# 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()) {
+ $defeats->add_vertex($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);
}
}
-print "# transitive closure A.6(5)\n";
+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];
+ return 0;
+}
+
+our $schwartz;
+
+for (;;) {
+ # loop from A6(5)
-my $tdefeats = $defeats->transitive_closure();
+ print "defeats graph: $defeats\n";
-print "# schwartz set A.6(6)\n";
+ print "\nTransitive closure A.6(5)\n";
-my $schwartz = $defeats->copy();
+ my $tdefeats = $defeats->transitive_closure();
-foreach my $ia (0..$#ch) {
- foreach my $ib (0..$#ch) {
- next if $tdefeats->has_edge($ia,$b);
- next if !$tdefeats->has_edge($b,$ia);
- print "not in Schwartz set: $choices[$ia] because $choices[$ib]\n";
- $schwartz->delete_vertex($ia);
- last;
+ print "closure graph: $tdefeats\n";
+
+ print "\nSchwartz set A.6(6)\n";
+
+ $schwartz = $defeats->copy();
+
+ foreach my $ia (chremain()) {
+ foreach my $ib (chremain()) {
+ next if $tdefeats->has_edge($ia,$ib);
+ next if !$tdefeats->has_edge($ib,$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";
-my @weakest = ();
+ our @weakest = ();
-foreach my $edge (@{ $schwartz->edges() }) {
- if (!@weakest) {
- # no weakest edges yet
- } elsif (weaker($edge, $weakest[0])) {
- # this edge is weaker than previous weakest, start new set
- @weakest = ();
- } elsif (weaker($weakest[0], $edge)) {
- # weakest edge is weaker than this one, ignore this one
- next;
- } else {
- # weakest edge is exactly as weak as this one, add this one
+ foreach my $edge ($schwartz->edges()) {
+ if (!@weakest) {
+ # no weakest edges yet
+ } elsif (weaker($edge, $weakest[0])) {
+ # this edge is weaker than previous weakest, start new set
+ @weakest = ();
+ } elsif (weaker($weakest[0], $edge)) {
+ # weakest edge is weaker than this one, ignore this one
+ next;
+ } else {
+ # weakest edge is exactly as weak as this one, add this one
+ }
+ push @weakest, $edge;
}
- push @weakest, $edge;
+
+ last unless @weakest;
+
+ printf "weakest defeats %d > %d",
+ (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,$ib);
+ }
+
+ print "defeats within the Schwartz set, round again\n";
}
-b#p %choices;
+print "no defeats within the Schwartz set\n";
+print "final schwartz set:\n\n";
+
+if ($schwartz->vertices() == 1) {
+ print "WINNER IS:\n";
+} else {
+ print "WINNER IS ONE OF (CASTING VOTE DECIDES):\n";
+}
+
+printf " %-5s %s\n", $choices[$_], $ch[$_]{Desc}
+ foreach ($schwartz->vertices());
+
+print ".\n";
+
+#p %choices;
#p @vab;