[maxerickson]

Statistically, more violence occurs between people that know each other than occurs randomly.

http://www.bjs.gov/content/pub/ascii/vvcs9310.txt

It's also the case that violence is so unlikely at any given encounter that it isn't rational to worry about it (in the US, there are billions of stranger-stranger encounters in a given year, millions of incidents of violence).

I guess someone might argue that arranging for encounters that are 99.9% likely to be violence free compared to encounters that are 99.8% likely to be violence free is worthwhile, but their glances probably aren't powerful enough to actually create that difference.