Airlines choose to bump passengers based on individual carrier policies. These determine the order in which passengers are bumped, and can be listed in the airline’s contract of carriage.
For example, United Airlines states unaccompanied minors and people with disabilities should be bumped last, while American Airlines will deny boarding based on the order of check-in. They also consider "severe hardships," ticket cost, and status within the carrier's loyalty program.
Delta Air Lines also uses check-in order and loyalty status as determining factors, as well as class fare such as economy or business class. Meaning, those ticketed in basic economy are likely to be bumped first. However, those with disabilities, unaccompanied minors, and members of the military are all protected from such practices.