[1] https://en.wikipedia.org/wiki/Coase_theorem [2] http://www.independent.org/publications/article.asp?id=757
Not so reassuring.
Let's think about a plausible scenario: I run an industrial facility and am secretly dumping industrial waste into the river. My neighbors start getting sick. When they analyze their drinking water, it shows the presence of a bunch of chemicals whose most probable source is my industrial facility. My neighbors realize I'm to blame, and complain to me about dumping chemicals into the water. I say I've got no idea what they're about and those chemicals must be from somewhere else. Obviously I refuse to hand over any records from my facility.
Getting nowhere, my neighbors file a lawsuit. Then we go through a years-long series of lawsuits where I deny any wrongdoing and maybe eventually have to pay some money, although it hardly brings back everyone killed by illnesses my facility caused.
Dumping waste in the river may be cheaper now, but won't be if you get hit by a fine, or have to deal with an angry mob at the factory gates, or end up polluting your own drinking water supply.
It's not a perfect system - in particular, it's reactionary, which means that enough people a.) need to be harmed and b.) need to complain effectively before the broken incentives are fixed. In practice, it seems to work a lot better than societies where people act for the nebulous "common good", which always seems to end up being defined in a way that suits the self-interests of the people doing the defining anyway.
But, as we often see, people act against their self-interest all the time.