X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=appendix-a6.git;a=blobdiff_plain;f=parse;h=a1ce9c587747aa906135ea656f98b04ccb3257fe;hp=82c896dcba4fe5ca376e07e2674024c4dab97af9;hb=0651d6b71fb087495c174faac376b5c9c60c0bfc;hpb=86f4cb40e07a6e1eac3eafe6b426145d06553ab4 diff --git a/parse b/parse index 82c896d..a1ce9c5 100755 --- a/parse +++ b/parse @@ -1,17 +1,20 @@ #!/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 $defcho; +our $quorum = 0; sub addchoice { my $choname = shift @_; @@ -34,6 +37,8 @@ while (<>) { } } elsif (m/^V:\s+(\S+)\s+(\S.*)/) { push @invotes, [ $1, $2 ]; + } elsif (m/^quorum = ([0-9.]+)$/) { + $quorum = $1+0.0; } else { die "invalid input"; } @@ -46,7 +51,13 @@ if (!$defcho) { 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)) + +# Go through the voters and construct V(A,B) + +print "\nDefeats matrix\n"; foreach my $iv (@invotes) { my ($votestr,$voter) = @$iv; @@ -67,44 +78,181 @@ foreach my $iv (@invotes) { foreach my $ib ($ia+1..$#vs) { my $va = $vs[$ia]; my $vb = $vs[$ib]; - if ($va < $vb) { $vab[$ia][$ib]++; } - elsif ($vb < $va) { $vab[$ib][$ia]++; } - print "\$vab[$ia][$ib]=$vab[$ia][$ib] # $voter $va<$vb\n"; - print "\$vab[$ib][$ia]=$vab[$ib][$ia] # $voter $va>$vb\n"; + if ($va < $vb) { push @{ $vab[$ia][$ib] }, $voter } + elsif ($vb < $va) { push @{ $vab[$ib][$ia] }, $voter } } } }; die "voter $voter $@" if $@; } -foreach my $iy (-2..$#choices) { - foreach my $ix (-2..$#choices) { +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] ); - $$v += 0; - if ($$v) { - printf "%5d ", $$v or die $!; + $$v ||= [ ]; + if (@$$v) { + printf "%5d ", (scalar @$$v); } else { - printf "%5s ", "" or die $!; + printf "%5s ", ""; } } } - printf "\n" or die $!; + printf "\n"; +} + +sub drop ($$) { + my ($i,$why) = @_; + print "dropping $choices[$i]: $why\n"; + $ch[$i]{Dropped} = $why; +} + +print "\nQuorum A.6(2) (quorum is $quorum)\n"; + +foreach my $i (0..$#choices) { + next if $ch[$i]{Dropped}; + next if $i == $defi; + my $v = $vab[$i][$defi]; + next if $v >= $quorum; + drop $i, "quorum ($v < $quorum)"; +} + +print "\nMajority ratio A.6(3)\n"; + +foreach my $i (0..$#choices) { + next if $ch[$i]{Dropped}; + next if $i == $defi; + my $majr = $ch[$i]{Smaj}; + $majr ||= [1,1]; # A.6(3)(3) + my $vad = scalar @{ $vab[$i][$defi] }; + my $vda = scalar @{ $vab[$defi][$i] }; + next if $vad * $majr->[1] > $vda * $majr->[0]; + drop $i, "majority ratio ($vad * $majr->[1] <= $vda * $majr->[0])"; +} + +my $defeats = Graph::Directed->new; # A.6(4) + +sub chremain () { + return grep { !$ch[$_]{Dropped} } (0..$#ch); +} + +foreach my $ia (chremain()) { + $defeats->add_vertex($choices[$ia]); + foreach my $ib (chremain()) { + my $vab = scalar @{ $vab[$ia][$ib] }; + my $vba = scalar @{ $vab[$ib][$ia] }; + next unless $vab > $vba; + print "defeat: $choices[$ia] beats $choices[$ib] ($vab > $vba)\n"; + $defeats->add_vertex($choices[$ia],$choices[$ib]); + } +} + +sub chvab ($$) { + 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"; + + 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"; + $schwartz->delete_vertex($ia); + last; + } + } + + print "\nDropping weakest defeats A.6(7)\n"; + + 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 + } + 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;