Poverty's greatest nuisance

sounds like a playground game from elementary school. Or maybe not...

It seems to me that poverty matters somewhat less than urban density, though both probably contribute. The key thing is self policing that you mention. I think some of that is a cultural thing, some cultures are more apt to look over your shoulder than others. In America where most people came to escape paternalism in some form or another, looking over your neighbors shoulder is less encouraged.

Interesting thought re: culture. Americans have been traditionally much more mobile than Europeans...or, at least, we had a head start into the mobile, rootless society. Our culture was formed in large part by the frontier experience -- the pulling up of roots and lighting out for the territory ahead of the rest. Frontiers have traditionally been unruly places; the Ukrainian steppe was a prime example in European history.

Even on the East Coast, huge percentages of urban populations have been recent arrivals -- people without thick, interlocking social networks to place informal restraints on behavior. People weren't looking over their neighbors' shoulders, because they didn't necessarily know their neighbors (who probably just got off the boat from Ireland or Italy or Germany) very well. The founding of America coincided very closely with the Industrial Revolution, which further disrupted traditional life and increased mobility. In fact, you could say American history has been a race between technology's rapid promotion of rootlessness and efforts to get things organized.

I'm a third-generation Californian, which practically makes me landed aristocracy. The vast majority of people in this country live on the vast percentage of America's land that wasn't occupied by the ancestors of today's residents more than a few decades ago. That kind of anonymity is something America has in spades, and which Europe has only recently begun to experience. Not surprisingly, their crime rates are starting to catch up to ours; in fact, in categories other than murder, most European countries are already ahead.

As to murder, I think a huge part of that problem is the legacy of slavery. As unseemly as it is to point out, if the murder rate among African-Americans were identical to the murder rate among whites, we'd pretty much have Canada's murder rate. Slavery helped create a grievance that it is easy to fixate on, leading to alienation from the broader society and its restraints -- even those that are useful. Also, slavery degraded whites in the areas where it was practiced, leading to increased rates of violent crime among white Southerners, both in the South and areas to which they migrated.