# Go through the voters and construct V(A,B)
+print "\nDefeats matrix\n";
+
foreach my $iv (@invotes) {
my ($votestr,$voter) = @$iv;
eval {
$ch[$i]{Dropped} = $why;
}
-print "# quorum A.6(2)\n";
+print "\nQuorum A.6(2) (quorum is $quorum)\n";
foreach my $i (0..$#choices) {
next if $ch[$i]{Dropped};
drop $i, "quorum ($v < $quorum)";
}
-print "# maj. ratio A.6(3)\n";
+print "\nMajority ratio A.6(3)\n";
foreach my $i (0..$#choices) {
next if $ch[$i]{Dropped};
my $defeats = Graph::Directed->new; # A.6(4)
-foreach my $ia (0..$#ch) {
- foreach my $ib (0..$#ch) {
- my $vab = $vab[$ia][$ib];
- my $vba = $vab[$ib][$ia];
+sub chremain () {
+ return grep { !$ch[$_]{Dropped} } (0..$#ch);
+}
+
+foreach my $ia (chremain()) {
+ $defeats->add_vertex($choices[$ia]);
+ foreach my $ib (chremain()) {
+ my $vab = scalar @{ $vab[$ia][$ib] };
+ my $vba = scalar @{ $vab[$ib][$ia] };
next unless $vab > $vba;
print "defeat: $choices[$ia] beats $choices[$ib] ($vab > $vba)\n";
- $defeats->add_vertex($ia,$ib);
+ $defeats->add_vertex($choices[$ia],$choices[$ib]);
}
}
+sub chvab ($$) {
+ my ($ca,$cb) = @_;
+ return $vab[ $choices{$ca}{Index} ][ $choices{$cb}{Index} ];
+}
+
sub weaker ($$) {
# A.6(7)(1)
my ($def1,$def2) = @_;
- my ($ia,$ix) = @$def1;
- my ($ib,$iy) = @$def1;
- return 1 if $vab[$ia][$ix] < $vab[$ib][$iy];
- return 1 if $vab[$ia][$ix] == $vab[$ib][$iy]
- && $vab[$ix][$ia] > $vab[$iy][$ib];
+ my ($ca,$cx) = @$def1;
+ my ($cb,$cy) = @$def1;
+ return 1 if chvab($ca, $cx) < chvab($cb, $cy);
+ return 1 if chvab($ca, $cx) == chvab($cb, $cy)
+ && chvab($cx, $ca) > chvab($cy, $cb);
return 0;
}
for (;;) {
# loop from A6(5)
- print "# transitive closure A.6(5)\n";
+ print "defeats graph: $defeats\n";
+
+ print "\nTransitive closure A.6(5)\n";
my $tdefeats = $defeats->transitive_closure();
- print "# schwartz set A.6(6)\n";
+ print "closure graph: $tdefeats\n";
+
+ print "\nSchwartz set A.6(6)\n";
$schwartz = $defeats->copy();
- foreach my $ia (0..$#ch) {
- foreach my $ib (0..$#ch) {
- next if $tdefeats->has_edge($ia,$b);
- next if !$tdefeats->has_edge($b,$ia);
+ foreach my $ia (chremain()) {
+ foreach my $ib (chremain()) {
+ next if $tdefeats->has_edge($choices[$ia],$choices[$ib]);
+ next if !$tdefeats->has_edge($choices[$ib],$choices[$ia]);
print "not in Schwartz set: $choices[$ia] because $choices[$ib]\n";
$schwartz->delete_vertex($ia);
last;
}
}
- print "# dropping weakest defeats A.6(7)\n";
+ print "\nDropping weakest defeats A.6(7)\n";
our @weakest = ();
- foreach my $edge (@{ $schwartz->edges() }) {
+ foreach my $edge ($schwartz->edges()) {
if (!@weakest) {
# no weakest edges yet
} elsif (weaker($edge, $weakest[0])) {
last unless @weakest;
printf "weakest defeats %d > %d",
- (scalar @{ $vab[$_->[0]][$_->[1]]) },
- (scalar @{ $vab[$_->[1]][$_->[0]]) };
+ (scalar @{ $vab[$_->[0]][$_->[1]] }),
+ (scalar @{ $vab[$_->[1]][$_->[0]] });
foreach my $weakest (@weakest) {
my ($ia,$ib) = @$weakest;
print "weakest defeat $choices[$ia] > $choices[$ib]\n";
- $defeats->delete_edge($ia,$ib);
+ $defeats->delete_edge($choices[$ia],$choices[$ib]);
}
- print "# defeats within the Schwartz set, round again\n";
+ print "defeats within the Schwartz set, round again\n";
}
-print "# no defeats within the Schwartz set\n";
-print "FINAL SCHWARTZ SET:\n";
+print "no defeats within the Schwartz set\n";
+print "final schwartz set:\n\n";
+
+if ($schwartz->vertices() == 1) {
+ print "WINNER IS:\n";
+} else {
+ print "WINNER IS ONE OF (CASTING VOTE DECIDES):\n";
+}
-print $choices[$_] foreach (@{ $schwartz->nodes() });
+printf " %-5s %s\n", $_, $choices{$_}{Desc}
+ foreach ($schwartz->vertices());
print ".\n";