#!/usr/bin/perl -w
use strict;
use utf8;
+use autodie;
use Data::Printer;
+use Graph::Directed;
-binmode STDIN, 'encoding(UTF-8)' or die;
-binmode STDOUT, 'encoding(UTF-8)' or die;
-binmode STDERR, 'encoding(UTF-8)' or die;
+binmode STDIN, 'encoding(UTF-8)';
+binmode STDOUT, 'encoding(UTF-8)';
+binmode STDERR, 'encoding(UTF-8)';
our @choices;
our %choices;
our @invotes;
our $defcho;
+our $quorum = 0;
sub addchoice {
my $choname = shift @_;
}
} elsif (m/^V:\s+(\S+)\s+(\S.*)/) {
push @invotes, [ $1, $2 ];
+ } elsif (m/^quorum = ([0-9.]+)$/) {
+ $quorum = $1+0.0;
} else {
die "invalid input";
}
my $defi = $defcho->{Index};
die "FD has smaj?!" if $defcho->{Smaj};
-our @vab; # $vab[$ia][$ib] = V(A,B)
+our @vab;
+# $vab[$ia][$ib] = V(A,B)
+# Actually, it's a list of voters who prefer A to B (A.6(3)(1))
+
+# Go through the voters and construct V(A,B)
+
+print "\nDefeats matrix\n";
foreach my $iv (@invotes) {
my ($votestr,$voter) = @$iv;
foreach my $ib ($ia+1..$#vs) {
my $va = $vs[$ia];
my $vb = $vs[$ib];
- if ($va < $vb) { $vab[$ia][$ib]++; }
- elsif ($vb < $va) { $vab[$ib][$ia]++; }
- p $va; p $vb;
+ if ($va < $vb) { push @{ $vab[$ia][$ib] }, $voter }
+ elsif ($vb < $va) { push @{ $vab[$ib][$ia] }, $voter }
}
}
};
die "voter $voter $@" if $@;
}
-foreach my $iy (-2..$#choices) {
- foreach my $ix (-2..$#choices) {
+our @ch = map { $choices{$_} } @choices;
+
+# Print the counts V(A,B)
+foreach my $iy (-2..$#ch) {
+ foreach my $ix (-2..$#ch) {
if ($iy==-1) {
if ($ix==-1) {
- printf "+" or die;
+ printf "+";
} else {
- printf "------" or die;
+ printf "------";
}
} elsif ($ix==-1) {
- printf "|" or die;
+ printf "|";
} elsif ($ix==-2 && $iy==-2) {
- printf "V(Y,X)" or die;
+ printf "V(Y,X)";
} elsif ($iy==-2) {
- printf "%5s ", $choices[$ix] or die $!;
+ printf "%5s ", $choices[$ix];
} elsif ($ix==-2) {
- printf "%5s ", $choices[$iy] or die $!;
+ printf "%5s ", $choices[$iy];
} else {
my $v = \( $vab[$iy][$ix] );
- $$v += 0;
- if ($$v) {
- printf "%5d ", $$v or die $!;
+ $$v ||= [ ];
+ if (@$$v) {
+ printf "%5d ", (scalar @$$v);
} else {
- printf "%5s ", "" or die $!;
+ printf "%5s ", "";
}
}
}
- printf "\n" or die $!;
+ printf "\n";
+}
+
+sub drop ($$) {
+ my ($i,$why) = @_;
+ print "dropping $choices[$i]: $why\n";
+ $ch[$i]{Dropped} = $why;
+}
+
+print "\nQuorum A.6(2) (quorum is $quorum)\n";
+
+foreach my $i (0..$#choices) {
+ next if $ch[$i]{Dropped};
+ next if $i == $defi;
+ my $v = $vab[$i][$defi];
+ next if $v >= $quorum;
+ drop $i, "quorum ($v < $quorum)";
+}
+
+print "\nMajority ratio A.6(3)\n";
+
+foreach my $i (0..$#choices) {
+ next if $ch[$i]{Dropped};
+ next if $i == $defi;
+ my $majr = $ch[$i]{Smaj};
+ $majr ||= [1,1]; # A.6(3)(3)
+ my $vad = scalar @{ $vab[$i][$defi] };
+ my $vda = scalar @{ $vab[$defi][$i] };
+ next if $vad * $majr->[1] > $vda * $majr->[0];
+ drop $i, "majority ratio ($vad * $majr->[1] <= $vda * $majr->[0])";
+}
+
+my $defeats = Graph::Directed->new; # A.6(4)
+
+sub chremain () {
+ return grep { !$ch[$_]{Dropped} } (0..$#ch);
+}
+
+foreach my $ia (chremain()) {
+ $defeats->add_vertex($ia);
+ foreach my $ib (chremain()) {
+ my $vab = scalar @{ $vab[$ia][$ib] };
+ my $vba = scalar @{ $vab[$ib][$ia] };
+ next unless $vab > $vba;
+ print "defeat: $choices[$ia] beats $choices[$ib] ($vab > $vba)\n";
+ $defeats->add_vertex($ia,$ib);
+ }
+}
+
+sub weaker ($$) {
+ # 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)
+
+ 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 $tdefeats->has_edge($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 "\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";
+ $defeats->delete_edge($ia,$ib);
+ }
+
+ print "defeats within the Schwartz set, round again\n";
}
+print "no defeats within the Schwartz set\n";
+print "final schwartz set:\n\n";
+
+if ($schwartz->vertices() == 1) {
+ print "WINNER IS:\n";
+} else {
+ print "WINNER IS ONE OF (CASTING VOTE DECIDES):\n";
+}
+
+printf " %-5s %s\n", $choices[$_], $ch[$_]{Desc}
+ foreach ($schwartz->vertices());
+
+print ".\n";
+
#p %choices;
#p @vab;
~ian / appendix-a6.git / blobdiff