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<?php
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/**
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* @file
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*
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* This file implements a ranking mode, where n options are ranked
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* from 1 to n
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*/
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// $Id: ranking.module,v 1.23 2009/10/26 20:41:27 anarcat Exp $
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/**
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* Implementation of hook_help()
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*/
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function ranking_help($section) {
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$help = '';
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switch ($section) {
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case 'admin/modules#description':
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break;
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default:
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if ($section == 'node/add#decisions-ranking') {
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$help = t('Creates a vote where n options are ranked from 1 to n.');
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}
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break;
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}
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return $help;
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}
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function ranking_perm() { return decisions_perm(); }
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function ranking_acces($op, $node, $account) { return decisions_access($op, $node, $account); }
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function ranking_form(&$node) { return decisions_form($node); }
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function ranking_node_info() {
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$info = array();
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$info['decisions_ranking'] = array(
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'name' => 'Decisions - ranking',
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'module' => 'decisions',
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'description' => 'Creates a vote where n options are ranked from 1 to n.',
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'title_label' => t('Ranking decision'),
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'body_label' => t('Description'),
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);
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return $info;
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}
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/**
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* Implementation of the decisions_algorithms() hook
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*/
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function ranking_decisions_algorithms() {
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return array('instant runoff' => t('Instant run-off voting, also known as IVR or Alternative Voting, is an algorithm by which the candidate having the least ballots gets its votes redistributed to the other candidates. See <a href="http://en.wikipedia.org/wiki/Instant-runoff_voting">Instant runoff voting on Wikipedia</a> for more information.'),
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'borda count' => t('Borda count is an algorithm by which each candidate gets a number of points assigned based on the number of candidates standing. See the <a href="http://en.wikipedia.org/wiki/Borda_count">Borda count article on Wikipedia</a> for more information.'),
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'condorcet' => t('Condorcet finds the one candidate who would beat all other candidates in all possible two-person races. In this implementation, ties are broken using Schulze method. See the <a href="http://en.wikipedia.org/wiki/Schulze_method">Schulze method article on Wikipedia</a> for more information.'));
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}
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/**
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* Implementation of the decisions_voting_hook_form() hook for the runoff module.
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*
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* This displays a textfield per choice, that should be filled with a
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* ranking.
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*/
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function ranking_decisions_voting_form(&$node, $teaser, $page) {
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$weight = 0;
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$form = array();
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if ($node->choice) {
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$list = array();
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// Put options in random order if randomize option
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// selected on node create/edit form.
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if($node->randomize) {
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$node->choice = _decisions_randomize_options($node->choice, $node->choices);
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}
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$num_choices = count($node->choice);
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// Generate the list of possible rankings
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$choices[0] = '--';
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for ($i = 1; $i <= $num_choices; $i++) {
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if ($i == 1) {
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$val = t('1st');
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}
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elseif ($i == 2) {
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$val = t('2nd');
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}
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elseif ($i == 3) {
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$val = t('3rd');
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}
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else {
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$val = t('!{num}th', array('!{num}' => $i));
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}
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$choices[$i] = $val;
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}
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$form['choice'] = array(
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'#type' => 'fieldset',
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'#tree' => TRUE,
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'#title' => t('Choices'),
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'#description' => t('Rank the following options in your prefered order, the lower the number the better'),
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);
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foreach ($node->choice as $key => $choice) {
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if ($choice['label']) {
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$form['choice'][$key] = array(
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'#type' => 'select',
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'#title' => check_plain($choice['label']),
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'#options' => $choices,
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);
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}
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}
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}
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$form['nid'] = array(
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'#type' => 'hidden',
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'#value' => $node->nid,
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'#weight' => $weight++,
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);
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$form['vote'] = array(
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'#type' => 'submit',
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'#value' => t('Vote'),
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'#weight' => $weight++,
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);
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$form['#action'] = url('node/'. $node->nid);
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return $form;
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}
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/**
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* implementation of the decisions_view_results() hook for the runoff
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* module
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*/
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function ranking_decisions_view_results($node, $teaser, $page) {
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$results = _ranking_decisions_calculate_results($node);
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$output = '';
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if ($node->algorithm == 'condorcet') { // Use this display method only if using condorcet.
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$rows[0][] = "";
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$options = count($node->choice);
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for ($i = 1; $i<=$options; $i++) {
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$rows[0][] = array('data' => check_plain($node->choice[$i]['label']), 'header' => 1);
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}
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for ($i = 1; $i<=$options; $i++) {
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$rows[$i][0] = array('data' => check_plain($node->choice[$i]['label']), 'header' => 1);
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for ($j = 1; $j<=$options; $j++) {
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if ($i==$j) {
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$rows[$i][$j] = "N/A";
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} else {
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if ($results->matrix[$i][$j]) {
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$rows[$i][$j] = $results->matrix[$i][$j];
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} else {
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$rows[$i][$j] = 0;
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}
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}
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}
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}
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$output .= theme_table(array(), $rows, array(), "The table below indicates the number of voters who preferred the row to the column.");
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// Display the outcome of the Schulze count.
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$output .= '<p>Results</p><ul>';
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for ($i=1; $i<=count($results->ranking); $i++) {
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$output .= "<li><em>Round ". $i ."</em>: ". $results->ranking[$i][0] .": ";
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$first_one = TRUE;
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for ($j=1; $j<count($results->ranking[$i]); $j++) {
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if (!$first_one) {$output .= ", ";}
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$output .= check_plain($node->choice[$results->ranking[$i][$j]]['label']);
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$first_one=FALSE;
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}
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$output .= "</li>";
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}
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$output .= "</ul>";
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} else {
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// If no one has voted, $results = array() and thus is empty
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if (!empty($results)) {
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$output .= t('Results: ') .'<ol>';
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for ($i = 0; $i < count($results->ranking); $i++) {
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$output .= '<li> ';
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$first_one = TRUE;
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// Loop through all choices with this ranking
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foreach ($results->ranking[$i]['choices'] as $choice) {
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$output .= ($first_one? '' : ', ') . check_plain($node->choice[$choice]['label']);
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$first_one = FALSE;
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}
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// Show the ranking's score if it exists (depends on algorithm)
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if (isset($results->ranking[$i]['viewscore'])) {
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$output .= ' ('. $results->ranking[$i]['viewscore'] .')';
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}
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$output .= '</li>';
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}
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$output .= '</ol>';
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if (user_access('inspect all votes') && isset($results->matrix)) {
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$header[0] = "Rounds";
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$round = 1;
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if (count($results->matrix) > 0) {
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foreach ($results->matrix as $a_round) {
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$header[$round] = $round;
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$round++;
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}
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}
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$round = 1;
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$i = 0;
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if (count($results->matrix) > 0) {
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foreach ($results->matrix as $a_round) {
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foreach ($node->choice as $key => $choicename) {
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$rows[$i][0] = $choicename['label'];
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$rows[$i][$round] = count($a_round[$key]);
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$i++;
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}
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$i=0;
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$round++;
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}
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}
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$output .= theme('table', $header, $rows);
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}
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}
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} // end condorcet else.
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return $output;
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}
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/**
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* implementation of the format_votes() hook.
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*
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* formats how a user's votes should be displayed.
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*
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* @returns a formatted string
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*/
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function ranking_decisions_format_votes($node, $votes) {
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$ordered_votes = array();
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foreach ($votes as $vote) {
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// Need two dimensional results (if equal rankings are allowed)
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$ordered_votes[$vote->value][] = check_plain($node->choice[$vote->tag]['label']);
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}
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asort($ordered_votes);
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$rankings = array();
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foreach ($ordered_votes as $value => $choices) {
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$rankings[$value] = implode(' = ', $choices);
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ksort($rankings);
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}
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return implode(' > ', $rankings);
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}
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/**
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* Implementation of the vote hook for the runoff module.
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*
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* This takes care of registering the vote in runoff nodes.
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*/
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function ranking_decisions_vote($node, $form_values) {
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$votes = array();
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foreach ( $form_values['choice'] as $choice => $rank ) {
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// A zero value indicates they didn't rank that choice
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if ($rank != 0) {
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$vote = array('value' => $rank,
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'content_type' => 'decisions',
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'content_id' => $node->nid,
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'value_type' => 'option',
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'tag' => $choice);
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$votes[] = $vote;
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}
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}
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votingapi_add_votes($votes);
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}
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/**
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* implementation of the vote validation hook for the runoff module.
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*
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* This checks if the submitted values are within range, if they are
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* not empty, and if they are not repeated.
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*
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* @returns boolean false on invalid forms, true otherwise.
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*/
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function ranking_decisions_vote_validate($node, $form_values) {
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$ok = TRUE;
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// array used to check which values are set
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$setvalues = array();
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$numchoices = 0;
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foreach ($node->choice as $key => $choice) {
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// count the number of choices that are ranked
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if (!empty($form_values['choice'][$key])) {
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$numchoices++;
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}
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$intvalue = intval($form_values['choice'][$key]);
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// mark this value as seen
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if (!array_key_exists($intvalue, $setvalues)) {
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$setvalues[$intvalue] = 1;
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}
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else {
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$setvalues[$intvalue]++;
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}
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// check range
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if ($intvalue > count($node->choice) || $intvalue < 0) {
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form_set_error('Choice_'. $key, "illegal rank for choice $key: $intvalue (min: 1, max: ". count($node->choice) .")");
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$ok = FALSE;
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}
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}
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// too many choices ranked
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if ($node->maxchoices != 0 && $numchoices > $node->maxchoices) {
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form_set_error('choice', t('@num choices were selected but only @max are allowed.', array('@num' => $numchoices, '@max' => $node->maxchoices)));
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$ok = FALSE;
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}
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// not enough choices ranked
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$minchoices = 1;
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if ($numchoices < $minchoices) {
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form_set_error('choice', t('At least one choice must be selected.'));
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$ok = FALSE;
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}
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// Check that multiple choices are not set to the same value
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if ($node->algorithm != "condorcet") { // condorcet uses ties.
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foreach ($setvalues as $val => $count) {
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if ($val != 0 && $count > 1) {
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form_set_error('choice', t('Multiple choices given the rank of @val.', array('@val' => $val)));
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$ok = FALSE;
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}
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}
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} // end condorcet if.
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return $ok;
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}
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/***********************************************************************
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* INTERNAL FUNCTIONS
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**********************************************************************/
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/**
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* Calculate the results for a ranking decision based on the algorithm
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*
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* @param $node
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* The node object for the current decision
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*
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* @return
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* Should return an object that include the following attributes
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* -results : 2d array listing the aggregate preference, including ties
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* -rounds : 2d array listing the per-choice vote count for each round and
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* a status message indicating who was eliminated
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* -totalVoters : the total number of voters who participated
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*/
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function _ranking_decisions_calculate_results($node) {
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if ($node->algorithm == 'borda count') {
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return _decisions_calculate_bordacount($node);
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}
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else if ($node->algorithm == 'instant runoff') {
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return _decisions_calculate_instantrunoff($node);
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}
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else {
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return _decisions_calculate_condorcet($node);
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}
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}
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/**
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* Calculate the results using borda count
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*
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* @param $node
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* The node object for the current decision
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*
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* @return
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* Should return an object that include the following attributes
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| 371 |
* -results : 2d array listing the aggregate preference, including ties
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| 372 |
* -rounds : 2d array listing the per-choice vote count for each round and
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| 373 |
* a status message indicating who was eliminated
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| 374 |
* -totalVoters : the total number of voters who participated
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*/
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| 377 |
function _decisions_calculate_bordacount($node) {
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$votes = _decisions_votes($node);
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| 380 |
if (count($votes) == 0) {
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| 381 |
// no votes yet
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| 382 |
return array();
|
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}
|
| 384 |
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// aggregate votes by user (uid if logged in, IP if anonymous)
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// in ascending order of value
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$user_votes = array();
|
| 388 |
|
| 389 |
foreach ($votes as $vote) {
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| 390 |
if ($vote['uid'] == 0) {
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| 391 |
// anonymous user
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| 392 |
$key = $vote['vote_source'];
|
| 393 |
}
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| 394 |
else {
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| 395 |
// logged-in user
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| 396 |
$key = $vote['uid'];
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}
|
| 398 |
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| 399 |
$user_votes[$key][$vote['value']] = $vote['tag'];
|
| 400 |
}
|
| 401 |
|
| 402 |
$choice_votes = array();
|
| 403 |
|
| 404 |
$total_choices = count($node->choice);
|
| 405 |
|
| 406 |
// Loop through each user's vote
|
| 407 |
foreach ($user_votes as $uid => $user_vote) {
|
| 408 |
foreach ($user_vote as $ranking => $choice) {
|
| 409 |
// Negative values are possible if choices were removed after vote
|
| 410 |
$vote_value = max($total_choices - $ranking, 0);
|
| 411 |
if (!array_key_exists($choice, $choice_votes)) {
|
| 412 |
$choice_votes[$choice] = 0;
|
| 413 |
}
|
| 414 |
$choice_votes[$choice] += $vote_value;
|
| 415 |
}
|
| 416 |
}
|
| 417 |
|
| 418 |
// sort descending (although there may be ties)
|
| 419 |
arsort($choice_votes);
|
| 420 |
|
| 421 |
// Figure out the final ranking
|
| 422 |
$ranking = array();
|
| 423 |
$previous_total = -1;
|
| 424 |
$cur_result = -1;
|
| 425 |
|
| 426 |
foreach ($choice_votes as $choice => $total) {
|
| 427 |
if ($total != $previous_total) {
|
| 428 |
// Didn't tie with the previous score
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| 429 |
$cur_result++;
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}
|
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$ranking[$cur_result]['choices'][] = $choice;
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$ranking[$cur_result]['rawscore'] = $total;
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$ranking[$cur_result]['viewscore'] = $total .' point'. ($total == 1? '' : 's');
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}
|
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| 436 |
$total_votes = count($user_votes);
|
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| 438 |
$result_obj->ranking = $ranking;
|
| 439 |
$result_obj->total_votes = $total_votes;
|
| 440 |
return $result_obj;
|
| 441 |
}
|
| 442 |
|
| 443 |
|
| 444 |
/**
|
| 445 |
* Calculate the results using instant-runoff voting
|
| 446 |
*
|
| 447 |
* @param $node
|
| 448 |
* The node object for the current decision
|
| 449 |
*
|
| 450 |
* @return
|
| 451 |
* Should return an object that include the following attributes
|
| 452 |
* -results : 2d array listing the aggregate preference, including ties
|
| 453 |
* -rounds : 2d array listing the per-choice vote count for each round and
|
| 454 |
* a status message indicating who was eliminated
|
| 455 |
* -totalVoters : the total number of voters who participated
|
| 456 |
*/
|
| 457 |
|
| 458 |
function _decisions_calculate_instantrunoff($node) {
|
| 459 |
$votes = _decisions_votes($node);
|
| 460 |
|
| 461 |
if (count($votes) == 0) {
|
| 462 |
// no votes yet
|
| 463 |
return array();
|
| 464 |
}
|
| 465 |
|
| 466 |
// aggregate votes by user (uid if logged in, IP if anonymous)
|
| 467 |
// in ascending order of value
|
| 468 |
$user_votes = array();
|
| 469 |
|
| 470 |
foreach ($votes as $vote) {
|
| 471 |
if ($vote['uid'] == 0) {
|
| 472 |
// anonymous user
|
| 473 |
$key = $vote['vote_source'];
|
| 474 |
}
|
| 475 |
else {
|
| 476 |
// logged-in user
|
| 477 |
$key = $vote['uid'];
|
| 478 |
}
|
| 479 |
|
| 480 |
// Note: relies on ORDER BY value ASC in vote-getting SQL query
|
| 481 |
// Otherwise a later vote might have a lower value
|
| 482 |
$user_votes[$key][] = $vote['tag'];
|
| 483 |
}
|
| 484 |
|
| 485 |
$total_votes = count($user_votes);
|
| 486 |
|
| 487 |
/*
|
| 488 |
if ($vote['value'] == 1) {
|
| 489 |
$cur_round[$vote['tag']]++;
|
| 490 |
// TODO: This method of counting total votes is inaccurate because users
|
| 491 |
// may vote but not choose a 1st-place vote
|
| 492 |
$totalvotes++;
|
| 493 |
}
|
| 494 |
*/
|
| 495 |
|
| 496 |
|
| 497 |
|
| 498 |
// log of 1st-place votes per choice in each round
|
| 499 |
$round_log = array();
|
| 500 |
|
| 501 |
//
|
| 502 |
$reverse_ranking = array();
|
| 503 |
|
| 504 |
|
| 505 |
|
| 506 |
// If we eliminate one choice per round and have n choices, we should
|
| 507 |
// not be able to do more than n - 1 rounds
|
| 508 |
$max_rounds = count($node->choice);
|
| 509 |
for ($round = 0; $round < $max_rounds; $round++) {
|
| 510 |
|
| 511 |
// Initialize cur_round
|
| 512 |
$cur_round = array();
|
| 513 |
$total_choices = count($node->choice);
|
| 514 |
foreach ($node->choice as $chi => $temp) {
|
| 515 |
$cur_round[$chi] = array();
|
| 516 |
}
|
| 517 |
|
| 518 |
|
| 519 |
// Loop through each user
|
| 520 |
foreach ($user_votes as $key => $user_vote) {
|
| 521 |
// $user_vote[0] contains the user's first remaining preference
|
| 522 |
$cur_round[$user_vote[0]][] = $key;
|
| 523 |
}
|
| 524 |
|
| 525 |
if ($round == 0) {
|
| 526 |
// This is the first round
|
| 527 |
// Any choices with no first-place votes are considered eliminated
|
| 528 |
foreach ($cur_round as $ch => $choice_votes) {
|
| 529 |
if (count($choice_votes) == 0) {
|
| 530 |
unset($cur_round[$ch]);
|
| 531 |
$reverse_ranking[0]['choices'][] = $ch;
|
| 532 |
}
|
| 533 |
}
|
| 534 |
}
|
| 535 |
|
| 536 |
|
| 537 |
// Add the current round to the matrix
|
| 538 |
$round_log[] = $cur_round;
|
| 539 |
|
| 540 |
//Calculate the min and max number of votes
|
| 541 |
$min_votes = -1;
|
| 542 |
$max_votes = 0;
|
| 543 |
|
| 544 |
// Number of choices that have already been discarded
|
| 545 |
$num_discarded = 0;
|
| 546 |
|
| 547 |
// examine the number of votes each choice received this round
|
| 548 |
foreach ($cur_round as $ch => $choice_votes) {
|
| 549 |
$num_votes = count($choice_votes);
|
| 550 |
|
| 551 |
if ($num_votes > $max_votes) {
|
| 552 |
$max_votes = $num_votes;
|
| 553 |
$cur_winner = $ch; // store current winner in case it has a majority
|
| 554 |
}
|
| 555 |
|
| 556 |
// This choice has already been eliminated (theoretically)
|
| 557 |
// so don't count it as the minimum
|
| 558 |
if ($num_votes == 0) {
|
| 559 |
$num_discarded++; // probably don't need this variable any more
|
| 560 |
}
|
| 561 |
else if ($num_votes != 0 && ($num_votes < $min_votes || $min_votes == -1)) {
|
| 562 |
$min_votes = $num_votes;
|
| 563 |
}
|
| 564 |
}
|
| 565 |
|
| 566 |
// If one choice has a majority of remaining users it wins
|
| 567 |
// Note: we use count($user_votes) because some users may have incomplete
|
| 568 |
// ballots and may have already had all of their choices eliminated
|
| 569 |
if ($max_votes > count($user_votes) / 2) {
|
| 570 |
|
| 571 |
// Prune out the winning choice if it's still in there
|
| 572 |
if (isset($cur_round[$cur_winner])) {
|
| 573 |
unset($cur_round[$cur_winner]);
|
| 574 |
}
|
| 575 |
|
| 576 |
// Keep computing until we figure out all final rankings
|
| 577 |
while (count($cur_round) > 0) {
|
| 578 |
// Loop through non-winning choices
|
| 579 |
$current_place = array();
|
| 580 |
$min = -1;
|
| 581 |
foreach ($cur_round as $ch => $choice_votes) {
|
| 582 |
// Choice has already been eliminated, just unset it
|
| 583 |
if (count($choice_votes) == 0) {
|
| 584 |
unset($cur_round[$ch]);
|
| 585 |
}
|
| 586 |
else if ($min == -1
|
| 587 |
|| count($choice_votes) < $min) {
|
| 588 |
// New minimum
|
| 589 |
$current_place = array($ch);
|
| 590 |
$min = count($choice_votes);
|
| 591 |
//drupal_set_message('New minimum: '. $ch .'('
|
| 592 |
//. count($choice_votes) . ')');
|
| 593 |
}
|
| 594 |
else if (count($choice_votes) == $min) {
|
| 595 |
// Tied for minimum
|
| 596 |
$current_place[] = $ch;
|
| 597 |
}
|
| 598 |
}
|
| 599 |
|
| 600 |
// current_place will be empty the first iteration if some
|
| 601 |
// choices had no first-place votes and were eliminated
|
| 602 |
// at the beginning
|
| 603 |
if (count($current_place) > 0) {
|
| 604 |
$reverse_ranking[]['choices'] = $current_place;
|
| 605 |
// Remove all choices that had the minimum
|
| 606 |
foreach ($current_place as $ch_key) {
|
| 607 |
unset($cur_round[$ch_key]);
|
| 608 |
}
|
| 609 |
}
|
| 610 |
}
|
| 611 |
|
| 612 |
// Save a reversed version of the round log to help compute winnerPercent
|
| 613 |
$revmat = array_reverse($round_log);
|
| 614 |
|
| 615 |
// The winner finally gets added
|
| 616 |
$reverse_ranking[]['choices'] = array($cur_winner);
|
| 617 |
$index = count($reverse_ranking) - 1;
|
| 618 |
$reverse_ranking[$index]['rawscore'] = round(count($revmat[0][$cur_winner]) * 100 / count($user_votes), 1);
|
| 619 |
$reverse_ranking[$index]['viewscore'] = $reverse_ranking[$index]['rawscore'] .'%';
|
| 620 |
|
| 621 |
$result_obj->matrix = $round_log;
|
| 622 |
$result_obj->total_votes = $total_votes;
|
| 623 |
$result_obj->ranking = array_reverse($reverse_ranking);
|
| 624 |
return $result_obj;
|
| 625 |
}
|
| 626 |
|
| 627 |
// Since we're still here, no one has won, so eliminate one of the
|
| 628 |
// choices with the lowest number of votes.
|
| 629 |
|
| 630 |
// Find all choices with the minimum number of votes
|
| 631 |
$min_choices = array();
|
| 632 |
foreach ($cur_round as $ch => $choice_votes) {
|
| 633 |
if (count($choice_votes) == $min_votes) {
|
| 634 |
$min_choices[] = $ch;
|
| 635 |
}
|
| 636 |
}
|
| 637 |
|
| 638 |
// Randomly select the choice to eliminate out of the available choices
|
| 639 |
// TODO: due to the randomness, this result must be cached after each vote
|
| 640 |
$round_loser = array_rand($min_choices);
|
| 641 |
//drupal_set_message('Round ' . ($round + 1) . ' eliminated: '
|
| 642 |
//. strval($min_choices[$round_loser])
|
| 643 |
//. ' (min = ' . $min_votes . ') ' . count($cur_round));
|
| 644 |
$reverse_ranking[]['choices'] = array($min_choices[$round_loser]);
|
| 645 |
|
| 646 |
// Loop through the users who voted for the loser and redistribute
|
| 647 |
foreach ($cur_round[$min_choices[$round_loser]] as $user_key) {
|
| 648 |
// Remove their current first preference
|
| 649 |
array_shift($user_votes[$user_key]);
|
| 650 |
|
| 651 |
// Keep eliminating first preference until we run out or find an choice
|
| 652 |
// that hasn't been eliminated
|
| 653 |
while ($cur_round[$user_votes[$user_key][0]] == array()
|
| 654 |
&& count($user_votes[$user_key]) > 0) {
|
| 655 |
array_shift($user_votes[$user_key]);
|
| 656 |
}
|
| 657 |
|
| 658 |
// If they have no more preferences, remove from list for simplicity
|
| 659 |
if (count($user_votes[$user_key]) == 0) {
|
| 660 |
unset($user_votes[$user_key]);
|
| 661 |
}
|
| 662 |
}
|
| 663 |
}
|
| 664 |
// loop detected. signal user and record.
|
| 665 |
drupal_set_message("Could not reach a decision within $max_rounds iterations.");
|
| 666 |
$result_obj->matrix = $round_log;
|
| 667 |
$result_obj->total_votes = $total_votes;
|
| 668 |
return $result_obj;
|
| 669 |
|
| 670 |
}
|
| 671 |
|
| 672 |
/**
|
| 673 |
* Calculate the results using condorcet voting.
|
| 674 |
*
|
| 675 |
* @param $node
|
| 676 |
* The node object for the current decision
|
| 677 |
*
|
| 678 |
* @return
|
| 679 |
* Should return an object that include the following attributes
|
| 680 |
* -matrix: 2d array listing the aggregate preferences
|
| 681 |
* -ranking : 2d array listing the results of the Schulze count.
|
| 682 |
* -total_votes : the total number of voters who participated
|
| 683 |
*/
|
| 684 |
function _decisions_calculate_condorcet ($node) {
|
| 685 |
$votes = _decisions_votes($node);
|
| 686 |
|
| 687 |
if (count($votes) == 0) {
|
| 688 |
// no votes yet
|
| 689 |
return array();
|
| 690 |
}
|
| 691 |
|
| 692 |
// aggregate votes by user (uid if logged in, IP if anonymous)
|
| 693 |
// in ascending order of value
|
| 694 |
$user_votes = array();
|
| 695 |
|
| 696 |
foreach ($votes as $vote) {
|
| 697 |
if ($vote['uid'] == 0) {
|
| 698 |
// anonymous user
|
| 699 |
$key = $vote['vote_source'];
|
| 700 |
}
|
| 701 |
else {
|
| 702 |
// logged-in user
|
| 703 |
$key = $vote['uid'];
|
| 704 |
}
|
| 705 |
|
| 706 |
$user_votes[$key][$vote['tag']] = $vote['value']; // TAG and Value had to be reversed here to allow for ties.
|
| 707 |
}
|
| 708 |
|
| 709 |
$choice_votes = array();
|
| 710 |
|
| 711 |
$total_choices = count($node->choice);
|
| 712 |
$total_votes = count($user_votes);
|
| 713 |
|
| 714 |
// Loop through each user's vote
|
| 715 |
foreach ($user_votes as $uid => $user_vote) {
|
| 716 |
// Create an array of choice ranks, so we don't look for any of them more than once.
|
| 717 |
$choice_ranks = array();
|
| 718 |
// Go through all the node choices, and find their ranking.
|
| 719 |
for ($choice = 1; $choice <= $total_choices; $choice++) {
|
| 720 |
$ranking = 256; // default value applied to anything that isn't ranked. Tied for last. Problem if there were more than 256 options.
|
| 721 |
if (array_key_exists($choice, $user_vote)) { $ranking = $user_vote[$choice]; } // Pull the ranking from the vote.
|
| 722 |
$choice_ranks[$choice] = 0 - $ranking; // We inverse the numerical values so a high ranking is bad, negatives work fine.
|
| 723 |
}
|
| 724 |
// Loop through to compare every choice.
|
| 725 |
for ($choice_A = 1; $choice_A <= $total_choices-1; $choice_A++) {
|
| 726 |
// Loop through all choices to which choice_A has not been compared, excluding itself.
|
| 727 |
for ($choice_B = $choice_A+1; $choice_B <= $total_choices; $choice_B++) {
|
| 728 |
// Figure out where to put the points.
|
| 729 |
if ($choice_ranks[$choice_A]>$choice_ranks[$choice_B]) {
|
| 730 |
// Indicate A beat B
|
| 731 |
$choice_votes[$choice_A][$choice_B] = $choice_votes[$choice_A][$choice_B] + 1;
|
| 732 |
$choice_votes[$choice_B][$choice_A] = $choice_votes[$choice_B][$choice_A] + 0;
|
| 733 |
} else if ($choice_ranks[$choice_B]>$choice_ranks[$choice_A]) {
|
| 734 |
// Indicate B beat A
|
| 735 |
$choice_votes[$choice_B][$choice_A] = $choice_votes[$choice_B][$choice_A] + 1;
|
| 736 |
$choice_votes[$choice_A][$choice_B] = $choice_votes[$choice_A][$choice_B] + 0;
|
| 737 |
} else {
|
| 738 |
// Indicate a Tie
|
| 739 |
$choice_votes[$choice_B][$choice_A] = $choice_votes[$choice_B][$choice_A] + 0.5;
|
| 740 |
$choice_votes[$choice_A][$choice_B] = $choice_votes[$choice_A][$choice_B] + 0.5;
|
| 741 |
} // end if
|
| 742 |
} // end for
|
| 743 |
} // end for
|
| 744 |
} // end foreach
|
| 745 |
|
| 746 |
//Return the results.
|
| 747 |
$result_obj->matrix = $choice_votes;
|
| 748 |
$result_obj->ranking = _decisions_shultz($choice_votes);
|
| 749 |
$result_obj->total_votes = $total_votes;
|
| 750 |
return $result_obj;
|
| 751 |
}
|
| 752 |
|
| 753 |
function _compare_beatpaths($a, $b) {
|
| 754 |
return strcmp($b[2],$a[2]);
|
| 755 |
}
|
| 756 |
|
| 757 |
/**
|
| 758 |
* Determine the shultz method winner from a pairwise matrix.
|
| 759 |
*
|
| 760 |
* @param $matrix;
|
| 761 |
* A pair-wise matrix of results.
|
| 762 |
*
|
| 763 |
* @return
|
| 764 |
* Should return an array appropriate for the condorcet display method.
|
| 765 |
*
|
| 766 |
* Note: There is another heuristic where strongest
|
| 767 |
* beatpaths are locked in, and weaker beatpaths that conflict with them are ignored.
|
| 768 |
* From my understanding, that would eliminate entirely the need for the second half of the
|
| 769 |
* Floyd-Warshall algorithm.
|
| 770 |
* I think that would be much faster to implement and run, but I would want to satisfy myself that
|
| 771 |
* the results were the same either way, so I went for the hard way first.
|
| 772 |
*/
|
| 773 |
function _decisions_shultz($matrix) {
|
| 774 |
$ranking = array();
|
| 775 |
$candidates = count($matrix);
|
| 776 |
// Create a matrix of path strengths. Based on the Floyd-Warshall algorithm.
|
| 777 |
$strongest_paths = array();
|
| 778 |
for ($i = 1; $i<=$candidates; $i++) {
|
| 779 |
for ($j = 1; $j<=$candidates; $j++) {
|
| 780 |
if ($i!=$j) {
|
| 781 |
if ($matrix[$i][$j]>$matrix[$j][$i]) {
|
| 782 |
$strongest_paths[$i][$j] = $matrix[$i][$j];
|
| 783 |
} else {
|
| 784 |
$strongest_paths[$i][$j] = 0;
|
| 785 |
}
|
| 786 |
}
|
| 787 |
}
|
| 788 |
}
|
| 789 |
for ($i = 1; $i<=$candidates; $i++) {
|
| 790 |
for ($j = 1; $j<=$candidates; $j++) {
|
| 791 |
if ($i != $j) {
|
| 792 |
for ($k = 1; $k<=$candidates; $k++) {
|
| 793 |
if (($j!=$k) && ($i != $k)) {
|
| 794 |
$strongest_paths[$j][$k] = max ($strongest_paths[$j][$k], min ($strongest_paths[$j][$i], $strongest_paths[$i][$k]));
|
| 795 |
}
|
| 796 |
}
|
| 797 |
}
|
| 798 |
}
|
| 799 |
}
|
| 800 |
// Create an array of for,against,strength values from the strongest_paths array to allow sorting.
|
| 801 |
$beatpath = array();
|
| 802 |
for ($i = 1; $i<=$candidates; $i++) {
|
| 803 |
for ($j = 1; $j<=$candidates; $j++) {
|
| 804 |
if ($i!=$j && $strongest_paths[$i][$j] != 0) {
|
| 805 |
$beatpath[] = array($i, $j, $strongest_paths[$i][$j]);
|
| 806 |
}
|
| 807 |
}
|
| 808 |
}
|
| 809 |
// sort the array so that we're starting with the strongest links.
|
| 810 |
usort($beatpath,"_compare_beatpaths");
|
| 811 |
|
| 812 |
$round_count = 0;
|
| 813 |
$original_candidates = $candidates;
|
| 814 |
$orig_beatpath = count($beatpath);
|
| 815 |
$pathed_out = array(); // 1 indicates that the candidate has been pathed out. 2 indicates their beatpaths have been removed.
|
| 816 |
while ($candidates>1 && count($beatpath)>0) {
|
| 817 |
// Find if there are any candidates that have been pathed out.
|
| 818 |
// Pathed out means that A has a path to beat B, but B has no path to beat A, so B is eliminated.
|
| 819 |
$round_count++;
|
| 820 |
if ($round_count > $original_candidates) { // We have a problem.
|
| 821 |
$broken = TRUE;
|
| 822 |
break;
|
| 823 |
}
|
| 824 |
for ($i=1; $i<$original_candidates; $i++) {
|
| 825 |
for ($j=$i+1; $j<=$original_candidates; $j++) {
|
| 826 |
$forward = FALSE;
|
| 827 |
$reverse = FALSE;
|
| 828 |
for ($k=0; $k<count($beatpath); $k++){
|
| 829 |
if (($beatpath[$k][0] == $i) && ($beatpath[$k][1] == $j)) {
|
| 830 |
$forward = TRUE;
|
| 831 |
}
|
| 832 |
if (($beatpath[$k][1] == $i) && ($beatpath[$k][0] == $j)) {
|
| 833 |
$reverse = TRUE;
|
| 834 |
}
|
| 835 |
}
|
| 836 |
if ($forward == TRUE && $reverse == FALSE) {
|
| 837 |
$pathed_out[$j] = 1;
|
| 838 |
}
|
| 839 |
if ($forward == FALSE && $reverse == TRUE) {
|
| 840 |
$pathed_out[$i] = 1;
|
| 841 |
}
|
| 842 |
}
|
| 843 |
}
|
| 844 |
$pathed_out_count = 0;
|
| 845 |
for ($i=1; $i<=$original_candidates; $i++) {
|
| 846 |
if ($pathed_out[$i] == 1) {$pathed_out_count++;}
|
| 847 |
}
|
| 848 |
if ($pathed_out_count>0) { // Some candidate was eliminated this round.
|
| 849 |
// Remove all of the beatpaths associated with them.
|
| 850 |
$ranking[$round_count][] = "Eliminated";
|
| 851 |
for ($i=1; $i<=$original_candidates; $i++) {
|
| 852 |
if ($pathed_out[$i] == 1) {
|
| 853 |
$ranking[$round_count][] = $i;
|
| 854 |
$candidates--;
|
| 855 |
for ($j=0; $j<$orig_beatpath; $j++) {
|
| 856 |
if (($beatpath[$j][0]) == $i || ($beatpath[$j][1] == $i)) {
|
| 857 |
unset($beatpath[$j]);
|
| 858 |
}
|
| 859 |
}
|
| 860 |
$pathed_out[$i] = 2;
|
| 861 |
}
|
| 862 |
}
|
| 863 |
} else { // No candidates were eliminated this round. There is a Cyclical Tie.
|
| 864 |
// Drop all the beatpaths tied for weakest.
|
| 865 |
$index = count($beatpath)-1;
|
| 866 |
$value = $beatpath[$index][2];
|
| 867 |
do {
|
| 868 |
unset($beatpath[$index]);
|
| 869 |
$new = $beatpath[$index-1][2];
|
| 870 |
$index--;
|
| 871 |
} while ($new == $value);
|
| 872 |
$ranking[$round_count][] = "Cyclical Tie";
|
| 873 |
}
|
| 874 |
}
|
| 875 |
// Everyone left is tied for the win.
|
| 876 |
$round_count++;
|
| 877 |
$ranking[$round_count][] = "Winner";
|
| 878 |
for ($i=1; $i<=$original_candidates; $i++) {
|
| 879 |
if (!$pathed_out[$i]) {
|
| 880 |
$ranking[$round_count][] = $i;
|
| 881 |
$winner_count++;
|
| 882 |
}
|
| 883 |
}
|
| 884 |
if ($winner_count>1) {
|
| 885 |
$ranking[$round_count][0] = "Tie for Win";
|
| 886 |
}
|
| 887 |
return $ranking;
|
| 888 |
}
|
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