Voting methods with polars dataframes

requirements.txt

polars
jupyter
numpy
pyarrow
pandas
altair

voting.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import polars as pl\n",
    "import numpy as np\n",
    "import altair as alt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "rs = np.random.RandomState(np.random.MT19937(np.random.SeedSequence(123457789))) #seeded random state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "voters = pl.DataFrame({ # imagine that voters opinions can be mapped into a 2d plane\n",
    "    \"x\": pl.Series(values=rs.normal(size=100, ).tolist()),\n",
    "    \"y\": pl.Series(values=rs.normal(size=100).tolist())\n",
    "})\n",
    "candidates = pl.DataFrame({ # and that they prefer candidates that are close to them\n",
    "    \"x\": pl.Series(values=rs.normal(size=7).tolist()),\n",
    "    \"y\": pl.Series(values=rs.normal(size=7).tolist()),\n",
    "    \"name\": [\"a\", \"b\", \"c\", \"d\", \"e\", \"f\", \"g\"]\n",
    "})\n",
    "election = voters.join(candidates, how=\"cross\", suffix=\"_candidate\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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       "shape: (7, 2)\n",
       "┌──────┬───────┐\n",
       "│ name ┆ count │\n",
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     "metadata": {},
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    }
   ],
   "source": [
    "xdist = (pl.col(\"x\") - pl.col(\"x_candidate\")).pow(2)\n",
    "ydist = (pl.col(\"y\") - pl.col(\"y_candidate\")).pow(2)\n",
    "distance = (xdist + ydist).sqrt().alias(\"distance\")\n",
    "approval_vote = distance <= 1 # simple approval voting strategy; vote for anyone within a set distance o fyou\n",
    "\n",
    "election.lazy().select([ # approval voting can be calculated with a single expression!\n",
    "    pl.col(\"name\").filter(approval_vote),\n",
    "]).groupby(\"name\").agg([pl.count()]).sort(\"count\", reverse=True).collect()"
   ]
  },
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       "vote\n",
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       "shape: (3, 3)\n",
       "┌──────────┬───────────┬─────────────────────┐\n",
       "│ x        ┆ y         ┆ vote                │\n",
       "│ ---      ┆ ---       ┆ ---                 │\n",
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       "╞══════════╪═══════════╪═════════════════════╡\n",
       "│ 0.361286 ┆ -1.464302 ┆ [\"f\", \"b\", ... \"a\"] │\n",
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       "│ 0.25419  ┆ -0.841139 ┆ [\"b\", \"f\", ... \"d\"] │\n",
       "└──────────┴───────────┴─────────────────────┘"
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   ],
   "source": [
    "ballots = election.lazy().select([ # ranked methods are more complicated. Generate a frame of ballots to start with.\n",
    "    \"x\",\n",
    "    \"y\",\n",
    "    \"name\",\n",
    "    distance\n",
    "]).groupby([\"x\", \"y\"]).agg([pl.col(\"name\").sort_by(\"distance\").list().alias(\"vote\")]).collect()\n",
    "ballots.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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       "shape: (7, 2)\n",
       "┌───────────┬───────┐\n",
       "│ candidate ┆ count │\n",
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       "│ d         ┆ 3     │\n",
       "└───────────┴───────┘"
      ]
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     "execution_count": 6,
     "metadata": {},
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   ],
   "source": [
    "first = pl.col(\"vote\").arr.eval(pl.element().first()).explode().alias(\"first\") # selection expression; who's winning right now?\n",
    "count_ballots = lambda df: (df # function to count ballots. We'll need to apply this repeatedly for each round of IRV.\n",
    "    .filter(pl.col(\"vote\").arr.eval(pl.element().len()).explode() > 0)\n",
    "    .select(first.alias(\"candidate\"))\n",
    "    .groupby(\"candidate\")\n",
    "    .agg([pl.count()])\n",
    "    .sort(\"count\"))\n",
    "\n",
    "first_round = count_ballots(ballots) # if we were doing plurality voting, we'd stop here and whoever was on top would win.\n",
    "first_round.reverse()"
   ]
  },
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   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('c', 21), ('b', 19), ('f', 18), ('a', 16), ('e', 13), ('g', 13)]\n",
      "[('b', 24), ('a', 23), ('c', 21), ('f', 18), ('e', 14)]\n",
      "[('a', 33), ('c', 25), ('b', 24), ('f', 18)]\n",
      "[('b', 37), ('a', 33), ('c', 30)]\n",
      "[('b', 67), ('a', 33)]\n"
     ]
    }
   ],
   "source": [
    "rounds = [first_round]\n",
    "live_ballots = ballots\n",
    "loser = first_round[\"candidate\"].take(0)\n",
    "tail = lambda loser: pl.col(\"vote\").arr.eval(pl.element().filter(pl.element() != loser)).alias(\"vote\")\n",
    "frontrunner_votes = rounds[-1][\"count\"].reverse().take(0)[0] # how many votes does the frontrunner have?\n",
    "while frontrunner_votes < 50: # until the frontrunner has a majority, we keep going\n",
    "    live_ballots = live_ballots.select([\"x\", \"y\", tail(loser)])\n",
    "    n_round = count_ballots(live_ballots)\n",
    "    rounds.append(n_round)\n",
    "    loser = n_round[\"candidate\"].take(0)\n",
    "    frontrunner_votes = n_round[\"count\"].reverse().take(0)[0]\n",
    "    print(list(zip(list(n_round[\"candidate\"].reverse()), list(n_round[\"count\"].reverse()))))"
   ]
  },
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       "  })({\"config\": {\"view\": {\"continuousWidth\": 400, \"continuousHeight\": 300}}, \"data\": {\"name\": \"data-92c2ea8da9f039451aa5417bfe50b5fa\"}, \"mark\": \"bar\", \"encoding\": {\"facet\": {\"field\": \"round\", \"type\": \"quantitative\"}, \"x\": {\"field\": \"candidate\", \"type\": \"nominal\"}, \"y\": {\"field\": \"count\", \"type\": \"quantitative\"}}, \"$schema\": \"https://vega.github.io/schema/vega-lite/v4.17.0.json\", \"datasets\": {\"data-92c2ea8da9f039451aa5417bfe50b5fa\": [{\"candidate\": \"d\", \"count\": 3, \"round\": 1}, {\"candidate\": \"g\", \"count\": 13, \"round\": 1}, {\"candidate\": \"e\", \"count\": 13, \"round\": 1}, {\"candidate\": \"a\", \"count\": 16, \"round\": 1}, {\"candidate\": \"f\", \"count\": 17, \"round\": 1}, {\"candidate\": \"c\", \"count\": 19, \"round\": 1}, {\"candidate\": \"b\", \"count\": 19, \"round\": 1}, {\"candidate\": \"g\", \"count\": 13, \"round\": 2}, {\"candidate\": \"e\", \"count\": 13, \"round\": 2}, {\"candidate\": \"a\", \"count\": 16, \"round\": 2}, {\"candidate\": \"f\", \"count\": 18, \"round\": 2}, {\"candidate\": \"b\", \"count\": 19, \"round\": 2}, {\"candidate\": \"c\", \"count\": 21, \"round\": 2}, {\"candidate\": \"e\", \"count\": 14, \"round\": 3}, {\"candidate\": \"f\", \"count\": 18, \"round\": 3}, {\"candidate\": \"c\", \"count\": 21, \"round\": 3}, {\"candidate\": \"a\", \"count\": 23, \"round\": 3}, {\"candidate\": \"b\", \"count\": 24, \"round\": 3}, {\"candidate\": \"f\", \"count\": 18, \"round\": 4}, {\"candidate\": \"b\", \"count\": 24, \"round\": 4}, {\"candidate\": \"c\", \"count\": 25, \"round\": 4}, {\"candidate\": \"a\", \"count\": 33, \"round\": 4}, {\"candidate\": \"c\", \"count\": 30, \"round\": 5}, {\"candidate\": \"a\", \"count\": 33, \"round\": 5}, {\"candidate\": \"b\", \"count\": 37, \"round\": 5}, {\"candidate\": \"a\", \"count\": 33, \"round\": 6}, {\"candidate\": \"b\", \"count\": 67, \"round\": 6}]}}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.Chart(...)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_rounds = pl.concat([round.select([pl.all(), pl.lit(i + 1).alias(\"round\")]) for i, round in enumerate(rounds)]).to_pandas()\n",
    "alt.Chart(all_rounds).mark_bar().encode(\n",
    "    facet='round',\n",
    "    x='candidate',\n",
    "    y='count'\n",
    ")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.8.10 64-bit",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.6"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "949777d72b0d2535278d3dc13498b2535136f6dfe0678499012e853ee9abcab1"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}

Sad that altair charts don't seem to work in gists, but the random seed should mean that this is runnable locally if you are curious.