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 {
# Go through the voters and construct V(A,B)
-foreach my $iv (@invotes) {
+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";
$ch[$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};
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};
drop $i, "majority ratio ($vad * $majr->[1] <= $vda * $majr->[0])";
}
-my $defeats = Graph::Directed->new; # A.6(4)
+print "\nDefeats A.6(4)\n";
+
+my $defeats = Graph::Directed->new;
-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";
- $defeats->add_vertex($ia,$ib);
+ my $diff = $vab - $vba;
+ print "defeat: $choices[$ia] beats $choices[$ib]",
+ " ($vab > $vba = +$diff)\n";
+ $defeats->add_edge($choices[$ia],$choices[$ib]);
}
}
-print "# transitive closure A.6(5)\n";
+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)
-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 $tdefeats->has_edge($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 "# dropping weakest defeats A.6(7)\n";
+ print "set: ", (join " ", $schwartz->vertices()), "\n";
-my @weakest = ();
+ print "\nDropping weakest defeats A.6(7)\n";
-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
+ 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;
}
- 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";
}
-b#p %choices;
+printf " %-5s %s\n", $_, $choices{$_}{Desc}
+ foreach ($schwartz->vertices());
+
+print ".\n";
+
+#p %choices;
#p @vab;
~ian / appendix-a6.git / blobdiff