Neutral third parties (i.e. doctors) are not going to be able to convince the person to get help. Family and friends must get involved. Additionally, the family/friends have to be extremely motivated and invested in getting their loved one to consent to treatment. Take the whole day off, because it won't be a quick process. And everyone has to be prepared to perform similar large scale interventions multiple times, as dropout from treatment is generally high.

We can argue the social policy implications of psychiatry's paralysis (or its excess of power—again, depends on your perspective) all we want, but it doesn't change the reality. Much of our current laws were brought about by the courts in reaction to the "gross" (depending on the perspective) disregard for personal freedoms of the earlier days of psychiatry, and the current principle that having a mental illness does not therefore negate one's freedoms—or their own personal responsibility for their behavior.

It's a tricky balance, and one that is also very difficult to formalize. But here we deal with the practical:

If your loved one is in danger, drag him or her to an ER or call the police. If he/she is not in immediate danger, and are refusing to get treatment, call as many people as you know to come over.