I run a randomiser down the list of slot preferences. I then sort high to low, and slot by slot I assign players to games in order of preference. If your first slot is full, I check your second and so on, until we hopefully find you a berth. There is sometimes an amount of executive override to ensure that as many people have games they've opted for, but that is rare. We will also reach out to players who didn't get a game booking (either as they only put one or two choices or because they've been really unlucky on how the randomiser has worked out for them).
Once the first pass is complete, we review any games that have no takers and try and get the GM a playing spot (if they want one). We then look at games that may have too few players to run and check with the GM that they are okay (for example, two players in a four-player game). If they are okay to go ahead, then the game stands. If not, we will try and consolidate the under-booked games or find players and the GM berths elsewhere. We aim to find as many players games as possible.
Also, in the background, we deal with a limited number of X who doesn't want to play with Y requests. Fortunately, these tend to be limited in number.
We've just completed our initial pass and are reaching out to players & GMs; keep an eye on your inboxes.