(Originally posted by Pat in 2/2012)
In a famous paper (“The impossibility of a Paretian liberal”, 1970),
Amartya Sen proved a mathematical theorem that shows how the
requirements of even rather basic libertarianism (what he at the time
called “liberalism”), the idea that in certain spheres we have absolute
authority over our own personal decisions, can be incompatible with
Pareto-efficiency, the requirement that nobody could be made better off
without someone else being worse off. Both requirements seem intuitively
plausible, but in certain cases, they simply cannot both apply.
theorem is valid, so my concern here is not to refute it. Rather, my
goal is twofold: First, to offer an example that I think captures the
situation better than the one Sen uses, and second, to provide an
intuitively plausible constraint on libertarianism which allows it to be
reconciled with Pareto-efficiency.
example is as follows, and I think you'll see why it's less than ideal.
He imagines two individuals, A, a Bohemian, and B, a prude, trying to
decide who (if anyone) should use pornography. B would prefer that
nobody use porn; A would prefer that everyone use porn. On
libertarianism, it's A's business whether A uses porn, and likewise it's
B's business whether B uses porn. So far, so good.
But in order
to make the paradox work, Sen has to assign two more requirements,
namely: That A prefers that B be the only one who use porn (rather than
A), and similarly that B concurs on this issue. This is, well, weird. It
implies that it's more important for A to force his love of porn upon B
than it is for A to even get the chance to use porn in the first place.
It furthermore implies that B would rather use porn himself than let A
use it. Both of these value systems seem inherently anti-libertarian,
and so it's not all that surprising that the result turns out that
libertarianism doesn't satisfy people's preferences. In a very real
sense, we seem to have a preference against freedom itself. Without
these requirements, there either is no Pareto-superior alternative, or
else the Pareto-superior alternative is the libertarian alternative,
namely that A uses porn and B doesn't.
I have an example that is
mathematically isomorphic but seems in real life a lot more justifiable.
Suppose now that A is an environmentalist, and B is an oil company
executive. The question is this: Who will be subject to pollution
Obviously A prefers that everyone be subject to
regulation rather than nobody—that's what makes him an environmentalist.
But he also has his own self-interest to consider, and if you're not
going to obey the regulations, he'd rather not either. In fact, strictly
speaking he prefers that you be the only one obeying (so that his water
is clean but he can still burn firewood).
Conversely, B of course
prefers not to be regulated. He also prefers that A be regulated,
because there are some small ways that burning firewood could
potentially cut into his oil business (e.g. by cutting demand for
heating oil). His worst-case scenario is that he gets regulated but A
doesn't (which is of course A's best-case scenario).
regulation is a purely opt-in matter (as libertarianism would demand),
then nobody will obey regulations, which is strictly worse for everyone
than the case where everyone is regulated.
You'll note that this
is isomorphic to the Prisoner's Dilemma, as in fact Sen's original
scenario is as well. (It's harder to see in that case, because the
“mutual cooperation” scenario is the one where B uses porn and A
doesn't—which just seems bizarre.) Also, the items don't correspond in
the most obvious way: A using porn is not equivalent to A being
regulated, but instead to nobody being regulated. B using porn is not
equivalent to B being regulated, but rather to everyone being regulated.
Everyone using porn corresponds to B being regulated, and no one using
porn corresponds to A being regulated. I blame this lack of
correspondence on Sen's poor choice of example.
There is however
one advantage of Sen's example: It seems to naturally coincide with what
we ordinarily think of as the space of individual liberty. What right
do I have to decide whether you use porn? It seems fundamentally tyrannical for me to assert this kind of authority, whatever my preferences.
regulations, on the other hand, don't naturally coincide to this space
of personal freedoms; it doesn't make much sense to say I have the
individual liberty to pollute the air you breathe.
What makes this difference? It seems quite obvious, at least in hindsight: My pollution affects you; my porn does not. In economic terms, pollution carries obvious externalities
that pornography does not. (You could argue otherwise, I suppose; but
if you could convince me that porn carries heavy externalities, I would
also be convinced that it doesn't belong in the realm of personal
Sen's paradox crucially depends upon these
externalities. Without it, we end up asserting some sort of “mere
preference”, in which A just happens to prefer that B use porn, and has
no actual reason for doing so (it certainly won't affect A in any way).
This is why the characters in Sen's original example seem like such
busybodies; they are poking their noses into matters which ought not to
To put it another way, Sen's paradox can only be
formalized in terms of utility in the presence of externalities. Without
externalities, A must be indifferent to what B does, and B must be
indifferent to what A does, and so the libertarian solution is the
Pareto-superior (and utility-maximizing) one.
Indeed, a utilitarian (as increasingly I'm coming to think of myself) has a very clear quantitative breaking
point for deciding when to apply the libertarian rule and when not to:
Do the externalities exceed the internalities? Does the harm to A of B's
actions exceed the benefit to B (or vice-versa)? If so, then
libertarianism will fail Pareto-efficiency. If not, then libertarianism
works just fine.
Hence, we have the standard caveat that even
libertarians will generally apply: “I am free to act however I wish, so
long as in doing so I do not harm others or infringe upon their
liberty.” If the libertarian principle is formulated in this way, then
Sen's paradox simply can't arise, and the result is guaranteed to be