Do many voluntarily commit themselves to a psychiatric hospital?

Most: Most inpatient psychiatric admissions are voluntary. It is not considered being committed if it's voluntary. Most involuntary patients come under the attention of state mental hospital systems. Private psychiatric hospitals, for the most part, care for patients who are admitted voluntarily. Most states have various mechanisms to court commit someone who is a danger and who refuses to go voluntary.

Voluntary admissions: The majority of psychiatric admissions are voluntary.