# The Scottish Local Government Elections Order 2007
use strict;
+use bigrat;
# Data structures:
#
# vote is
# { Voter => opaque,
-# Prefs => [ list ],
+# Prefs => [ [ CAND, ...], ... ],
# Weight => 1.0 }
# We edit Prefs as we go
# $cands{CAND}{Desc}
# $cands{CAND}{Votes}
-
-our $stage=0;
+# $cands{CAND}{Total}
+# $cands{CAND}{Continuing}
our $seats=0;
+our $stage=0;
+our $quota;
+our %tie;
+
sub unkopt ($$) {
my ($what,$opt) = @_;
if ($opt =~ m/^[A-Z]/) {
foreach $_ (split / /, $') {
if (m/^_?[Ss]eats=(\d+)/) {
$seats = $1;
+ } elsif (m/^_?[Tt]ie=(.*)\>(.*)$/) {
+ my @more = split /\,/, $1;
+ my @less = split /\,/, $2;
+ my @all = join ',', sort (@more, @less);
+ $tie{"@all"}{Win} = $more[0] if @more == 1;
+ $tie{"@all"}{Lose} = $less[0] if @less == 1;
} else {
unkopt "election", $_;
}
}
}
+$_->{Continuing} = 1 foreach values %cands;
+
sub sortballots (@) {
# Takes each argument, which should be a ballot, sorts
# it into $cand{CAND}{Votes} according to first preference.
# and looks for further preferences.
foreach my $v (@_) {
my $firstprefs = shift @{ $v->{Prefs} };
+ my $w = $v->{Weight};
if (!$firstprefs || !@$firstprefs) {
vlog $v, "no more preferences, non transferable";
push @non_transferable, $v;
foreach my $fpref (@$firstprefs) {
my $v2 = {
%$v,
- Weight => $v->{Weight} / @$firstprefs,
+ Weight => $w / @$firstprefs,
Prefs => [ [ $fpref ], @{ $v->{Prefs} } ],
- };
+ };
vlog $v, "split for $fpref";
-
-
- Voter => $
-
- my @prefs
- my $nprefs = scalar @{ $v->{Prefs}
- my @input = @_;
-
+ }
+ next;
+ }
+ my $fp = $firstprefs[0];
+ my $c = $cands{$fp};
+ if (!$c->{Continuing}) {
+ vlog $v, "dropping pref $fp, not a continuing candidate";
+ sortvallots $v;
+ next;
+ }
+ vlog $v, "sorted into pile for candidate $fp weight $w";
+ push @{ $c->{Votes} }, $v;
+ }
+}
+
+sub prf {
+ my $fmt = shift;
+ printf "stage %d: ".$_, $stage, @_;
+}
+
+sub countballots () {
+ foreach my $c (values %cand) {
+ $c->{Total} = 0;
+ $c->{Total} += $_->{Weight} foreach @{ $c->{Voters} };
+ }
+ foreach my $cand (sort keys %cand) {
+ $c = $cands{$cand};
+ next unless $c->{Continuing};
+ prf "cand %s: %s votes\n", $stage, $cand, $c->{Total};
+ $c->{History}[$stage-1] = $c->{Total};
+ }
+}
+
+sub computequota () {
+ my $totalvalid = 0;
+ $totalvalid += $_->{Total} foreach keys %cands;
+ $quota = floor($totalvalid / (1 + $seats));
+}
-# $cands
+sub total_history_cmp () {
+ my $ha = $cands{a}{History};
+ my $hb = $cands{a}{History};
+ foreach my $s (reverse 1 .. $stage) {
+ my $d = $ha->[$s] <=> $hb->[$s];
+ next unless $d;
+ print DEBUG "history cmp $a $b => $d (#$s $ha->[$s] $hb->[$s])\n";
+ return $e;
+ }
+ return 0;
+}
+
+sortballots @allvotes;
for (;;) {
+ $stage++;
+ countballots();
+
+ my @maybe_elect = reverse sort total_history_cmp keys %cands;
+ my $nelect=0;
+ for (;;) {
+ my $nextcand = $maybe_elect[$nelect];
+ my $nextc = $cands{$nextcand};
+
+ # We certainly only consider those who meet quota
+ last unless $nextc->{Total} >= $quota;
+ last unless $nextc->{Total} > $quota && $nextel;
+ # ... if equal we can do them one by one, since order
+ # does not matter (SLGEO 49 talks about `two or more ... exceeds')
+
+ last if $nelect &&
+ (total_history_cmp $maybe_elect[0], $nextcand) > 0;
+ # ... only interested in those who compare equal
+ # according ot the history (SLGEO 49(2)); NB our history
+ # includes the current round.
+
+ $nelect++;
+ }
+
+ if ($nelect) {
+ my $elect;
+ if ($nelect > 1) {
+ my @all = @maybe_elect[0 .. $nelect-1];
+ my $elect = $tie{"@all"}{Win};
+ die "need tie break, want winner from @all" unless defined $win;
+ prf "electing %s due to tie break amongst %s\n",
+ $elect, "@all";
+ } else {
+ $elect = $maybe_elect[0];
+ prf "electing %s\n";
+ }
+
+ prf "*** ELECT %s ***\n", $elect;
+ $c->{Continuing} = 0;
+ votelog $_, "helped elect $elect" foreach @{ $c->{Votes} };
+
+ # SLGEO 48
+ my $c = $cands{$elect};
+ my $surplus = $c->{Total} - $quota;
+
+ if ($surplus <= 0) {
+ prf "no surplus\n";
+ next;
+ }
+
+ my $B = $c->{Weight};
+
+ foreach my $v (@{ $c->{Votes} }) {
+ my $A = $surplus * $v->{Weight};
+ my $F = 100000;
+ my $xfervalue = floor(($A * $F) / $B) / $f;
+ # SLGEO 48(3): we do arithmetic to 5 d3ecimal places,
+ # but always rounding down
+ votelog $v, "transferring with value $xfervalue (A=$A B=$B)";
+ $v->{Weight} = $xfervalue;
+ sortballots $v;
+ }
+ $c->{Votes} = { }; # will crash if we access it again
+ next;
+ }
+