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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 | use OOUI\StackLayout; |
| 10 | |
| 11 | /** |
| 12 | * A STVTallier class, |
| 13 | * This implementation is based mainly on |
| 14 | * https://web.archive.org/web/20210225045400/https://prfound.org/resources/reference/reference-meek-rule/ |
| 15 | * and |
| 16 | * Hill's programmatic implementation - We follow NZ implementation found in this paper |
| 17 | * https://web.archive.org/web/20210723092928/https://ucid.es/system/files/meekm_0.pdf |
| 18 | * Major differences being |
| 19 | * 1. We do not use pseudo random elimination of candidates. |
| 20 | * |
| 21 | * Other sources |
| 22 | * https://web.archive.org/web/20210723092923/https://rangevoting.org/MeekSTV2.html |
| 23 | * https://web.archive.org/web/20200712142326/http://www.votingmatters.org.uk/ISSUE1/P1.HTM |
| 24 | */ |
| 25 | class STVTallier extends Tallier { |
| 26 | |
| 27 | /** |
| 28 | * An array of vote combinations keyed by underscore-delimited |
| 29 | * and ranked options. Each vote has a rank array (which allows |
| 30 | * index-1 access to each ranked option) and a count |
| 31 | * @var array |
| 32 | */ |
| 33 | public $rankedVotes = []; |
| 34 | |
| 35 | /** |
| 36 | * An array of results, gets populated per round |
| 37 | * holds current round, both elected and eliminated candidate and the total votes per round. |
| 38 | * @var array[] |
| 39 | */ |
| 40 | public $resultsLog = [ |
| 41 | 'elected' => [], |
| 42 | 'eliminated' => [], |
| 43 | 'rounds' => [] |
| 44 | ]; |
| 45 | |
| 46 | /** |
| 47 | * The precision for all fixed-point arithmetic done while tallying. All |
| 48 | * arithmetic done in this class must use bc math function paired with this |
| 49 | * precision value (T361077). |
| 50 | */ |
| 51 | private const PRECISION = 10; |
| 52 | |
| 53 | /** |
| 54 | * Number of seats to be filled. |
| 55 | * @var int |
| 56 | */ |
| 57 | private $seats; |
| 58 | |
| 59 | /** |
| 60 | * An array of all candidates in the election. |
| 61 | * @var array<int, string> |
| 62 | */ |
| 63 | private $candidates = []; |
| 64 | |
| 65 | /** |
| 66 | * @param Context $context |
| 67 | * @param ElectionTallier $electionTallier |
| 68 | * @param Question $question |
| 69 | */ |
| 70 | public function __construct( $context, $electionTallier, $question ) { |
| 71 | parent::__construct( $context, $electionTallier, $question ); |
| 72 | foreach ( $question->getOptions() as $option ) { |
| 73 | $this->candidates[ $option->getId() ] = $option->getMessage( 'text' ); |
| 74 | } |
| 75 | $this->seats = $question->getProperty( 'min-seats' ); |
| 76 | } |
| 77 | |
| 78 | /** |
| 79 | * @inheritDoc |
| 80 | */ |
| 81 | public function addVote( $scores ) { |
| 82 | $id = implode( '_', $scores ); |
| 83 | $rank = []; |
| 84 | foreach ( $scores as $ranked => $optionId ) { |
| 85 | $rank[ $ranked + 1 ] = $optionId; |
| 86 | } |
| 87 | |
| 88 | if ( !isset( $this->rankedVotes[ $id ] ) ) { |
| 89 | $this->rankedVotes[ $id ] = [ |
| 90 | 'count' => 1, |
| 91 | 'rank' => $rank, |
| 92 | ]; |
| 93 | } else { |
| 94 | $this->rankedVotes[ $id ][ 'count' ] += 1; |
| 95 | } |
| 96 | |
| 97 | return true; |
| 98 | } |
| 99 | |
| 100 | /** @inheritDoc */ |
| 101 | public function loadJSONResult( array $data ) { |
| 102 | $this->resultsLog = $data['resultsLog']; |
| 103 | $this->rankedVotes = $data['rankedVotes']; |
| 104 | } |
| 105 | |
| 106 | /** @inheritDoc */ |
| 107 | public function getJSONResult() { |
| 108 | return [ |
| 109 | 'resultsLog' => $this->resultsLog, |
| 110 | 'rankedVotes' => $this->rankedVotes, |
| 111 | ]; |
| 112 | } |
| 113 | |
| 114 | /** @inheritDoc */ |
| 115 | public function getHtmlResult() { |
| 116 | $htmlFormatter = new HtmlFormatter( |
| 117 | $this->resultsLog, |
| 118 | $this->rankedVotes, |
| 119 | $this->seats, |
| 120 | $this->candidates |
| 121 | ); |
| 122 | $htmlPreamble = $htmlFormatter->formatPreamble( |
| 123 | $this->resultsLog['elected'], |
| 124 | $this->resultsLog['eliminated'] |
| 125 | ); |
| 126 | $htmlRounds = $htmlFormatter->formatRoundsPreamble(); |
| 127 | $htmlRounds->appendContent( $htmlFormatter->formatRound() ); |
| 128 | return new StackLayout( [ |
| 129 | 'items' => [ |
| 130 | $htmlPreamble, |
| 131 | $htmlRounds, |
| 132 | ], |
| 133 | 'continuous' => true, |
| 134 | 'expanded' => false, |
| 135 | 'classes' => [ 'election-tally-results--stv' ] |
| 136 | ] ); |
| 137 | } |
| 138 | |
| 139 | /** @inheritDoc */ |
| 140 | public function getTextResult() { |
| 141 | $wikitextFormatter = new WikitextFormatter( |
| 142 | $this->resultsLog, |
| 143 | $this->rankedVotes, |
| 144 | $this->seats, |
| 145 | $this->candidates |
| 146 | ); |
| 147 | $wikitext = $wikitextFormatter->formatPreamble( |
| 148 | $this->resultsLog['elected'], |
| 149 | $this->resultsLog['eliminated'] |
| 150 | ); |
| 151 | $wikitext .= $wikitextFormatter->formatRoundsPreamble(); |
| 152 | $wikitext .= $wikitextFormatter->formatRound(); |
| 153 | return $wikitext; |
| 154 | } |
| 155 | |
| 156 | /** |
| 157 | * @inheritDoc |
| 158 | */ |
| 159 | public function finishTally() { |
| 160 | // Instantiate first round for the iterator |
| 161 | $keepFactors = array_fill_keys( array_keys( $this->candidates ), '1.0' ); |
| 162 | $voteCount = $this->distributeVotes( $this->rankedVotes, $keepFactors ); |
| 163 | $quota = $this->calculateDroopQuota( $voteCount['totalVotes'], (string)$this->seats ); |
| 164 | $round = [ |
| 165 | 'round' => 1, |
| 166 | 'surplus' => '0', |
| 167 | 'rankings' => $voteCount['ranking'], |
| 168 | 'totalVotes' => $voteCount['totalVotes'], |
| 169 | 'keepFactors' => $keepFactors, |
| 170 | 'quota' => $quota, |
| 171 | 'elected' => [], |
| 172 | 'eliminated' => [] |
| 173 | ]; |
| 174 | $this->resultsLog['rounds'][] = $round; |
| 175 | |
| 176 | // Iterate |
| 177 | $this->calculateRound( $round ); |
| 178 | } |
| 179 | |
| 180 | /** |
| 181 | * @param array $prevRound |
| 182 | */ |
| 183 | private function calculateRound( $prevRound ) { |
| 184 | if ( count( $this->resultsLog['elected'] ) >= $this->seats ) { |
| 185 | return; |
| 186 | } |
| 187 | |
| 188 | // Advance the round |
| 189 | $round = [ |
| 190 | 'round' => $prevRound['round'] + 1, |
| 191 | 'elected' => [], |
| 192 | 'eliminated' => [], |
| 193 | 'surplus' => '0.0', |
| 194 | ]; |
| 195 | |
| 196 | $keepFactors = |
| 197 | $round['keepFactors'] = |
| 198 | $this->calculateKeepFactors( |
| 199 | $this->candidates, |
| 200 | $prevRound['quota'], |
| 201 | $prevRound['keepFactors'], |
| 202 | $this->resultsLog['elected'], |
| 203 | $this->resultsLog['eliminated'], |
| 204 | $prevRound['rankings'] |
| 205 | ); |
| 206 | |
| 207 | $voteCount = $this->distributeVotes( $this->rankedVotes, $keepFactors, $prevRound['rankings'] ); |
| 208 | $round['quota'] = $this->calculateDroopQuota( $voteCount['totalVotes'], (string)$this->seats ); |
| 209 | $round['rankings'] = $voteCount['ranking']; |
| 210 | $round['totalVotes'] = $voteCount['totalVotes']; |
| 211 | |
| 212 | // Check for unique winners |
| 213 | $allWinners = $this->declareWinners( $round['rankings'], $round['quota'] ); |
| 214 | $roundWinners = $round['elected'] = array_diff( $allWinners, $this->resultsLog['elected'] ); |
| 215 | |
| 216 | // If no winners, check for eliminated (no distribution happens here) |
| 217 | $round['surplus'] = $this->calculateSurplus( $round['rankings'], $allWinners, $round['quota'] ); |
| 218 | $allEliminated = $this->declareEliminated( |
| 219 | $round['rankings'], |
| 220 | $round['surplus'], |
| 221 | $this->resultsLog['eliminated'], |
| 222 | $this->resultsLog['elected'], |
| 223 | $prevRound['surplus'] |
| 224 | ); |
| 225 | $roundEliminated = $round['eliminated'] = !$roundWinners ? |
| 226 | array_diff( $allEliminated, $this->resultsLog['eliminated'] ) : []; |
| 227 | |
| 228 | $this->resultsLog['rounds'][] = $round; |
| 229 | $this->resultsLog['elected'] = array_merge( $this->resultsLog['elected'], $roundWinners ); |
| 230 | $this->resultsLog['eliminated'] = array_merge( $this->resultsLog['eliminated'], $roundEliminated ); |
| 231 | |
| 232 | // Recurse? |
| 233 | $hopefuls = array_diff( |
| 234 | array_keys( $this->candidates ), |
| 235 | array_merge( $this->resultsLog['elected'], $this->resultsLog['eliminated'] ) |
| 236 | ); |
| 237 | if ( $hopefuls ) { |
| 238 | $this->calculateRound( $round ); |
| 239 | } |
| 240 | } |
| 241 | |
| 242 | /** |
| 243 | * Distribute votes per ballot |
| 244 | * For each ballot: set ballot weight($weight) to 1, |
| 245 | * and then for each candidate, |
| 246 | * in order of rank on that ballot: |
| 247 | * add $weight multiplied by the keep factor ($voteValue) of the candidate ($keepFactors[$candidate]) |
| 248 | * to that candidate’s vote $voteTotals[$candidate]['total'], and reduce $weight by $voteValue, |
| 249 | * until no further candidate remains on the ballot. |
| 250 | * @param array $ballots |
| 251 | * @param array $keepFactors |
| 252 | * @param null $prevDistribution |
| 253 | * @return array |
| 254 | */ |
| 255 | private function distributeVotes( $ballots, $keepFactors, $prevDistribution = null ): array { |
| 256 | $voteTotals = []; |
| 257 | $totalVotes = '0.0'; |
| 258 | foreach ( $keepFactors as $candidate => $kf ) { |
| 259 | $voteTotals[$candidate] = [ |
| 260 | 'votes' => '0', |
| 261 | 'earned' => '0', |
| 262 | 'total' => '0', |
| 263 | ]; |
| 264 | } |
| 265 | |
| 266 | // Apply previous round's votes to the count to get "earned" votes |
| 267 | if ( $prevDistribution ) { |
| 268 | foreach ( $prevDistribution as $candidate => $candidateVotes ) { |
| 269 | $voteTotals[$candidate]['votes'] = $candidateVotes['total']; |
| 270 | |
| 271 | // earned = earned - total |
| 272 | $voteTotals[$candidate]['earned'] = bcsub( |
| 273 | $voteTotals[$candidate]['earned'], |
| 274 | $candidateVotes['total'], |
| 275 | self::PRECISION |
| 276 | ); |
| 277 | } |
| 278 | } |
| 279 | |
| 280 | foreach ( $ballots as $ballot ) { |
| 281 | $weight = '1.0'; |
| 282 | |
| 283 | foreach ( $ballot['rank'] as $candidate ) { |
| 284 | // weight > 0 |
| 285 | if ( bccomp( $weight, '0.0', self::PRECISION ) === 1 ) { |
| 286 | // voteValue = weight * keepFactor |
| 287 | $voteValue = bcmul( $weight, $keepFactors[$candidate], self::PRECISION ); |
| 288 | |
| 289 | // earned = earned + (voteValue * ballotCount) |
| 290 | $voteTotals[$candidate]['earned'] = bcadd( |
| 291 | $voteTotals[$candidate]['earned'], |
| 292 | bcmul( $voteValue, (string)$ballot['count'], self::PRECISION ), |
| 293 | self::PRECISION |
| 294 | ); |
| 295 | |
| 296 | // total = total + (voteValue * ballotCount) |
| 297 | $voteTotals[$candidate]['total'] = bcadd( |
| 298 | $voteTotals[$candidate]['total'], |
| 299 | bcmul( $voteValue, (string)$ballot['count'], self::PRECISION ), |
| 300 | self::PRECISION |
| 301 | ); |
| 302 | |
| 303 | // weight = weight - voteValue |
| 304 | $weight = bcsub( $weight, $voteValue, self::PRECISION ); |
| 305 | |
| 306 | // totalVotes = totalVotes + (voteValue + ballotCount) |
| 307 | $totalVotes = bcadd( |
| 308 | $totalVotes, |
| 309 | bcmul( $voteValue, $ballot['count'], self::PRECISION ), |
| 310 | self::PRECISION |
| 311 | ); |
| 312 | } else { |
| 313 | break; |
| 314 | } |
| 315 | } |
| 316 | } |
| 317 | |
| 318 | return [ |
| 319 | 'ranking' => $voteTotals, |
| 320 | 'totalVotes' => $totalVotes, |
| 321 | ]; |
| 322 | } |
| 323 | |
| 324 | /** |
| 325 | * @param string $votes |
| 326 | * @param string $seats |
| 327 | * @return string |
| 328 | */ |
| 329 | private function calculateDroopQuota( $votes, $seats ): string { |
| 330 | // droopQuota = (votes / (seats + 1)) + 0.000001 |
| 331 | return bcadd( |
| 332 | bcdiv( $votes, bcadd( $seats, '1.0', self::PRECISION ), self::PRECISION ), |
| 333 | '0.000001', |
| 334 | self::PRECISION |
| 335 | ); |
| 336 | } |
| 337 | |
| 338 | /** |
| 339 | * Calculates keep factors of all elected candidate at every round |
| 340 | * calculated as: current keepfactor multiplied by current quota divided by candidates current vote($voteTotals) |
| 341 | * @param array $candidates |
| 342 | * @param string $quota |
| 343 | * @param array $currentFactors |
| 344 | * @param array $winners |
| 345 | * @param array $eliminated |
| 346 | * @param array $voteTotals |
| 347 | * @return array |
| 348 | */ |
| 349 | private function calculateKeepFactors( $candidates, $quota, $currentFactors, $winners, $eliminated, $voteTotals ) { |
| 350 | $keepFactors = []; |
| 351 | |
| 352 | foreach ( $candidates as $candidateId => $candidateName ) { |
| 353 | $keepFactors[$candidateId] = in_array( $candidateId, $eliminated ) ? '0.0' : '1.0'; |
| 354 | } |
| 355 | |
| 356 | foreach ( $winners as $winner ) { |
| 357 | $voteCount = $voteTotals[$winner]['total']; |
| 358 | $prevKeepFactor = $currentFactors[$winner]; |
| 359 | |
| 360 | // keepFactor = (prevKeepFactor * quota) / voteCount |
| 361 | $keepFactors[$winner] = bcdiv( |
| 362 | bcmul( $prevKeepFactor, $quota, self::PRECISION ), |
| 363 | $voteCount, |
| 364 | self::PRECISION |
| 365 | ); |
| 366 | } |
| 367 | |
| 368 | return $keepFactors; |
| 369 | } |
| 370 | |
| 371 | /** |
| 372 | * @param array $ranking |
| 373 | * @param array $winners |
| 374 | * @param string $quota |
| 375 | * @return string |
| 376 | */ |
| 377 | private function calculateSurplus( $ranking, $winners, $quota ) { |
| 378 | $voteSurplus = '0.0'; |
| 379 | foreach ( $winners as $winner ) { |
| 380 | $voteTotal = $ranking[$winner]['total']; |
| 381 | |
| 382 | // voteSurplus = (voteSurplus + voteTotal) - quota |
| 383 | $voteSurplus = bcsub( bcadd( $voteSurplus, $voteTotal, self::PRECISION ), $quota, self::PRECISION ); |
| 384 | } |
| 385 | return $voteSurplus; |
| 386 | } |
| 387 | |
| 388 | /** |
| 389 | * @param array $ranking |
| 390 | * @param string $quota |
| 391 | * @return array |
| 392 | */ |
| 393 | private function declareWinners( $ranking, $quota ) { |
| 394 | $winners = []; |
| 395 | foreach ( $ranking as $option => $votes ) { |
| 396 | // voteTotal >= quota |
| 397 | if ( bccomp( $votes['total'], $quota, self::PRECISION ) >= 0 ) { |
| 398 | $winners[] = $option; |
| 399 | } |
| 400 | } |
| 401 | return $winners; |
| 402 | } |
| 403 | |
| 404 | /** |
| 405 | * @param array $ranking |
| 406 | * @param string $surplus |
| 407 | * @param array $eliminated |
| 408 | * @param array $elected |
| 409 | * @param string $prevSurplus |
| 410 | * @return array |
| 411 | */ |
| 412 | private function declareEliminated( $ranking, $surplus, $eliminated, $elected, $prevSurplus ) { |
| 413 | // Make sure it's ordered by vote totals |
| 414 | uksort( |
| 415 | $ranking, |
| 416 | static function ( $aKey, $bKey ) use ( $ranking ) { |
| 417 | $a = $ranking[$aKey]; |
| 418 | $b = $ranking[$bKey]; |
| 419 | // $a['total'] === $b['total'] |
| 420 | if ( bccomp( $a['total'], $b['total'], self::PRECISION ) === 0 ) { |
| 421 | // ascending sort ($aKey <=> $bKey) |
| 422 | return bccomp( $aKey, $bKey, self::PRECISION ); |
| 423 | } |
| 424 | // descending sort ($b['total'] <=> $a['total']) |
| 425 | return bccomp( $b['total'], $a['total'], self::PRECISION ); |
| 426 | } |
| 427 | ); |
| 428 | |
| 429 | // Remove anyone who was already eliminated or elected |
| 430 | $ranking = array_filter( $ranking, static function ( $key ) use ( $eliminated ) { |
| 431 | return !in_array( $key, $eliminated ); |
| 432 | }, ARRAY_FILTER_USE_KEY ); |
| 433 | |
| 434 | // Manually implement array_unique with higher precision than the default function |
| 435 | $voteTotals = []; |
| 436 | foreach ( $ranking as $candidate ) { |
| 437 | // Since it's already been ordered by vote totals, we only need to check the |
| 438 | // difference against the last recorded unique value |
| 439 | if ( count( $voteTotals ) === 0 ) { |
| 440 | // First value is always unique |
| 441 | $voteTotals[] = $candidate['total']; |
| 442 | } elseif ( isset( $voteTotals[ count( $voteTotals ) - 1 ] ) ) { |
| 443 | if ( |
| 444 | // abs(candidateTotal - voteTotal[lastSeat]) > 0 |
| 445 | bccomp( $this->bcabs( bcsub( |
| 446 | $candidate['total'], |
| 447 | $voteTotals[ count( $voteTotals ) - 1 ], |
| 448 | self::PRECISION |
| 449 | ) ), '0.0', self::PRECISION ) === 1 |
| 450 | ) { |
| 451 | $voteTotals[] = $candidate['total']; |
| 452 | } |
| 453 | } |
| 454 | } |
| 455 | |
| 456 | // If everyone left is tied and no one made quota |
| 457 | // Everyone left gets eliminated |
| 458 | if ( count( $voteTotals ) === 1 ) { |
| 459 | return array_keys( $ranking ); |
| 460 | } |
| 461 | |
| 462 | // Get the lowest ranking candidates |
| 463 | [ $secondLowest, $lowest ] = array_slice( $voteTotals, -2 ); |
| 464 | |
| 465 | // Check if we can eliminate the lowest candidate |
| 466 | // using Hill's surplus-based short circuit elimination |
| 467 | $bcabs = [ $this, 'bcabs' ]; |
| 468 | $lastPlace = array_keys( array_filter( $ranking, static function ( $ranked ) use ( $bcabs, $lowest, $elected ) { |
| 469 | // abs(rankedTotal - lowest) <= 0 |
| 470 | return bccomp( $bcabs( bcsub( $ranked['total'], $lowest, self::PRECISION ) ), '0.0', self::PRECISION ) <= 0 |
| 471 | && !in_array( key( $ranked ), $elected ); |
| 472 | } ) ); |
| 473 | |
| 474 | if ( |
| 475 | // (lowest * lastPlaceCount) + surplus < secondLowest |
| 476 | bccomp( bcadd( bcmul( $lowest, (string)count( $lastPlace ) ), $surplus ), $secondLowest ) === -1 || |
| 477 | // abs(surplus - prevSurplus) <= 0 |
| 478 | bccomp( $this->bcabs( bcsub( $surplus, $prevSurplus, self::PRECISION ) ), '0.0', self::PRECISION ) <= 0 |
| 479 | ) { |
| 480 | return $lastPlace; |
| 481 | } |
| 482 | |
| 483 | return []; |
| 484 | } |
| 485 | |
| 486 | /** |
| 487 | * A custom fixed-point abs function since PHP doesn't provide one. |
| 488 | * |
| 489 | * @param string $number |
| 490 | * @return string |
| 491 | */ |
| 492 | private function bcabs( $number ) { |
| 493 | // number < 0 |
| 494 | if ( bccomp( $number, '0.0', self::PRECISION ) === -1 ) { |
| 495 | // number * -1 |
| 496 | return bcmul( $number, '-1.0', self::PRECISION ); |
| 497 | } |
| 498 | return $number; |
| 499 | } |
| 500 | } |