is {D}\n",
      "Plurality winners are {C, D}\n",
      "Stable Voting winner is {B}\n",
      "Simple Stable Voting winner is {B}\n",
      "Beat Path winners are {B, C, D}\n",
      "Ranked Pairs winners are {B, C, D}\n"
     ]
    }
   ],
   "source": [
    "A = 0\n",
    "B = 1 \n",
    "C = 2\n",
    "D = 3\n",
    "\n",
    "cmap = {A: \"A\", B: \"B\", C: \"C\", D: \"D\" }\n",
    "prof = Profile(\n",
    "    [\n",
    "        (C, B, A, D),\n",
    "        (D, A, C, B), \n",
    "        (D, B, A, C),\n",
    "        (B, D, A, C)\n",
    "], \n",
    "    rcounts = [2, 1, 1, 1], \n",
    "    cmap=cmap\n",
    ")\n",
    "\n",
    "\n",
    "prof.display()\n",
    "\n",
    "prof.display_margin_graph()\n",
    "\n",
    "instant_runoff.display(prof)\n",
    "plurality.display(prof)\n",
    "stable_voting.display(prof)\n",
    "simple_stable_voting.display(prof)\n",
    "beat_path_Floyd_Warshall.display(prof)\n",
    "ranked_pairs.display(prof)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example C\n",
    "\n",
    "A different profile generating the same margin graph as in Example 2 above. This is an example without a Condorcet winner where the Instant Runoff winner ($C$), the Plurality winners ($B$ and $C$), and the Beat Path and Ranked Pairs winners ($B$, $C$ and $D$) are all different than the SV winner ($B$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---+---+---+---+---+\n",
      "| 1 | 1 | 1 | 1 | 1 |\n",
      "+---+---+---+---+---+\n",
      "| A | B | C | C | B |\n",
      "| D | D | B | D | A |\n",
      "| C | A | D | B | D |\n",
      "| B | C | A | A | C |\n",
      "+---+---+---+---+---+\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Instant Runoff winner is {C}\n",
      "Plurality winners are {B, C}\n",
      "Stable Voting winner is {B}\n",
      "Simple Stable Voting winner is {B}\n",
      "Beat Path winners are {B, C, D}\n",
      "Ranked Pairs winners are {B, C, D}\n"
     ]
    }
   ],
   "source": [
    "A = 0\n",
    "B = 1 \n",
    "C = 2\n",
    "D = 3\n",
    "\n",
    "cmap = {A: \"A\", B: \"B\", C: \"C\", D: \"D\" }\n",
    "prof = Profile(\n",
    "    [\n",
    "        (A, D, C, B),\n",
    "        (B, D, A, C),\n",
    "        (C, B, D, A),\n",
    "        (C, D, B, A), \n",
    "        (B, A, D, C)\n",
    "],\n",
    "    rcounts = [1, 1, 1, 1, 1], \n",
    "    cmap=cmap\n",
    ")\n",
    "\n",
    "prof.display()\n",
    "\n",
    "prof.display_margin_graph()\n",
    "\n",
    " \n",
    "instant_runoff.display(prof)\n",
    "plurality.display(prof)\n",
    "stable_voting.display(prof)\n",
    "simple_stable_voting.display(prof)\n",
    "beat_path_Floyd_Warshall.display(prof)\n",
    "ranked_pairs.display(prof)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example D\n",
    "\n",
    "An example in which the Ranked Pairs winners ($D$) is different than the Beat Path winners ($A$ and $D$), and both differ from the Stable Voting winner ($A$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---+---+---+---+---+---+---+---+\n",
      "| 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |\n",
      "+---+---+---+---+---+---+---+---+\n",
      "| D | A | B | A | D | A | C | C |\n",
      "| A | C | D | B | A | D | B | A |\n",
      "| C | B | A | D | B | C | D | B |\n",
      "| B | D | C | C | C | B | A | D |\n",
      "+---+---+---+---+---+---+---+---+\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Instant Runoff winner is {D}\n",
      "Plurality winners are {A, D}\n",
      "Stable Voting winner is {A}\n",
      "Simple Stable Voting winner is {A}\n",
      "Beat Path winners are {A, D}\n",
      "Ranked Pairs winner is {D}\n"
     ]
    }
   ],
   "source": [
    "A = 0\n",
    "B = 1 \n",
    "C = 2\n",
    "D = 3\n",
    "\n",
    "cmap = {A: \"A\", B: \"B\", C: \"C\", D: \"D\" }\n",
    "prof = Profile(\n",
    "    [\n",
    "        (D, A, C, B),\n",
    "        (A, C, B, D), \n",
    "        (B, D, A, C),\n",
    "        (A, B, D, C), \n",
    "        (D, A, B, C), \n",
    "        (A, D, C, B), \n",
    "        (C, B, D, A), \n",
    "        (C, A, B, D)\n",
    "],\n",
    "    rcounts = [2, 1, 1, 1, 1, 1, 1, 1], \n",
    "    cmap=cmap\n",
    ")\n",
    "\n",
    "prof.display()\n",
    "\n",
    "prof.display_margin_graph()\n",
    "\n",
    " \n",
    "instant_runoff.display(prof)\n",
    "plurality.display(prof)\n",
    "stable_voting.display(prof)\n",
    "simple_stable_voting.display(prof)\n",
    "beat_path_Floyd_Warshall.display(prof)\n",
    "ranked_pairs.display(prof)"
   ]
  }
 ],
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