FWIW, here my attempts with different reciprocal functions and evaluation of distribution. See also Re^3: Randomly choosing from a set of alternatives with varying popularity for interpretation.

use strict;
use warnings;
use Data::Dump qw/pp dd/;


my %vote = ( alligator => 100, bear => 90, cat => 80, jellyfish => 10 
+);
my $N =0;
$N += $_ for values %vote;


# --- invert by division, proportion of non-voters
my $N2 = 0;
my %vote2 = map {
    my $v2 = 1/$vote{$_};
    $N2 += $v2;
    $_ => $v2
} keys %vote;


# --- invert by subtraction, number of non-voters
my $N3 = 0;
my %vote3 = map {
    my $v3 = $N-$vote{$_};
    $N3 += $v3;
    $_ => $v3
} keys %vote;




my (%dist1,%dist2,%dist3);

my $e=5;

$dist1{pick($N,\%vote)}++ for 1..10**$e;

$dist2{pick($N2,\%vote2)}++ for 1..10**$e;

$dist3{pick($N3,\%vote3)}++ for 1..10**$e;


pp \%dist1,\%dist2,\%dist3;







sub pick {

    my ($N,$h_vote)=@_;
    my @deb;
    my $r   =rand($N);
    push @deb,$r;
    scalar keys %$h_vote;                 # reset each
    while ( my ($k,$v) = each %$h_vote) {
        $r -= $v;
        push @deb,[$r,$k,$v];
        return $k if $r <=0;
    }
    die "ERROR", pp \@deb;
}
[download]

(
  { alligator => 35891, bear => 31807, cat => 28792, jellyfish => 3510
+ },
  { alligator => 7497, bear => 8300, cat => 9481, jellyfish => 74722 }
+,
  { alligator => 21416, bear => 22542, cat => 23870, jellyfish => 3217
+2 },
)
[download]

On a tangent: had to debug why each failed me. Needed reset.