#!/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;
# Go through the voters and construct V(A,B)
+print "\nDefeats matrix\n";
+
foreach my $iv (@invotes) {
my ($votestr,$voter) = @$iv;
eval {
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] );
$$v ||= [ ];
if (@$$v) {
- printf "%5d ", (scalar @$$v) or die $!;
+ printf "%5d ", (scalar @$$v);
} else {
- printf "%5s ", "" or die $!;
+ printf "%5s ", "";
}
}
}
- printf "\n" or die $!;
+ printf "\n";
}
sub drop ($$) {
$ch[$i]{Dropped} = $why;
}
-print "# quorum A.6(2)\n" or die $!;
+print "\nQuorum A.6(2) (quorum is $quorum)\n";
foreach my $i (0..$#choices) {
next if $ch[$i]{Dropped};
drop $i, "quorum ($v < $quorum)";
}
-print "# maj. ratio A.6(3)\n" or die $!;
+print "\nMajority ratio A.6(3)\n";
foreach my $i (0..$#choices) {
next if $ch[$i]{Dropped};
my $defeats = Graph::Directed->new; # A.6(4)
-foreach my $ia (0..$#ch) {
- foreach my $ib (0..$#ch) {
- my $vab = $vab[$ia][$ib];
- my $vba = $vab[$ib][$ia];
+sub chremain () {
+ return grep { !$ch[$_]{Dropped} } (0..$#ch);
+}
+
+foreach my $ia (chremain()) {
+ $defeats->add_vertex($choices[$ia]);
+ foreach my $ib (chremain()) {
+ my $vab = scalar @{ $vab[$ia][$ib] };
+ my $vba = scalar @{ $vab[$ib][$ia] };
next unless $vab > $vba;
- print "defeat: $choices[$ia] beats $choices[$ib] ($vab > $vba)\n"
- or die $!;
- $defeats->add_vertex($ia,$ib);
+ print "defeat: $choices[$ia] beats $choices[$ib] ($vab > $vba)\n";
+ $defeats->add_vertex($choices[$ia],$choices[$ib]);
}
}
-print "# transitive closure A.6(5)\n" or die $!;
+sub chvab ($$) {
+ 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";
-my $tdefeats = $defeats->transitive_closure();
+ print "\nTransitive closure A.6(5)\n";
-print "# schwartz set A.6(6)\n" or die $!;
+ my $tdefeats = $defeats->transitive_closure();
-my $schwartz = $defeats->copy();
+ print "closure graph: $tdefeats\n";
-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 "\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 "# dropping weakest defeats A.6(7)\n" or die $!;
+ 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";
+ $defeats->delete_edge($choices[$ia],$choices[$ib]);
+ }
+
+ print "defeats within the Schwartz set, round again\n";
}
+print "no defeats within the Schwartz set\n";
+print "final schwartz set:\n\n";
+
+if ($schwartz->vertices() == 1) {
+ print "WINNER IS:\n";
+} else {
+ print "WINNER IS ONE OF (CASTING VOTE DECIDES):\n";
+}
+
+printf " %-5s %s\n", $_, $choices{$_}{Desc}
+ foreach ($schwartz->vertices());
+
+print ".\n";
+
#p %choices;
#p @vab;
~ian / appendix-a6.git / blobdiff