+ printf "\n";
+}
+
+sub drop ($$) {
+ my ($i,$why) = @_;
+ print "dropping $choices[$i]: $why\n";
+ $ch[$i]{Dropped} = $why;
+}
+
+print "\nQuorum A.6(2) (quorum is $quorum)\n";
+
+foreach my $i (0..$#choices) {
+ next if $ch[$i]{Dropped};
+ next if $i == $defi;
+ my $v = $vab[$i][$defi];
+ next if $v >= $quorum;
+ drop $i, "quorum ($v < $quorum)";
+}
+
+print "\nMajority ratio A.6(3)\n";
+
+foreach my $i (0..$#choices) {
+ next if $ch[$i]{Dropped};
+ next if $i == $defi;
+ my $majr = $ch[$i]{Smaj};
+ $majr ||= [1,1]; # A.6(3)(3)
+ my $vad = scalar @{ $vab[$i][$defi] };
+ my $vda = scalar @{ $vab[$defi][$i] };
+ next if $vad * $majr->[1] > $vda * $majr->[0];
+ drop $i, "majority ratio ($vad * $majr->[1] <= $vda * $majr->[0])";
+}
+
+my $defeats = Graph::Directed->new; # A.6(4)
+
+sub chremain () {
+ return grep { !$ch[$_]{Dropped} } (0..$#ch);
+}
+
+foreach my $ia (chremain()) {
+ $defeats->add_vertex($choices[$ia]);
+ foreach my $ib (chremain()) {
+ my $vab = scalar @{ $vab[$ia][$ib] };
+ my $vba = scalar @{ $vab[$ib][$ia] };
+ next unless $vab > $vba;
+ print "defeat: $choices[$ia] beats $choices[$ib] ($vab > $vba)\n";
+ $defeats->add_vertex($choices[$ia],$choices[$ib]);
+ }
+}
+
+sub chvab ($$) {
+ my ($ca,$cb) = @_;
+ return $vab[ $choices{$ca}{Index} ][ $choices{$cb}{Index} ];
+}
+
+sub weaker ($$) {
+ # A.6(7)(1)
+ my ($def1,$def2) = @_;
+ my ($ca,$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;
+}
+
+our $schwartz;
+
+for (;;) {
+ # loop from A6(5)
+
+ print "defeats graph: $defeats\n";
+
+ print "\nTransitive closure A.6(5)\n";
+
+ my $tdefeats = $defeats->transitive_closure();
+
+ 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 $tdefeats->has_edge($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 "\nDropping weakest defeats A.6(7)\n";
+
+ 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
+ }
+ 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";
+ $defeats->delete_edge($choices[$ia],$choices[$ib]);
+ }
+
+ print "defeats within the Schwartz set, round again\n";