my @names =
  map $_->[0],
  sort { $b->[1] <=> $a->[1] }
  map [ $_, ask_monkey_about($_) ],
  @castaways;

Because the map and sort operators are right to left, you have to read this construct from the bottom up. Take a list of @castaways, create some arrayrefs by asking the monkey a simple question, sort the list of arrayrefs, and then extract the names from each arrayref. This gives you the list of names in the desired order.

This construct is commonly called the Schwartzian Transform, which was named after me (but not by me), thanks to a Usenet posting I made many years ago. It has proven to be a very nice thing to have in your bag of sorting tricks.

If this transform looks like it might be too complex to memorize or come up with from first principles, it might help to look at the flexible and constant parts:

my @output_data =
  map $_->[0],
  sort { SORT COMPARISON USING $a->[1] AND $b->[1] }
  map [ $_, EXPENSIVE FUNCTION OF $_ ],
  @input_data;