Wednesday, January 05, 2005

Flatus Comitatus

A recent car trip got me thinking about a well-known but little-discussed social convention: the suppression of flatulence. (If you don’t care to think about the economics of flatulence, stop reading now.)

Convention dictates that, when you feel the need to pass gas, you ought to suppress it as a courtesy to others in the vicinity. But is this an efficient social convention? If the relief that derives from passing one’s own gas exceeds the discomfort that results from smelling everyone else’s, then we might be happier with a different convention – namely, one that allows unhindered flatulence.

To be more specific, let r be the relief from passing gas, and let d be the olfactory discomfort experienced by each person for each passage of gas. For simplicity, assume these parameters are the same for all persons. Suppose there are n people, each with an equal likelihood of needing to pass gas.

In these circumstances, we might observe a kind of tragedy of the commons. Absent an effective social convention against passing gas, each person rationally chooses to let loose if:
r > d
But the collective flatulence will make everyone worse off if:
nd > r
If so, then everyone will choose to cut loose, even though they'd all be better off if they all restrained themselves. So a convention that successfully induced people to restrain their flatulence would make everyone better off. Note that I can reach this conclusion without comparing one person’s happiness to another’s. Under the suppression convention, I lose satisfaction of r from having to suppress my own, but I gain nd from everyone else suppressing theirs. So if nd > r, I’m better off under the suppression convention than under a free-emission rule.

But note that the mathematical condition above depends crucially on the number of people involved. The larger is n, the more likely is suppression to be efficient. Yet for a small enough number of people, we might find that r > nd, in which case letting loose would be preferable.

Thus, the convention of suppressing flatulence makes most sense in large-number situations. Sadly, those are the situations in which enforcement of the convention is most difficult. When n = 2, finding the guilty party is easy – if you know you didn’t do it, the other guy must have. But when n = 10 (say, at a dinner party), identifying the culprit is much harder, depending on our ability to detect flatulence vectors (where did it come from? where is the scent strongest? etc.).

The dilemma resembles that of a cartel like OPEC. A collusive agreement to cut back production (thereby raising prices) is most easily sustained with a small number of producers, but typically crumbles as the number of producers rises. The difficulty of identifying and punishing cheaters makes cheating more worthwhile, leading to a breakdown of cooperation.

Flatulence-suppression and cartel-maintenance share other features as well. For instance, if individuals differ substantially in their need to pass gas (i.e., some have larger r), then some individuals will face a greater temptation to break convention and let loose. If others follow suit, the convention may disintegrate entirely (think of a frat house). Similarly, cartels are more difficult to maintain when the cartel’s members differ in size, production capacity, or cost of production, since that means some producers face a greater incentive to cheat than others. Their choice to cheat can lead to the cartel’s downfall.

The difficulty of detecting flatulators might explain the relatively high punishment associated with it. Given that flatulence is a completely natural impulse, and that others’ discomfort is usually minor and temporary, social ostracism and public shaming might seem out of proportion to the crime. Yet when the probability of conviction is low, the magnitude of punishment must be correspondingly high to provide a sufficient disincentive. Moreover, if your bad behavior can lead to a breakdown of the convention itself, then the real cost of your behavior exceeds the discomfort caused by just your own flatulence. In such circumstances, harsh punishments make good sense.


lemuel said...

Flatulence-suppression convention as a social cartel? That never occurred to me. That sharp whooshing sound you might have heard right now was my mind blowing – (so don’t accuse me of disturbing the airwaves or tempering with gas prices.)

Anonymous said...

Deontology, man! We hold it in in deference to the non-agression principle.

Anonymous said...

Somehow the assumption that everyone has an equal likelihood of needing to pass gas seems unrealistic to me. I wonder if the suppression convention in fact was evolved by a majority of less-frequent-gas-passers to protect themselves from the olfactory offense given by the more-frequent-gas-passers.

But I have nothing but intuition behind this. Probably someone has done a study on the distribution of gas frequency in the population. If not, surely one could get federal funding for such a project. :-)

Nick Weininger

andrea said...

well, we can probably assume that the larger the n, the smaller the d. This comes from variables that aren't captured yet - such as the size of the space and the option to relocate out of the "line of fire".

I do love this analysis, though. Just love it.

Steven Horwitz said...

Glen, you rock.

What's interesting about this is that it explains one of my wife's complaints about me (no, it's not THAT long a list), which goes like this:

"Why is it that you manage to hold your gas when we're out in public, but around me, you feel no such restraint?"

Now I have an answer: "Honey, with small numbers, supression simply isn't socially efficient. My relief is much more likely to outweigh your discomfort. In a crowd, the combined discomfort of those present is much more likely to outweigh my relief. If you don't buy that, here's Glen's phone number - ask him to explain it."

Of course, more seriously, the key to this analysis is that the noxious odor is a public bad, and that the size of "n" doesn't impact the per capita "d."

And if you'd like to complicate the model Glen, perhaps you could have separate terms for the noise and the odor. After all, some farts don't smell. And if they are silent and benign, isn't d=0?

Anonymous said...

A fascinating analysis, but other factors must be considered also. All social situations are not equivalent: compare watching a ball game in a bar vs. a papal audience. Also, there is a significant gender aspect. A group of guys will often glory in a massive fart, while I suspect this is unlikely in an all-female group.

Anonymous said...

You need to take into account the risk of "sharting" accidentally in public. Though slight, the repercussions of this will far outweigh any relief from passign gas.