EDIT: Oops, had to update code for people with identical scores, and people who weren't on previous listing.

use strict;
use warnings;

my (%lrank, $c, $s, $name, $score, $lrank, $lscore);

my @lrank = ('RUBYKAT','SAPER','PETDANCE','AMBS','BARBIE');
my @nrank = (
  ['PETDANCE',12.4],
  ['SAPER',15.78],
  ['AMBS',15.5],
  ['RUBYKAT',15.97],
  ['BARBIE',16.06],
  ['NEWBIE',12.4],
);

$lrank{$_} = $c++ for @lrank;
$s = '%' . (length($#nrank+1)+1) . 's';
@nrank = sort {@$b[1] <=> @$a[1] || @$a[0] cmp @$b[0]} @nrank;

$c = 0; $lscore = 0;
for (@nrank) {
    ($name, $score) = @$_;
    if (exists $lrank{$name}) {
        $lrank = $lrank{$name};
        print $lrank > $c ? '^' : $lrank < $c ? 'v' : ' ';
    }
    else { print ' '; }
    print sprintf $s, $lscore == $score ? '' : $c;
    print ": $name\n";
    $lscore = $score; $c++;
}
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Note that people of the same score are currently sorted alphabetically. Could be you'd want them sorted according to first come, first served, in which case a more complicated algorithm would be necessary.