X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?a=blobdiff_plain;ds=sidebyside;f=parse;h=7ca1ed6aa70817165ca476ac6323a37f4404506e;hb=708d36a1a95409c926ac4be1a343faa41cf09052;hp=16f09266a2471eff0551b4f25f31e5ba1a6951c8;hpb=6c044868abff470bc659ffd315bcf5a1cea20ded;p=appendix-a6.git

diff --git a/parse b/parse
index 16f0926..7ca1ed6 100755
--- a/parse
+++ b/parse
@@ -57,6 +57,8 @@ our @vab;
 
 # Go through the voters and construct V(A,B)
 
+print "\nDefeats matrix\n";
+
 foreach my $iv (@invotes) {
     my ($votestr,$voter) = @$iv;
     eval {
@@ -122,7 +124,7 @@ sub drop ($$) {
     $ch[$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};
@@ -132,7 +134,7 @@ foreach my $i (0..$#choices) {
     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};
@@ -147,52 +149,105 @@ foreach my $i (0..$#choices) {
 
 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;