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Adding fraction math to allocated score #303

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merged 2 commits into from
Jun 26, 2023
Merged

Adding fraction math to allocated score #303

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39c377a
Adding fraction math to allocated score
mikefranze Jun 23, 2023
53c4426
Merge branch 'Equal-Vote:main' into main
mikefranze Jun 23, 2023
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18 changes: 18 additions & 0 deletions backend/package-lock.json
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1 change: 1 addition & 0 deletions backend/package.json
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Original file line number Diff line number Diff line change
Expand Up @@ -29,6 +29,7 @@
"dotenv": "^16.0.0",
"express": "^4.17.3",
"express-async-handler": "^1.2.0",
"fraction.js": "^4.2.0",
"jsonwebtoken": "^9.0.0",
"luxon": "^3.3.0",
"multer": "^1.4.5-lts.1",
Expand Down
106 changes: 60 additions & 46 deletions backend/src/Tabulators/AllocatedScore.ts
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Original file line number Diff line number Diff line change
@@ -1,6 +1,8 @@
import { ballot, candidate, fiveStarCount, allocatedScoreResults, allocatedScoreSummaryData, summaryData, totalScore } from "./ITabulators";

import { IparsedData } from './ParseData'
import Fraction from 'fraction.js'

const ParseData = require("./ParseData");
declare namespace Intl {
class ListFormat {
Expand All @@ -14,10 +16,12 @@ const maxScore = 5;

interface winner_scores {
index: number
ballot_weight: number,
weighted_score: number
ballot_weight: Fraction,
weighted_score: Fraction
}

type ballotFrac = Fraction[]

export function AllocatedScore(candidates: string[], votes: ballot[], nWinners = 3, breakTiesRandomly = true, enablefiveStarTiebreaker = true) {
// Determines STAR-PR winners for given election using Allocated Score
// Parameters:
Expand Down Expand Up @@ -52,29 +56,29 @@ export function AllocatedScore(candidates: string[], votes: ballot[], nWinners =

// Find number of voters and quota size
const V = scoresNorm.length;
const quota = V / nWinners;
const quota = new Fraction(V).div(nWinners);
var num_candidates = candidates.length

var ballot_weights: number[] = Array(V).fill(1);
var ballot_weights: Fraction[] = Array(V).fill(new Fraction(1));

var ties = [];
// var weightedSumsByRound = []
var candidatesByRound: candidate[][] = []
// run loop until specified number of winners are found
while (results.elected.length < nWinners) {
// weight the scores
var weighted_scores: ballot[] = Array(scoresNorm.length);
var weighted_sums: number[] = Array(num_candidates).fill(0);
var weighted_scores: ballotFrac[] = Array(scoresNorm.length);
var weighted_sums: Fraction[] = Array(num_candidates).fill(new Fraction(0));
scoresNorm.forEach((ballot, b) => {
weighted_scores[b] = [];
ballot.forEach((score, s) => {
weighted_scores[b][s] = score * ballot_weights[b];
weighted_sums[s] += weighted_scores[b][s]
weighted_scores[b][s] = score.mul(ballot_weights[b]);
weighted_sums[s] = weighted_sums[s].add(weighted_scores[b][s])
});
// sum scores for each candidate
// weighted_sums[r] = sumArray(weighted_scores[r]);
});
summaryData.weightedScoresByRound.push(weighted_sums)
summaryData.weightedScoresByRound.push(weighted_sums.map(w => w.valueOf()))
candidatesByRound.push([...remainingCandidates])
// get index of winner
var maxAndTies = indexOfMax(weighted_sums, breakTiesRandomly);
Expand All @@ -88,7 +92,7 @@ export function AllocatedScore(candidates: string[], votes: ballot[], nWinners =
results.elected.push(summaryData.candidates[w]);
// Set all scores for winner to zero
scoresNorm.forEach((ballot, b) => {
ballot[w] = 0
ballot[w] = new Fraction(0)
})
remainingCandidates = remainingCandidates.filter(c => c != summaryData.candidates[w])
// remainingCandidates.splice(w, 1);
Expand Down Expand Up @@ -116,27 +120,27 @@ export function AllocatedScore(candidates: string[], votes: ballot[], nWinners =

var split_point = findSplitPoint(cand_df_sorted, quota);

summaryData.splitPoints.push(split_point);
summaryData.splitPoints.push(split_point.valueOf());

var spent_above = 0;
var spent_above = new Fraction(0);
cand_df.forEach((c, i) => {
if (c.weighted_score > split_point) {
spent_above += c.ballot_weight;
if (c.weighted_score.compare(split_point) > 0) {
spent_above = spent_above.add(c.ballot_weight);
}
});
summaryData.spentAboves.push(spent_above);
summaryData.spentAboves.push(spent_above.valueOf());

if (spent_above > 0) {
if (spent_above.valueOf() > 0) {
cand_df.forEach((c, i) => {
if (c.weighted_score > split_point) {
cand_df[i].ballot_weight = 0;
if (c.weighted_score.compare(split_point) > 0) {
cand_df[i].ballot_weight = new Fraction(0);
}
});
}

var weight_on_split = findWeightOnSplit(cand_df, split_point);

summaryData.weight_on_splits.push(weight_on_split);
summaryData.weight_on_splits.push(weight_on_split.valueOf());
ballot_weights = updateBallotWeights(
cand_df,
ballot_weights,
Expand Down Expand Up @@ -263,25 +267,25 @@ function sortData(summaryData: allocatedScoreSummaryData, order: candidate[]): a

function updateBallotWeights(
cand_df: winner_scores[],
ballot_weights: number[],
weight_on_split: number,
quota: number,
spent_above: number,
split_point: number
ballot_weights: Fraction[],
weight_on_split: Fraction,
quota: Fraction,
spent_above: Fraction,
split_point: Fraction
) {
if (weight_on_split > 0) {
var spent_value = (quota - spent_above) / weight_on_split;
if (weight_on_split.compare(0) > 0) {
var spent_value = quota.sub(spent_above).div(weight_on_split);
cand_df.forEach((c, i) => {
if (c.weighted_score === split_point) {
cand_df[i].ballot_weight = cand_df[i].ballot_weight * (1 - spent_value);
if (c.weighted_score.equals(split_point)) {
cand_df[i].ballot_weight = cand_df[i].ballot_weight.mul( (new Fraction(1).sub(spent_value) ) );
}
});
}
cand_df.forEach((c, i) => {
if (c.ballot_weight > 1) {
ballot_weights[i] = 1;
} else if (c.ballot_weight < 0) {
ballot_weights[i] = 0;
if (c.ballot_weight.compare(1) > 0) {
ballot_weights[i] = new Fraction(1);
} else if (c.ballot_weight.compare(0) < 0) {
ballot_weights[i] = new Fraction(0);
} else {
ballot_weights[i] = c.ballot_weight;
}
Expand All @@ -290,17 +294,17 @@ function updateBallotWeights(
return ballot_weights;
}

function findWeightOnSplit(cand_df: winner_scores[], split_point: number) {
var weight_on_split = 0;
function findWeightOnSplit(cand_df: winner_scores[], split_point: Fraction) {
var weight_on_split = new Fraction(0);
cand_df.forEach((c, i) => {
if (c.weighted_score === split_point) {
weight_on_split += c.ballot_weight;
if (c.weighted_score.equals(split_point)) {
weight_on_split = weight_on_split.add(c.ballot_weight);
}
});
return weight_on_split;
}

function indexOfMax(arr: number[], breakTiesRandomly: boolean) {
function indexOfMax(arr: Fraction[], breakTiesRandomly: boolean) {
if (arr.length === 0) {
return { maxIndex: -1, ties: [] };
}
Expand All @@ -309,9 +313,9 @@ function indexOfMax(arr: number[], breakTiesRandomly: boolean) {
var maxIndex = 0;
var ties: number[] = [0];
for (var i = 1; i < arr.length; i++) {
if (Math.abs(max - arr[i]) < 1e-8) {
if (max.equals(arr[i])) {
ties.push(i);
} else if (arr[i] > max) {
} else if (arr[i].compare(max) > 0) {
maxIndex = i;
max = arr[i];
ties = [i];
Expand All @@ -329,28 +333,28 @@ function getRandomInt(max: number) {

function normalizeArray(scores: ballot[], maxScore: number) {
// Normalize scores array
var scoresNorm: ballot[] = Array(scores.length);
var scoresNorm: ballotFrac[] = Array(scores.length);
scores.forEach((row, r) => {
scoresNorm[r] = [];
row.forEach((score, s) => {
scoresNorm[r][s] = score / maxScore;
scoresNorm[r][s] = new Fraction(score).div(maxScore);
});
});
return scoresNorm;
}

function findSplitPoint(cand_df_sorted: winner_scores[], quota: number) {
function findSplitPoint(cand_df_sorted: winner_scores[], quota: Fraction) {
var under_quota = [];
var under_quota_scores: number[] = [];
var cumsum = 0;
var under_quota_scores: Fraction[] = [];
var cumsum = new Fraction(0);
cand_df_sorted.forEach((c, i) => {
cumsum += c.ballot_weight;
cumsum = cumsum.add(c.ballot_weight);
if (cumsum < quota) {
under_quota.push(c);
under_quota_scores.push(c.weighted_score);
}
});
return Math.min(...under_quota_scores);
return findMinFrac(under_quota_scores);
}

function sortMatrix(matrix: number[][], order: number[]) {
Expand All @@ -364,4 +368,14 @@ function sortMatrix(matrix: number[][], order: number[]) {
});
});
return newMatrix
}

function findMinFrac(fracs: Fraction[]) {
let minFrac = fracs[0]
fracs.forEach(frac => {
if (frac.compare(minFrac) < 0) {
minFrac = frac
}
})
return minFrac
}