U.S. DOT regs demand that carriers post their IDB prioritization rules (see the contract of carriage) but United is very non-specific. I paraphrase - 'We have a bunch of factors.'

Boarding Priorities - If a flight is Oversold, no one may be denied boarding against his/her will until UA or other carrier personnel first ask for volunteers who will give up their reservations willingly in exchange for compensation as determined by UA. If there are not enough volunteers, other Passengers may be denied boarding involuntarily in accordance with UA’s boarding priority:
Passengers who are Qualified Individuals with Disabilities, unaccompanied minors under the age of 18 years, or minors between the ages of 5 to 15 years who use the unaccompanied minor service, will be the last to be involuntarily denied boarding if it is determined by UA that such denial would constitute a hardship.

The priority of all other confirmed passengers may be determined based on a passenger’s fare class, itinerary, status of frequent flyer program membership, and the time in which the passenger presents him/herself for check-in without advanced seat assignment.

https://www.united.com/web/en-US/con...age.aspx#sec25