Many times, when you hear people attempting to justify the bans of smoking in public spaces, they bring up the argument that second hand smoke creates externalities (many make this argument even though they don't know what externalities are). The reasoning is this: smoking by one person imposes costs on other people, due to increased health risks, bad smells, and other external costs. Because of these external costs, or externalities, many people, including economists, seem to think that smoking bans are justified and will actually improve total welfare. However, I think that this argument fails pretty strongly. Why?
This line of reasoning forgets the observation that if people know about these costs a head of time, and still take the action that involves others placing an external cost onto them, they have internalized the cost and no externalize exists. For example, if a non-smoker enters a bar that they know to allow smoking, they are accepting and internalizing that cost when deciding if they want to enter that bar. Again, no externalities exists.
It may be easier to see this by looking at a different example. Suppose that there is an empty field, with no one living there. Now, a factory is built there and the owners of the factory own the adjacent land out to a one mile radius. In addition, the factory emits pollution that spreads out in an exact 1 mile radius, and no pollution extends beyond this one mile radius. Currently, no externalities exist. The owners of the factory and land bear the entire cost of the pollution. Now, what if the factory owner sells some of the land and a family purchases the land and builds a house within the one mile radius and lives there. Does the factory impose an externality onto the family that lives in that house? As long as the family knew about the pollution before purchasing the land, no there is not. They knew about the cost and they internalized the cost when they decided to move onto the land.
The same line of reasoning that was applied in the factory example can be applied to the smoking example. As long as customers, or employees, know about the smoking before they enter the restaurant, or bar, the smoking does not impose external costs on others. They gave internalized the externality. This may be a strong reason for why a law that requires all businesses to post their policy of smoking near all enterances may be a good idea, but it is not a good reason to ban smoking all together.
Admittedly, this externality example is only one of many reasons people give for why we need to ban smoking in private establishments. However, I find the externality to be the strongest case for why smoking should be banned from a private business. However, as you may notice, I find this argument to be particularly weak.