The card receiver is always selected randomly among those who don't have the card! It's just a fluke if a specific player gets the first card several times in a row.
This system certainly isn't perfect. When I've got the time I'm going to add a damage tracker to enemies and then give precedence to those players who helped damage it! Currently, as Fennal describes, you can kill an enemy all by yourself and still see the card sail away to another player. Infuriating!