Another interesting idea. I modified LanX's code to try this for several different values of c: 
#!/usr/bin/env perl
use 5.010;
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;
say "Vote";
show(\%vote, 1);

# --- invert by exponentiation
for my $C ( 0.9, 0.95, 0.96, 0.97, 0.98, 0.99) {
    my $N4=0;
    my %vote4 = map {
        my $v4 = $C ** $vote{$_};
        $N4 += $v4;
        $_ => $v4;
    } keys %vote;

    my %dist4;
    my $e=5;
    $dist4{pick($N4,\%vote4)}++ for 1..10**$e;
    say "C=$C";
    show( \%dist4, -1);
}

sub show { # show counts and percentages
    my $href = shift;
    my $dir = shift; # sort direction 1=ascending, -1=descending
    my $tot=0;
    $tot += $_ for values %$href;
    for my $k (sort {$dir * ($a cmp $b)} keys %$href) {
        printf "%s => %5d (%5.2f%%)  ", 
               $k, $href->{$k}, 100*($href->{$k}/$tot);
    }
    say '';
}

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]
Output: 
Vote
alligator =>   100 (35.71%)  bear =>    90 (32.14%)  cat =>    80 (28.
+57%)  jellyfish =>    10 ( 3.57%)
C=0.9
jellyfish => 99902 (99.90%)  cat =>    65 ( 0.07%)  bear =>    24 ( 0.
+02%)  alligator =>     9 ( 0.01%)
C=0.95
jellyfish => 94748 (94.75%)  cat =>  2712 ( 2.71%)  bear =>  1599 ( 1.
+60%)  alligator =>   941 ( 0.94%)
C=0.96
jellyfish => 89102 (89.10%)  cat =>  5269 ( 5.27%)  bear =>  3440 ( 3.
+44%)  alligator =>  2189 ( 2.19%)
C=0.97
jellyfish => 78766 (78.77%)  cat =>  9190 ( 9.19%)  bear =>  6939 ( 6.
+94%)  alligator =>  5105 ( 5.10%)
C=0.98
jellyfish => 62428 (62.43%)  cat => 15076 (15.08%)  bear => 12415 (12.
+41%)  alligator => 10081 (10.08%)
C=0.99
jellyfish => 42944 (42.94%)  cat => 20843 (20.84%)  bear => 18984 (18.
+98%)  alligator => 17229 (17.23%)

[download]

In reply to Re^2: Randomly choosing from a set of alternatives with varying popularity by ibm1620
in thread Randomly choosing from a set of alternatives with varying popularity by ibm1620

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