#!/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 @invotes_v;
+our @invotes_cc;
our $defcho;
our $quorum = 0;
s/\s+$//;
next if m/^\s*\#/;
next unless m/\S/;
+ next if m/^\s/;
if (m/^([A-Z]+)\s*\=\s*(\S.*)$/) {
my ($choname, $desc) = ($1,$2);
my $cho = addchoice($choname, Desc => $desc);
$defcho = $cho;
}
} elsif (m/^V:\s+(\S+)\s+(\S.*)/) {
- push @invotes, [ $1, $2 ];
+ push @invotes_v, [ $1, $2 ];
+ } elsif (m/^(\S+)\s*\:\:\s*/) {
+ push @invotes_cc, [ $1, "$'" ];
} elsif (m/^quorum = ([0-9.]+)$/) {
$quorum = $1+0.0;
} else {
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))
-foreach my $iv (@invotes) {
+# Go through the voters and construct V(A,B)
+
+print "\nPreference matrix\n";
+
+foreach my $iv (@invotes_cc) {
+ $_ = uc $iv->[1];
+ foreach my $chn (m/\b\w+\b/g) {
+ $choices{$chn} or addchoice($chn, Desc => "($chn from voter ballot)");
+ }
+}
+
+foreach my $iv (@invotes_cc) {
+ my ($voter) = $iv->[0];
+ $_ = uc $iv->[1];
+
+ s/\t/ /g;
+ s/\,/ /g;
+ while (s{\(([^()]+)\)}{
+ my $x = $1; $x =~ s/[ =]+/=/g; $x;
+ }ge) { }
+ s/[ =]*=[ =*]/=/g;
+ s/\s+/ /g;
+ print "# normalised $_ ($voter)\n";
+
+ my @ranks = (1000,) x @choices;
+ my $rank = 1;
+ foreach (split /\s+/) {
+ foreach (split /=/) {
+ my $cho = $choices{$_};
+ $cho or die "unknown option $_ ($voter)";
+ my $ix = $cho->{Index};
+ $ranks[$ix] = $rank;
+ }
+ $rank++;
+ }
+ my $vstr = join '', map {
+ $_ == 1000 ? "-" :
+ $_ < 10 ? (sprintf "%d", $_) :
+ $_ < 36 ? (chr(ord('A') + $_ - 10)) : die
+ } @ranks;
+ print "V: $vstr $voter\n";
+ push @invotes_v, [ $vstr, $voter ];
+}
+
+foreach my $iv (@invotes_v) {
my ($votestr,$voter) = @$iv;
eval {
length $votestr eq @choices or die "wrong vote vector length";
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] );
$$v ||= [ ];
if (@$$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 ($$) {
$ch[$i]{Dropped} = $why;
}
-print "# quorum\n" or die;
+print "\nQuorum A.6(2) (quorum is $quorum)\n";
foreach my $i (0..$#choices) {
next if $ch[$i]{Dropped};
drop $i, "quorum ($v < $quorum)";
}
-print "# maj. ratio\n" or die;
+print "\nMajority ratio A.6(3)\n";
foreach my $i (0..$#choices) {
next if $ch[$i]{Dropped};
next if $i == $defi;
my $majr = $ch[$i]{Smaj};
- $majr ||= [1,1];
+ $majr ||= [1,1]; # A.6(3)(3)
my $vad = scalar @{ $vab[$i][$defi] };
my $vda = scalar @{ $vab[$defi][$i] };
next if $vad * $majr->[1] > $vda * $majr->[0];
drop $i, "majority ratio ($vad * $majr->[1] <= $vda * $majr->[0])";
}
+print "\nDefeats A.6(4)\n";
+
+my $defeats = Graph::Directed->new;
+
+sub chremain () {
+ return grep { !$ch[$_]{Dropped} } (0..$#ch);
+}
+
+foreach my $ia (chremain()) {
+ $defeats->add_vertex($choices[$ia]);
+ foreach my $ib (chremain()) {
+ my $vab = scalar @{ $vab[$ia][$ib] };
+ my $vba = scalar @{ $vab[$ib][$ia] };
+ next unless $vab > $vba;
+ my $diff = $vab - $vba;
+ print "defeat: $choices[$ia] beats $choices[$ib]",
+ " ($vab > $vba = +$diff)\n";
+ $defeats->add_edge($choices[$ia],$choices[$ib]);
+ }
+}
+
+sub chvab ($$) {
+ my ($ca,$cb) = @_;
+ my $v = $vab[ $choices{$ca}{Index} ][ $choices{$cb}{Index} ];
+ return scalar @$v;
+}
+
+sub weaker ($$) {
+ # A.6(7)(1)
+ my ($def1,$def2) = @_;
+ my ($ca,$cx) = @$def1;
+ my ($cb,$cy) = @$def2;
+ 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";
+ $schwartz->delete_vertex($choices[$ia]);
+ last;
+ }
+ }
+
+ print "set: ", (join " ", $schwartz->vertices()), "\n";
+
+ print "\nDropping weakest defeats A.6(7)\n";
+
+ our @weakest = ();
+
+ foreach my $edge ($schwartz->edges()) {
+# print " considering @$edge\n";
+ if (!@weakest) {
+ # no weakest edges yet
+ } elsif (weaker($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;
+
+ my $w = $weakest[0];
+ printf "weakest defeats are %d > %d\n",
+ chvab($w->[0], $w->[1]),
+ chvab($w->[1], $w->[0]);
+ foreach my $weakest (@weakest) {
+ my ($ca,$cb) = @$weakest;
+ print "a weakest defeat is $ca > $cb\n";
+ $defeats->delete_edge($ca,$cb);
+ }
+
+ print "\nDefeats within the Schwartz set, go round again\n";
+}
+
+print "no defeats within the Schwartz set\n";
+print "final schwartz set:\n\n";
+
+if ($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