From 5dc538aedf489281785ce32f25dcaa18385ac6a5 Mon Sep 17 00:00:00 2001
From: Ian Jackson <ijackson@chiark.greenend.org.uk>
Date: Sun, 2 Feb 2014 20:16:11 +0000
Subject: [PATCH 1/1] wip

---
 parse | 64 +++++++++++++++++++++++++++++++++++++++++++++++++++++++----
 1 file changed, 60 insertions(+), 4 deletions(-)

diff --git a/parse b/parse
index 8828dee..e176ecc 100755
--- a/parse
+++ b/parse
@@ -3,6 +3,7 @@ use strict;
 use utf8;
 
 use Data::Printer;
+use Graph::Directed;
 
 binmode STDIN, 'encoding(UTF-8)' or die;
 binmode STDOUT, 'encoding(UTF-8)' or die;
@@ -49,7 +50,11 @@ if (!$defcho) {
 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)
 
 foreach my $iv (@invotes) {
     my ($votestr,$voter) = @$iv;
@@ -80,6 +85,7 @@ foreach my $iv (@invotes) {
 
 our @ch = map { $choices{$_} } @choices;
 
+# Print the counts V(A,B)
 foreach my $iy (-2..$#ch) {
     foreach my $ix (-2..$#ch) {
 	if ($iy==-1) {
@@ -115,7 +121,7 @@ sub drop ($$) {
     $ch[$i]{Dropped} = $why;
 }
 
-print "# quorum\n" or die;
+print "# quorum A.6(2)\n" or die $!;
 
 foreach my $i (0..$#choices) {
     next if $ch[$i]{Dropped};
@@ -125,19 +131,69 @@ foreach my $i (0..$#choices) {
     drop $i, "quorum ($v < $quorum)";
 }
 
-print "# maj. ratio\n" or die;
+print "# maj. ratio A.6(3)\n" or die $!;
 
 foreach my $i (0..$#choices) {
     next if $ch[$i]{Dropped};
     next if $i == $defi;
     my $majr = $ch[$i]{Smaj};
-    $majr ||= [1,1];
+    $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)
+
+foreach my $ia (0..$#ch) {
+    foreach my $ib (0..$#ch) {
+	my $vab = $vab[$ia][$ib];
+	my $vba = $vab[$ib][$ia];
+	next unless $vab > $vba;
+	print "defeat: $choices[$ia] beats $choices[$ib] ($vab > $vba)\n"
+	    or die $!;
+	$defeats->add_vertex($ia,$ib);
+    }
+}
+
+print "# transitive closure A.6(5)\n" or die $!;
+
+my $tdefeats = $defeats->transitive_closure();
+
+print "# schwartz set A.6(6)\n" or die $!;
+
+my $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);
+	print "not in Schwartz set: $choices[$ia] because $choices[$ib]\n"
+	    or die $!;
+	$schwartz->delete_vertex($ia);
+	last;
+    }
+}
+
+print "# dropping weakest defeats A.6(7)\n" or die $!;
+
+my @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;
+}
 
 #p %choices;
 #p @vab;
-- 
2.30.2