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| 1 | <?php |
| 2 | |
| 3 | namespace MediaWiki\Extension\SecurePoll\Talliers; |
| 4 | |
| 5 | use MediaWiki\Extension\SecurePoll\Context; |
| 6 | use MediaWiki\Extension\SecurePoll\Entities\Question; |
| 7 | use MediaWiki\Extension\SecurePoll\Talliers\STVFormatter\HtmlFormatter; |
| 8 | use MediaWiki\Extension\SecurePoll\Talliers\STVFormatter\WikitextFormatter; |
| 9 | |
| 10 | /** |
| 11 | * A STVTallier class, |
| 12 | * This implementation is based mainly on |
| 13 | * https://web.archive.org/web/20210225045400/https://prfound.org/resources/reference/reference-meek-rule/ |
| 14 | * and |
| 15 | * Hill's programmatic implementation - We follow NZ implementation found in this paper |
| 16 | * https://web.archive.org/web/20210723092928/https://ucid.es/system/files/meekm_0.pdf |
| 17 | * Major differences being |
| 18 | * 1. We do not use pseudo random elimination of candidates. |
| 19 | * |
| 20 | * Other sources |
| 21 | * https://web.archive.org/web/20210723092923/https://rangevoting.org/MeekSTV2.html |
| 22 | * https://web.archive.org/web/20200712142326/http://www.votingmatters.org.uk/ISSUE1/P1.HTM |
| 23 | */ |
| 24 | class STVTallier extends Tallier { |
| 25 | |
| 26 | /** |
| 27 | * An array of vote combinations keyed by underscore-delimited |
| 28 | * and ranked options. Each vote has a rank array (which allows |
| 29 | * index-1 access to each ranked option) and a count |
| 30 | * @var array |
| 31 | */ |
| 32 | public $rankedVotes = []; |
| 33 | |
| 34 | /** |
| 35 | * An array of results, gets populated per round |
| 36 | * holds current round, both elected and eliminated candidate and the total votes per round. |
| 37 | * @var array[] |
| 38 | */ |
| 39 | public $resultsLog = [ |
| 40 | 'elected' => [], |
| 41 | 'eliminated' => [], |
| 42 | 'rounds' => [] |
| 43 | ]; |
| 44 | |
| 45 | /** |
| 46 | * Number of seats to be filled. |
| 47 | * @var int |
| 48 | */ |
| 49 | private $seats; |
| 50 | |
| 51 | /** |
| 52 | * An array of all candidates in the election. |
| 53 | * @var array<int, string> |
| 54 | */ |
| 55 | private $candidates = []; |
| 56 | |
| 57 | /** |
| 58 | * @param Context $context |
| 59 | * @param ElectionTallier $electionTallier |
| 60 | * @param Question $question |
| 61 | */ |
| 62 | public function __construct( $context, $electionTallier, $question ) { |
| 63 | parent::__construct( $context, $electionTallier, $question ); |
| 64 | foreach ( $question->getOptions() as $option ) { |
| 65 | $this->candidates[ $option->getId() ] = $option->getMessage( 'text' ); |
| 66 | } |
| 67 | $this->seats = $question->getProperty( 'min-seats' ); |
| 68 | } |
| 69 | |
| 70 | /** |
| 71 | * @inheritDoc |
| 72 | */ |
| 73 | public function addVote( $scores ) { |
| 74 | $id = implode( '_', $scores ); |
| 75 | $rank = []; |
| 76 | foreach ( $scores as $ranked => $optionId ) { |
| 77 | $rank[ $ranked + 1 ] = $optionId; |
| 78 | } |
| 79 | |
| 80 | if ( !isset( $this->rankedVotes[ $id ] ) ) { |
| 81 | $this->rankedVotes[ $id ] = [ |
| 82 | 'count' => 1, |
| 83 | 'rank' => $rank, |
| 84 | ]; |
| 85 | } else { |
| 86 | $this->rankedVotes[ $id ][ 'count' ] += 1; |
| 87 | } |
| 88 | |
| 89 | return true; |
| 90 | } |
| 91 | |
| 92 | public function loadJSONResult( array $data ) { |
| 93 | $this->resultsLog = $data['resultsLog']; |
| 94 | $this->rankedVotes = $data['rankedVotes']; |
| 95 | } |
| 96 | |
| 97 | public function getJSONResult() { |
| 98 | return [ |
| 99 | 'resultsLog' => $this->resultsLog, |
| 100 | 'rankedVotes' => $this->rankedVotes, |
| 101 | ]; |
| 102 | } |
| 103 | |
| 104 | public function getHtmlResult() { |
| 105 | $htmlFormatter = new HtmlFormatter( |
| 106 | $this->resultsLog, |
| 107 | $this->rankedVotes, |
| 108 | $this->seats, |
| 109 | $this->candidates |
| 110 | ); |
| 111 | $htmlPreamble = $htmlFormatter->formatPreamble( |
| 112 | $this->resultsLog['elected'], |
| 113 | $this->resultsLog['eliminated'] |
| 114 | ); |
| 115 | $htmlRounds = $htmlFormatter->formatRoundsPreamble(); |
| 116 | $htmlRounds->appendContent( $htmlFormatter->formatRound() ); |
| 117 | return new \OOUI\StackLayout( [ |
| 118 | 'items' => [ |
| 119 | $htmlPreamble, |
| 120 | $htmlRounds, |
| 121 | ], |
| 122 | 'continuous' => true, |
| 123 | 'expanded' => false, |
| 124 | 'classes' => [ 'election-tally-results--stv' ] |
| 125 | ] ); |
| 126 | } |
| 127 | |
| 128 | public function getTextResult() { |
| 129 | $wikitextFormatter = new WikitextFormatter( |
| 130 | $this->resultsLog, |
| 131 | $this->rankedVotes, |
| 132 | $this->seats, |
| 133 | $this->candidates |
| 134 | ); |
| 135 | $wikitext = $wikitextFormatter->formatPreamble( |
| 136 | $this->resultsLog['elected'], |
| 137 | $this->resultsLog['eliminated'] |
| 138 | ); |
| 139 | $wikitext .= $wikitextFormatter->formatRoundsPreamble(); |
| 140 | $wikitext .= $wikitextFormatter->formatRound(); |
| 141 | return $wikitext; |
| 142 | } |
| 143 | |
| 144 | /** |
| 145 | * @inheritDoc |
| 146 | */ |
| 147 | public function finishTally() { |
| 148 | // Instantiate first round for the iterator |
| 149 | $keepFactors = array_fill_keys( array_keys( $this->candidates ), 1 ); |
| 150 | $voteCount = $this->distributeVotes( $this->rankedVotes, $keepFactors ); |
| 151 | $quota = $this->calculateDroopQuota( $voteCount['totalVotes'], $this->seats ); |
| 152 | $round = [ |
| 153 | 'round' => 1, |
| 154 | 'surplus' => 0, |
| 155 | 'rankings' => $voteCount['ranking'], |
| 156 | 'totalVotes' => $voteCount['totalVotes'], |
| 157 | 'keepFactors' => $keepFactors, |
| 158 | 'quota' => $quota, |
| 159 | 'elected' => [], |
| 160 | 'eliminated' => [] |
| 161 | ]; |
| 162 | $this->resultsLog['rounds'][] = $round; |
| 163 | |
| 164 | // Iterate |
| 165 | $this->calculateRound( $round ); |
| 166 | } |
| 167 | |
| 168 | /** |
| 169 | * @param array $prevRound |
| 170 | */ |
| 171 | private function calculateRound( $prevRound ) { |
| 172 | if ( count( $this->resultsLog['elected'] ) >= $this->seats ) { |
| 173 | return; |
| 174 | } |
| 175 | |
| 176 | // Advance the round |
| 177 | $round = [ |
| 178 | 'round' => $prevRound['round'] + 1, |
| 179 | 'elected' => [], |
| 180 | 'eliminated' => [], |
| 181 | 'surplus' => 0, |
| 182 | ]; |
| 183 | |
| 184 | $keepFactors = |
| 185 | $round['keepFactors'] = |
| 186 | $this->calculateKeepFactors( |
| 187 | $this->candidates, |
| 188 | $prevRound['quota'], |
| 189 | $prevRound['keepFactors'], |
| 190 | $this->resultsLog['elected'], |
| 191 | $this->resultsLog['eliminated'], |
| 192 | $prevRound['rankings'] |
| 193 | ); |
| 194 | |
| 195 | $voteCount = $this->distributeVotes( $this->rankedVotes, $keepFactors, $prevRound['rankings'] ); |
| 196 | $round['quota'] = $this->calculateDroopQuota( $voteCount['totalVotes'], $this->seats ); |
| 197 | $round['rankings'] = $voteCount['ranking']; |
| 198 | $round['totalVotes'] = $voteCount['totalVotes']; |
| 199 | |
| 200 | // Check for unique winners |
| 201 | $allWinners = $this->declareWinners( $round['rankings'], $round['quota'] ); |
| 202 | $roundWinners = $round['elected'] = array_diff( $allWinners, $this->resultsLog['elected'] ); |
| 203 | |
| 204 | // If no winners, check for eliminated (no distribution happens here) |
| 205 | $round['surplus'] = $this->calculateSurplus( $round['rankings'], $allWinners, $round['quota'] ); |
| 206 | $allEliminated = $this->declareEliminated( |
| 207 | $round['rankings'], |
| 208 | $round['surplus'], |
| 209 | $this->resultsLog['eliminated'], |
| 210 | $this->resultsLog['elected'], |
| 211 | $prevRound['surplus'] |
| 212 | ); |
| 213 | $roundEliminated = $round['eliminated'] = !$roundWinners ? |
| 214 | array_diff( $allEliminated, $this->resultsLog['eliminated'] ) : []; |
| 215 | |
| 216 | $this->resultsLog['rounds'][] = $round; |
| 217 | $this->resultsLog['elected'] = array_merge( $this->resultsLog['elected'], $roundWinners ); |
| 218 | $this->resultsLog['eliminated'] = array_merge( $this->resultsLog['eliminated'], $roundEliminated ); |
| 219 | |
| 220 | // Recurse? |
| 221 | $hopefuls = array_diff( |
| 222 | array_keys( $this->candidates ), |
| 223 | array_merge( $this->resultsLog['elected'], $this->resultsLog['eliminated'] ) |
| 224 | ); |
| 225 | if ( $hopefuls ) { |
| 226 | $this->calculateRound( $round ); |
| 227 | } |
| 228 | } |
| 229 | |
| 230 | /** |
| 231 | * Distribute votes per ballot |
| 232 | * For each ballot: set ballot weight($weight) to 1, |
| 233 | * and then for each candidate, |
| 234 | * in order of rank on that ballot: |
| 235 | * add $weight multiplied by the keep factor ($voteValue) of the candidate ($keepFactors[$candidate]) |
| 236 | * to that candidate’s vote $voteTotals[$candidate]['total'], and reduce $weight by $voteValue, |
| 237 | * until no further candidate remains on the ballot. |
| 238 | * @param array $ballots |
| 239 | * @param array $keepFactors |
| 240 | * @param null $prevDistribution |
| 241 | * @return array |
| 242 | */ |
| 243 | private function distributeVotes( $ballots, $keepFactors, $prevDistribution = null ): array { |
| 244 | $voteTotals = []; |
| 245 | $totalVotes = 0; |
| 246 | foreach ( $keepFactors as $candidate => $kf ) { |
| 247 | $voteTotals[$candidate] = [ |
| 248 | 'votes' => 0, |
| 249 | 'earned' => 0, |
| 250 | 'total' => 0, |
| 251 | ]; |
| 252 | } |
| 253 | |
| 254 | // Apply previous round's votes to the count to get "earned" votes |
| 255 | if ( $prevDistribution ) { |
| 256 | foreach ( $prevDistribution as $candidate => $candidateVotes ) { |
| 257 | $voteTotals[$candidate]['votes'] = $candidateVotes['total']; |
| 258 | $voteTotals[$candidate]['earned'] -= $candidateVotes['total']; |
| 259 | } |
| 260 | |
| 261 | } |
| 262 | |
| 263 | foreach ( $ballots as $ballot ) { |
| 264 | $weight = 1; |
| 265 | foreach ( $ballot['rank'] as $candidate ) { |
| 266 | if ( $weight > 0 ) { |
| 267 | $voteValue = $weight * $keepFactors[$candidate]; |
| 268 | $voteTotals[$candidate]['earned'] += ( $voteValue * $ballot['count'] ); |
| 269 | $voteTotals[$candidate]['total'] += ( $voteValue * $ballot['count'] ); |
| 270 | $weight -= $voteValue; |
| 271 | $totalVotes += ( $voteValue * $ballot['count'] ); |
| 272 | } else { |
| 273 | break; |
| 274 | } |
| 275 | } |
| 276 | |
| 277 | } |
| 278 | |
| 279 | return [ |
| 280 | 'ranking' => $voteTotals, |
| 281 | 'totalVotes' => $totalVotes, |
| 282 | ]; |
| 283 | } |
| 284 | |
| 285 | /** |
| 286 | * @param int|float $votes |
| 287 | * @param int $seats |
| 288 | * @return float |
| 289 | */ |
| 290 | private function calculateDroopQuota( $votes, $seats ): float { |
| 291 | return ( $votes / ( (float)$seats + 1 ) ) + 0.000001; |
| 292 | } |
| 293 | |
| 294 | /** |
| 295 | * Calculates keep factors of all elected candidate at every round |
| 296 | * calculated as: current keepfactor multiplied by current quota divided by candidates current vote($voteTotals) |
| 297 | * @param array $candidates |
| 298 | * @param float $quota |
| 299 | * @param array $currentFactors |
| 300 | * @param array $winners |
| 301 | * @param array $eliminated |
| 302 | * @param array $voteTotals |
| 303 | * @return array |
| 304 | */ |
| 305 | private function calculateKeepFactors( $candidates, $quota, $currentFactors, $winners, $eliminated, $voteTotals ) { |
| 306 | $keepFactors = []; |
| 307 | foreach ( $candidates as $candidateId => $candidateName ) { |
| 308 | $keepFactors[$candidateId] = in_array( $candidateId, $eliminated ) ? 0 : 1; |
| 309 | } |
| 310 | |
| 311 | foreach ( $winners as $winner ) { |
| 312 | $voteCount = $voteTotals[$winner]['total']; |
| 313 | $prevKeepFactor = $currentFactors[$winner]; |
| 314 | $keepFactors[$winner] = ( $prevKeepFactor * $quota ) / $voteCount; |
| 315 | } |
| 316 | return $keepFactors; |
| 317 | } |
| 318 | |
| 319 | /** |
| 320 | * @param array $ranking |
| 321 | * @param array $winners |
| 322 | * @param float $quota |
| 323 | * @return int|float |
| 324 | */ |
| 325 | private function calculateSurplus( $ranking, $winners, $quota ) { |
| 326 | $voteSurplus = 0; |
| 327 | foreach ( $winners as $winner ) { |
| 328 | $voteTotal = $ranking[$winner]['total']; |
| 329 | $voteSurplus += $voteTotal - $quota; |
| 330 | } |
| 331 | return $voteSurplus; |
| 332 | } |
| 333 | |
| 334 | /** |
| 335 | * @param array $ranking |
| 336 | * @param float $quota |
| 337 | * @return array |
| 338 | */ |
| 339 | private function declareWinners( $ranking, $quota ) { |
| 340 | $winners = []; |
| 341 | foreach ( $ranking as $option => $votes ) { |
| 342 | if ( $votes['total'] >= $quota ) { |
| 343 | $winners[] = $option; |
| 344 | } |
| 345 | } |
| 346 | return $winners; |
| 347 | } |
| 348 | |
| 349 | /** |
| 350 | * @param array $ranking |
| 351 | * @param int|float $surplus |
| 352 | * @param array $eliminated |
| 353 | * @param array $elected |
| 354 | * @param int|float $prevSurplus |
| 355 | * @return array |
| 356 | */ |
| 357 | private function declareEliminated( $ranking, $surplus, $eliminated, $elected, $prevSurplus ) { |
| 358 | // Make sure it's ordered by vote totals |
| 359 | uksort( |
| 360 | $ranking, |
| 361 | static function ( $aKey, $bKey ) use ( $ranking ) { |
| 362 | $a = $ranking[$aKey]; |
| 363 | $b = $ranking[$bKey]; |
| 364 | if ( $a['total'] === $b['total'] ) { |
| 365 | // ascending sort |
| 366 | return $aKey <=> $bKey; |
| 367 | } |
| 368 | // descending sort |
| 369 | return $b['total'] <=> $a['total']; |
| 370 | } |
| 371 | ); |
| 372 | |
| 373 | // Remove anyone who was already eliminated or elected |
| 374 | $ranking = array_filter( $ranking, static function ( $key ) use ( $eliminated ) { |
| 375 | return !in_array( $key, $eliminated ); |
| 376 | }, ARRAY_FILTER_USE_KEY ); |
| 377 | |
| 378 | // Manually implement array_unique with higher precision than the default function |
| 379 | $voteTotals = []; |
| 380 | foreach ( $ranking as $candidate ) { |
| 381 | // Since it's already been ordered by vote totals, we only need to check the |
| 382 | // difference against the last recorded unique value |
| 383 | if ( count( $voteTotals ) === 0 ) { |
| 384 | // First value is always unique |
| 385 | $voteTotals[] = $candidate['total']; |
| 386 | } elseif ( isset( $voteTotals[ count( $voteTotals ) - 1 ] ) ) { |
| 387 | if ( abs( $candidate['total'] - $voteTotals[ count( $voteTotals ) - 1 ] ) > PHP_FLOAT_EPSILON ) { |
| 388 | $voteTotals[] = $candidate['total']; |
| 389 | } |
| 390 | } |
| 391 | } |
| 392 | |
| 393 | // If everyone left is tied and no one made quota |
| 394 | // Everyone left gets eliminated |
| 395 | if ( count( $voteTotals ) === 1 ) { |
| 396 | return array_keys( $ranking ); |
| 397 | } |
| 398 | |
| 399 | // Get the lowest ranking candidates |
| 400 | [ $secondLowest, $lowest ] = array_slice( $voteTotals, -2 ); |
| 401 | |
| 402 | // Check if we can eliminate the lowest candidate |
| 403 | // using Hill's surplus-based short circuit elimination |
| 404 | $lastPlace = array_keys( array_filter( $ranking, static function ( $ranked ) use ( $lowest, $elected ) { |
| 405 | return abs( $ranked['total'] - $lowest ) < PHP_FLOAT_EPSILON && !in_array( key( $ranked ), $elected ); |
| 406 | } ) ); |
| 407 | if ( ( $lowest * count( $lastPlace ) ) + $surplus < $secondLowest || |
| 408 | abs( $surplus - $prevSurplus ) < PHP_FLOAT_EPSILON ) { |
| 409 | return $lastPlace; |
| 410 | } |
| 411 | return []; |
| 412 | } |
| 413 | } |