To those who are saying "not all hotels do this" - it's just never happened to you.
I worked for a massive American chain (here in the UK). Overbooking levels were set by head office, and done on stats. So any regular night there wouldn't be any overbooking allowed in the system. But on nights where popular events were happening in town, overbooking would he allowed in the system at a rate which has been calculated based on how many vacant rooms we had the same event prior years.
When we had to send someone to another hotel, it was a big deal, and the whole day will have been taken up worrying about it and searching for the right booking to send elsewhere.
We would rule out, in this order:-
Any loyalty card holders
Anyone booked on an event rate for an event held in our hotel (eg wedding, conference)
Anyone on an agreed corporate rate
Then, we would ring round everyone left to find out if they were still coming and what time they would arrive. Once we had spoken to them and got a check in time too, we would then scratch them off the list.
So, left on the list would be everyone we couldn't get through to on the phone who wasn't a rewards member attending an event at the hotel.
Then, we would scour the remaining bookings and allocate rooms to any lone female travellers. The disabled access rooms don't overbook so they would be fine too.
Then, it's first come first served. We may try and outlook someone at say 6pm, as its easier to deal with that then rather than wait til midnight, but if they then told us they were attending the wedding (but not booked on the wedding rate), or some other pertinent reason, we would check them in.
I worked there for 10 years and we probably only ever out booked reservations maybe 5 times?