I read in one of William Reed's or Kochi Tohei's books that when stared down, gaze at the middle of the other's forehead, just above the eyes. The person will soon lose interest.
I've done this successfully twice that I can recall, and it has worked like a charm. Perhaps it somehow unnerves the aggressor and makes him want to look elsewhere.
Now, this might not apply so perfectly to someone who is truly, aggressively psychotic, but like I said, I've had success with it. As far as psycho- and sociopaths, they make up 1% and 3% of the population, respectively. When I lived in St. Pete a couple years ago, I was on a poetry crusade and this is one I wrote back then. Psychologists believe there is no hope for these people, and they could be correct indeed. Sometimes I find it easy, and sometimes I find it difficult, to think they have any hope...I just try to believe that everyone has Buddha-nature, or inner-perfection corroded by ignorance.
Armed with charm
And replete with deceit,
Those without conscience
Most certainly exist.
Psychologists call them sociopaths,
And folklore names them vampires.
Their sinking of fangs into throats
Is their sapping of positive thought,
To convert the insecure to darkness.
Indeed an infectious disease—a contagion—is among us.
Established deeply and snowballing over time
Is their illusory dichotomous mentality:
Power versus weakness.
Their only cure resides in recognition of self-wrongfulness.
Precious few who seek healing survive—with anguish they comprehend
How many moments they have envenomed others,
As they bear a slowly melting iceberg of shame immeasurable.
But he who succeeds in thawing this burden,
And freeing himself from antisocial chains,
Will be showered in respect to an extent he never dreamt.