Query posts by meta_key whose value is an array

Let’s say I’m modifying the default posts query:

add_filter( 'pre_get_posts', 'my_filter' );

function my_filter( $query ) {

$query->set( 'meta_key', 'my_rating' );
$query->set( 'orderby', 'meta_value_num' );
$query->set( 'order', 'DESC' );

return $query;

}

I know this works for the meta_key my_rating if its value is a number. But let’s say its value is an array whose values are numbers. Like this for example:

array(
    "foo" => 1,
    "bar" => 2,
)

But the array would be serialized and I guess need to be unserialized to use it. Is there any way to pick which key in the array to sort by?