function runBallots($cands, $ballots)
{
$cprobs = array();
$final_probs = array();
$pairs = getAllPairs($cands);
foreach ($ballots as $b) {
$pairs = getBallotPairs($cands, $b, $pairs);
}
$ballots_with_neither = array();
foreach ($ballots as $ballot) {
foreach ($cands as $I) {
foreach ($cands as $J) {
if ($I != $J) {
if (!isset($ballots_with_neither[$I])) {
$ballots_with_neither[$I] = array();
}
if (!isset($ballots_with_neither[$I][$J])) {
$ballots_with_neither[$I][$J] = 0;
}
if (!in_array($I, $ballot) and !in_array($J, $ballot)) {
$ballots_with_neither[$I][$J] += 1;
}
}
}
}
}
//print_r($ballots_with_neither);exit;
foreach ($ballots as $ballot) {
foreach ($cands as $I) {
$cprobs[$I] = array();
foreach ($cands as $J) {
if ($I != $J) {
$cprobs[$I][$J] = '';
//per Tse-min algorithm
$V = count($ballots);
$M = floor($V / 2) + 1;
$C = count($cands);
$R = count($ballots) - $ballots_with_neither[$I][$J];
$S = $ballots_with_neither[$I][$J];
$T = $pairs[$I][$J];
$IbeatJ = $pairs[$I][$J];
$JbeatI = $pairs[$J][$I];
$prob = $IbeatJ / ($IbeatJ + $JbeatI);
$Q = $prob;
$k_range = $M - $T - 1;
if ($M - $S <= $T && $T < $M) {
$sum = 0;
foreach (range(0, $k_range) as $k) {
$sum += binomial($S, $Q, $k);
}
$new_prob = 1 - $sum;
}
if ($T + $S < $M) {
$new_prob = 0;
}
if ($T >= $M) {
$new_prob = 1;
}
$cprobs[$I][$J] = $new_prob;
global $PRINT;
if ($PRINT) {
print "\n----------------------\n";
print "I is {$I}\n";
print "J is {$J}\n";
print "V is {$V}\n";
print "M is {$M}\n";
print "C is {$C}\n";
print "R is {$R}\n";
print "S is {$S}\n";
print "T is {$T}\n";
print "Q is {$Q}\n";
print "k range is {$k_range}\n";
print "calculated probability is {$new_prob}\n";
}
}
// I != J
}
// foreach J
}
//foreach I
foreach ($cprobs as $I => $J_array) {
$final_probs[$I] = round(array_product($J_array), 4);
}
}
return $final_probs;
}
function rerunForNeitherOnBallot($cands, $pairs, $ballots)
{
$old_pairs = $pairs;
$new_pairs = $pairs;
foreach ($ballots as $ballot) {
$cands_missing_on_this_ballot = array();
foreach ($cands as $miss) {
if (!in_array($miss, $ballot)) {
$cands_missing_on_this_ballot[] = $miss;
}
}
foreach ($cands_missing_on_this_ballot as $I) {
foreach ($cands_missing_on_this_ballot as $J) {
if ($I != $J) {
$ballots_with_neither = array();
foreach ($ballots as $bal) {
if (!in_array($I, $bal) and !in_array($J, $bal)) {
$ballots_with_neither[] = $bal;
}
}
//per Tse-min algorithm
$V = count($ballots);
$M = floor($V / 2) + 1;
$C = count($cands);
$R = count($ballots) - count($ballots_with_neither);
$S = count($ballots_with_neither);
$T = $old_pairs[$I][$J];
$IbeatJ = $old_pairs[$I][$J];
$JbeatI = $old_pairs[$J][$I];
$prob = $IbeatJ / ($IbeatJ + $JbeatI);
$Q = $prob;
$k_range = $M - $T - 1;
if ($M - $S <= $T && $T < $M) {
$sum = 0;
foreach (range(0, $k_range) as $k) {
$sum += binomial($S, $Q, $k);
}
$new_prob = 1 - $sum;
}
if ($T + $S < $M) {
$new_prob = 0;
}
if ($T >= $M) {
$new_prob = 1;
}
global $PRINT;
if ($PRINT) {
print "\n----------------------\n";
print "I is {$I}\n";
print "J is {$J}\n";
print "V is {$V}\n";
print "M is {$M}\n";
print "C is {$C}\n";
print "R is {$R}\n";
print "S is {$S}\n";
print "T is {$T}\n";
print "Q is {$Q}\n";
print "k range is {$k_range}\n";
print "calculated probability is {$new_prob}\n";
}
if (flip($new_prob)) {
$new_pairs[$I][$J] += 1;
} else {
// $new_pairs[$J][$I] += 1;
}
}
}
}
}
return $new_pairs;
}
