# The Scottish Local Government Elections Order 2007
use strict;
+use Carp;
+use Data::Dumper;
+use Math::BigRat;
+use bigrat;
# Data structures:
#
# vote is
# { Voter => opaque,
-# Prefs => [ list ],
+# Prefs => [ [ CAND, ...], ... ],
# Weight => 1.0 }
# We edit Prefs as we go
+# $cands{CAND}{Cand}
# $cands{CAND}{Desc}
# $cands{CAND}{Votes}
+# $cands{CAND}{Total}
+# $cands{CAND}{NonCont} # undef, or Elected or Eliminated
+our $seats=0;
+
+our @allvotes;
+our @non_transferable;
+our %cands;
our $stage=0;
+our $quota;
+our %tie;
+our @elected;
-our $seats=0;
+our $DIGS = 5;
+our $F = (new Math::BigRat 10)->bpow($DIGS);
+
+open DEBUG, ">.compute.log" or die $!;
+DEBUG->autoflush(1);
+
+sub debug_dump () {
+ print DEBUG Dumper(\%tie,
+ \@non_transferable,
+ \%cands,
+ \@allvotes,
+ $stage, $quota);
+}
+
+$SIG{__WARN__} = sub {
+ $SIG{__DIE__} = undef;
+ debug_dump;
+ confess $_[0];
+};
+
+$SIG{__DIE__} = sub {
+ debug_dump;
+ die $_[0];
+};
+
+sub total_history_cmp ();
sub unkopt ($$) {
my ($what,$opt) = @_;
}
}
+my $display_cmp = \&total_history_cmp;
+
+while (@ARGV && $ARGV[0] =~ m/^\-/) {
+ $_ = shift @ARGV;
+ if (m/^--$/) {
+ last;
+ } elsif (m/^--sort=alpha$/) {
+ $display_cmp = sub { $b->{Cand} cmp $a->{Cand} };
+ } else {
+ die;
+ }
+}
+
for (;;) {
$_ = <>;
if (m/^\| /) {
foreach $_ (split / /, $') {
if (m/^_?[Ss]eats=(\d+)/) {
$seats = $1;
+ } elsif (m/^_?[Tt]ie=(.*)\>(.*)$/) {
+ my @more = split /\,/, $1;
+ my @less = split /\,/, $2;
+ my @all = join ',', sort (@more, @less);
+ $tie{"@all"}{Win} = $more[0] if @more == 1;
+ $tie{"@all"}{Lose} = $less[0] if @less == 1;
} else {
unkopt "election", $_;
}
}
} elsif (m/^(\w+) = (\S*) \|/) {
- my ($cand,$desc) = @_;
+ my ($cand,$desc) = ($1,$2);
unkopt "candidate $cand", $_ foreach split / /, $';
$cands{$cand}{Desc} = $desc;
} elsif (m/^(\w*) :\s*(.*)\s*\|(.*)/) {
my ($voter,$prefs,$opts) = ($1,$2,$3);
- $v = { Voter => $voter };
+ my $v = { Voter => $voter, Prefs => [ ] };
push @{ $v->{Prefs} }, [ $_ =~ m/\w+/g ]
foreach split /\s+/, $prefs;
foreach $_ (split / /, $opts) {
- if (m/^_?[Ww]eight=(\d+)/(\d+)$/) {
+ if (m/^_?[Ww]eight=(\d+)\/(\d+)$/) {
$v->{Weight} = $1 / $2;
} elsif (m/^_?[Ww]eight=([0-9.]+)$/) {
$v->{Weight} = new Math::BigRat $1;
}
}
+$cands{$_}{Cand} = $_ foreach keys %cands;
+$_->{Weight} //= 1/1 foreach @allvotes;
+$_->{TransferredSurplus} //= [ ] foreach @allvotes;
+$_->{OrigPrefs} //= [ @{ $_->{Prefs} } ] foreach @allvotes;
+
+sub votelog ($$) {
+ my ($vote,$m) = @_;
+ push @{ $vote->{Log} }, "stage $stage: $m";
+}
+
+sub sortballots (@);
sub sortballots (@) {
# Takes each argument, which should be a ballot, sorts
# it into $cand{CAND}{Votes} according to first preference.
# Strips that first preference from the ballot.
# If the first preference has been eliminated, strips it
# and looks for further preferences.
+ print DEBUG "sortballots ".(scalar @_)."...\n";
foreach my $v (@_) {
my $firstprefs = shift @{ $v->{Prefs} };
+ my $w = $v->{Weight};
if (!$firstprefs || !@$firstprefs) {
- vlog $v, "no more preferences, non transferable";
+ votelog $v, "no more preferences, non transferable";
push @non_transferable, $v;
next;
}
if (@$firstprefs > 1) {
- vlog $v, "splitting due to several equal first preferences";
+ votelog $v, "splitting due to several equal first preferences";
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 = @_;
-
-
-# $cands
+ };
+ votelog $v, "split for $fpref";
+ }
+ next;
+ }
+ my $fp = $firstprefs->[0];
+ my $c = $cands{$fp};
+ my $noncont = $c->{NonCont};
+ if ($noncont) {
+ votelog $v, "dropping pref $fp, $noncont";
+ sortballots $v;
+ next;
+ }
+ votelog $v, "sorted into pile for candidate $fp weight $w";
+ push @{ $c->{Votes} }, $v;
+ }
+}
+
+sub floor ($) {
+ my ($v) = @_;
+ $v = new Math::BigRat $v; # we need a copy
+ return $v->bfloor();
+}
+
+sub sv ($) {
+ my ($in) = @_;
+ my $v = new Math::BigRat $in; # just in case
+ my $intpart = floor($v);
+ my $frac = $v - $intpart;
+ my $good = floor($frac * $F);
+ my $bad = $frac * $F - $good;
+ my $s = sprintf "%7d", $intpart;
+ if ($frac) {
+ $s .= sprintf ".%0${DIGS}d", $good;
+ $s .= sprintf "%-4s", ($bad ? "+$bad" : "");
+ } else {
+ $s .= sprintf " %${DIGS}s%4s", '', '';
+ }
+#print STDERR "# $in => $s # (intpart=$intpart frac=$frac)\n";
+ return $s;
+}
+
+sub prf {
+ my $fmt = shift;
+ printf " ".$fmt, @_;
+}
+
+sub countballots () {
+ foreach my $c (values %cands) {
+ next if $c->{NonCont};
+ $c->{Total} = 0/1;
+ $c->{Total} += $_->{Weight} foreach @{ $c->{Votes} };
+ print DEBUG "counted $c->{Cand} $c->{Total}\n";
+ $c->{History}[$stage-1] = $c->{Total};
+ }
+
+ foreach my $c (reverse sort $display_cmp
+ grep { !$_->{NonCont} } values %cands) {
+ prf "candidate %-10s: %s votes\n", $c->{Cand}, sv $c->{Total};
+ }
+}
+
+sub computequota () {
+ my $totalvalid = 0/1;
+ $totalvalid += $_->{Total} foreach values %cands;
+ $quota = floor($totalvalid / (1 + $seats) + 1);
+ prf "total valid %s\n", sv $totalvalid;
+ prf "quota %s\n", sv $quota;
+}
+
+sub total_history_cmp () {
+ my $ha = $a->{History};
+ my $hb = $b->{History};
+ my $m = "stage $stage history cmp $a->{Cand} $b->{Cand}";
+ print DEBUG "$m...\n";
+ foreach my $s (reverse 0 .. $stage-1) {
+ my $d = $ha->[$s] <=> $hb->[$s];
+ next unless $d;
+ print DEBUG "$m => $d (#$s $ha->[$s] $hb->[$s])\n";
+ return $d;
+ }
+ print DEBUG "$m => 0\n";
+ return 0;
+}
+
+sub continuing () {
+ grep { !$_->{NonCont} } values %cands;
+}
+
+sub select_best_worst ($$$$) {
+ my ($wantcand, $wanttiebreak, $signum, $what) = @_;
+ # $wantcand->($c) = boolish
+ # $wanttiebreak->($total) = boolish
+ # Firstly candidates not meeting $wantcand are ignored
+ # Then we pick the best (worst) candiate by Total (or vote history).
+ # (SLGEO 49(2) and 51(2).
+ # If this does not help then totals are equal and we call wanttiebreak.
+ # If it returns 0 we return alphabetically first CAND. Otherwise
+ # we tie break.
+
+ my @maybe = grep { $wantcand->($_) } continuing();
+ @maybe = sort total_history_cmp @maybe;
+ @maybe = reverse @maybe if $signum > 0;
+
+ return undef unless @maybe;
+
+ my $nequal = 1;
+
+ for (;;) {
+ my $nextc = $maybe[$nequal];
+ last unless $nextc;
+
+ # Only interested in those who compare equal according to the
+ # history (SLGEO 49(2)); NB our history includes the current
+ # round.
+
+ last if $signum*($a = $maybe[0], $b = $nextc, total_history_cmp) > 0;
+ $nequal++;
+ }
+
+ if ($nequal > 1 && !$wanttiebreak->($maybe[0]{Total})) {
+ # ... if equal for election we can do them one by one, since
+ # order does not matter (SLGEO 49 talks about `two or more
+ # ... exceeds').
+ $nequal = 1;
+ }
+
+ my $selectcand;
+ if ($nequal > 1) {
+ my @all = map { $_->{Cand} } @maybe[0 .. $nequal-1];
+ my $tiekey = $signum > 0 ? 'Win' : 'Lose';
+ $selectcand = $tie{"@all"}{$tiekey};
+ die "need tie break, want $tiekey from @all"
+ unless defined $selectcand;
+ prf "$what %s due to tie break amongst %s\n",
+ $selectcand, "@all";
+ } else {
+ $selectcand = $maybe[0]{Cand};
+ prf "$what %s\n", $selectcand;
+ }
+
+ return $cands{$selectcand};
+}
+
+sub elect_core ($) {
+ my ($c) = @_;
+ prf "*** ELECT %s \`%s' ***\n", $c->{Cand}, $c->{Desc};
+ $c->{NonCont} = 'Elected';
+ push @elected, $c;
+}
+
+$stage = 0;
for (;;) {
-
+ $stage++;
+ printf "stage %3d:\n", $stage;
+
+ sortballots @allvotes if $stage == 1;
+
+ my $seats_remain = $seats - @elected;
+
+ prf "seats remaining %d\n", $seats_remain;
+
+ last unless $seats_remain;
+
+ if (continuing() <= $seats_remain) {
+ foreach my $c (continuing()) {
+ prf "electing %s to fill remaining place(s)\n", $c->{Cand};
+ elect_core $c;
+ }
+ last;
+ }
+
+ countballots();
+
+ computequota if $stage == 1;
+
+ my $c = select_best_worst
+ sub { $_->{Total} >= $quota },
+ sub { $_ > $quota },
+ +1, 'electing';
+
+ if ($c) {
+ elect_core $c;
+ votelog $_, "helped elect $c->{Cand}" foreach @{ $c->{Votes} };
+
+ # SLGEO 48
+ my $surplus = $c->{Total} - $quota;
+
+ if ($surplus <= 0/1) {
+ prf "no surplus\n";
+ next;
+ }
+
+ last if $seats_remain == 1; # don't bother doing more transfers
+
+ my $B = $c->{Total};
+ my %tspr;
+
+ prf "surplus %s\n", sv $surplus;
+
+ foreach my $v (@{ $c->{Votes} }) {
+ my $previously = $v->{TransferredSurplus};
+ push @$previously, $c->{Cand};
+
+ my $A = $surplus * $v->{Weight};
+ 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;
+
+ if (defined $tspr{"@$previously"}) {
+ die unless $tspr{"@$previously"} == $xfervalue;
+ } else {
+ $tspr{"@$previously"} = $xfervalue;
+ prf "transfer value of ballots %20s: %s\n",
+ "@$previously", sv $xfervalue;
+ }
+ }
+ sortballots @{ $c->{Votes} };
+
+ $c->{Votes} = { }; # will crash if we access it again
+ next;
+ }
+
+ # No-one to elect, must eliminate
+ $c = select_best_worst
+ sub { 1; },
+ sub { 1; },
+ -1, 'eliminating';
+
+ if ($c) {
+ prf "=== eliminating %s \`%s' ===\n", $c->{Cand}, $c->{Desc};
+ $c->{NonCont} = 'Eliminated';
+
+ sortballots @{ $c->{Votes} };
+ next;
+ }
+
+ die;
+}
+
+print "Winners:\n";
+
+foreach my $i (0..$#elected) {
+ my $c = $elected[$i];
+ printf " %3d. %-10s %s\n", $i+1, $c->{Cand}, $c->{Desc};
+}
+
+print "done.\n";
~ian / appendix-a6.git / blobdiff