Coase theorem

The Coase theorem gives a method of dealing with externalities when certain conditions are met. As set forth by Chicago school economist  and his followers, the theorem states that if two or more parties are affected by an externality, when property is well-defined and transaction costs (time and money spent) are negligible or non-existent, then bargaining will always lead to the most efficient outcome regardless of the initial allocation of the property. Coase originally made this argument with regard to assigning radio frequencies in 1960, saying that it didn't matter who was assigned what frequency — the station with the best ratings would have more money and thus pay off other stations not to intrude on the former's frequency. However, Coase notes that when transaction costs are not zero, these costs must be factored into the decision of who is assigned the property.

Hypothetical scenario
Say Farmer Brown has a bunch of cows. He lets them graze on an open field, which he does not own. The field is next to a nuclear reactor, Ten Mile Island, which decides to dump radioactive waste into the open field before it is transported to a storage site in Fried Chicken, Kentucky, which is a little far away. Farmer Brown loses $100 on his next shipment of milk because some of it is contaminated. (On a side note, one radioactive carton does escape, causing the person who drinks it to become a superhero called The Milkman in a case of a positive externality, but that's beside the point.) Suppose a small temporary storage facility made of lead bricks for the waste can be built for $50. To resolve this problem, we can assign property rights to either Farmer Brown or Ten Mile Island. If we give it to Farmer Brown, then Ten Mile Island must compensate him for every $100 worth of milk lost. However, it is easier just to pay the $50 once to build the storage facility. If we give the field to Ten Mile Island, then Farmer Brown suffers $100 worth of losses on every milk shipment. It's easier for him just to pay for the storage facility. And voila! The market, as always, leads to a perfectly efficient outcome!

Counter-hypothetical
Farmer Brown notices Ten Mile Island radioactive materials into the field. He tries to bargain with the plant owners, but they buy out the field and use the entire thing to dump waste. The waste seeps over into his property. Farmer Brown attempts legal action, but Ten Mile Island has a team of high-paid lawyers and they settle out of court for a pittance. Next year, all of Farmer Brown's cows are producing contaminated milk. Even though the waste is only weakly radioactive and is an unlikely carcinogen, people would rather prefer not to buy his milk. He loses his farm. The depleted uranium leaks into the nearby town's water supply, leading to anti-nuclear sentiments. Ten Mile Island must confront the possibility of being shut down, taking with it a major source of carbon-free energy.

Problem with even the ideal example
The Coase theorem is problematic because it does not necessarily prevent the externalities from inflicting damage in the first place. It's the difference between the law stopping someone from whacking your kid about the head with a baseball bat and the law allowing him to do so as long as you get sufficient This will only protect your child until someone with enough money decides that it's sufficiently fun or profitable to beat him or her up.

This is anything but an exaggeration. In a similar vein to the example above, for some odd reason some libertarians and conservatives keep forgetting that various forms of pollution may impair cognitive abilities (in children), and even death. To the tune of 28,000 premature deaths per year worldwide, just from diesel exhaust. Why is the public at large already not rebelling at this appalling waste of life? In all probability, it is because people do not necessarily notice as premature deaths due to pollution are rather common, especially when compared to, say, airplane-related fatalities, which are exceedingly rare and thus much more likely to make the headlines.

In real life
In reality, the situation is not necessarily so extreme. Significant transaction costs often exist, and preventing or solving a conflict through governmental regulation is frequently the simplest and most efficient solution. In the hypothetical scenario above, the government could require nuclear power plants to ensure proper handling of all radioactive materials at all times. That means storing waste products at a secure site before being disposed of elsewhere.

As another example, having "free" parking is very popular, and parking meters are reviled, even though a basic understanding of economics shows that people are, on average, better off with parking meters; there's no use to having "free" parking if none of the spaces are available. As is often the case, "free" parking is not really free. Since having more cars in a major city worsen traffic congestion, parking fees could be used to not only discourage the use of private vehicles within the city limits, but also subsidize public transportation.

Libertarian arguments
Many libertarians argue that externalities like pollution can be dealt with by making public land private to solve the tragedy of the commons. This idea is, of course, to be implemented using Nobel Prize-winning economist Ronald Coase's theorem. This is often used to justify ideas like the privatization of wildlife.