The Liberal Paradox is Neither Liberal nor a Paradox

Academics get a lot of flak for inventing artificial problems. For the most part, I chalk this up to laymen being unfamiliar with what academics do. Imagining things as-yet-unencountered-but-potentially-encounterable is a large part of their job description. Getting at hidden parts of our understanding – for which imagining unrealistic situations is surprisingly useful – is another. But occasionally I come across a model that makes me sympathize with the straw layman who thinks academics just sit around and fart all day. Today I found one of those in Amarta Sen’s Liberal Paradox.

This is apparently taken very seriously in political science as a proof that no liberal democracy dedicated to a minimal liberalism can promise pareto efficiency in all cases.

Let’s get the terms straight.

Pareto efficiency is any situation in which no change in the status quo can benefit one participant without harming another. You could call it "don’t leave money on the table" efficiency without doing too much damage to the concept. (Note the critical difference between this and maximizing utility. It can be possible to maximize utility by taking an action which leaves one of the participants worse off but the rest of them better off.) So, the classic example is if there’s a fixed amount of money that I’m tasked with handing out, then however I divy that money up between participants, so long as I give out all that I have to give out, the result is pareto efficient. This is true even if I give all the money to one participant: taking some of the money I gave to him and giving it to a different participant will harm the first participant (in the sense of "leave him worse off than he was before"). But if I withhold some of the money, again no matter how I distributed what I gave out, the system is NOT pareto efficient, because I can still give someone money without leaving any of the others worse off than they were before.

Minimal liberalism means that there is no single individual in a system who is "decisive" on all social outcomes – i.e. no one is a dictator/no one gets to make all the decisions about what final outcome is preferable.

The paradox is that it is impossible to guarantee that all outcomes, for any system in which all individuals have strict preference rankings on outcomes, will be both pareto efficient and minimally liberal.

Sen’s classic example.

Imagine Lewd and Prude are two people. Lewd likes racy books, Prude hates them. Prude prefers that such books be destroyed. However, if we’re in a situation where someone must read one, he’d prefer that person be him than anyone else. Lewd prefers that such books be read rather than destroyed. However, if we’re in a situation where only one person can read them, he thinks it’s funnier if that person is Prude, so he would prefer Prude read the book than himself.

Now imagine we’re in a situation where in fact only one person can read the book, or else the book can be destroyed. You can already see where the trap will spring: both Lewd and Prude (counterintuitively) prefer that Prude read the book, even though Prude prefers not to read the book at all.

Well, now we’re in a bind. Let L be Lewd reads, P be Prude reads and N be no one reads.

Lewd: P > L > N Prude: N > P > L

The pareto optimal outcomes are P and N. If we choose P, then Prude doesn’t get his optimal result, but switching to N would make Lewd less happy (and L both less happy). If we choose N, then Lewd is unhappy, but switching to L or P to make him happy would make Prude less happy. Choosing L is NOT pareto optimal, because there is a choice we can switch to (P) that leaves both Lewd and Prude happier. (If we were interested instead in maximizing total happiness, then P is the only solution, but this is maximal utility, not pareto optimality.)

The trouble is that neither choice can be arrived at unless one of Lewd or Prude gets to choose the final ranking. Obviously if Lewd is the dictator we’ll end up with P and if Prude is the dictator we’ll end up with N. But what if we give Lewd decisiveness over the ranking of L and N and Prude decisiveness between N and P. Then we end up with L – the only pareto non-optimal result. This is because Lewd decides that L is a more optimal solution than N, and Prude decides that N is a more optimal solution than P, and the ranking is L > N > P. Oops.

Of course, for other distributions of decisions, it works. So, for example, we could give Prude decisiveness over L and P and Lewd decisiveness over P and N, in which case we get either P > N > L or P > L > N, but with the pareto efficient P winning in either case. But this is beside the point. The point is that we can’t guarantee pareto efficiency if we have minimal liberalism because there are some distributions of decision power that don’t result in it.

So, it’s a clever little trap. It shows, decisively, that there always exist orderings of preferences where you have to choose between pareto optimality and minimal liberalism.

But it seems to me that it has a ton of flaws, all related to how artificial it is.

The immediate question that springs to mind is why Prude has any say over what Lewd does in the first place, and vice versa. We could say that the preference that Lewd has that Prude read the book is an infringement on Prude’s prerogative to decide whether to read the book or not. Likewise, Prude’s preference that no one read the book is an infringement on Lewd’s right to decide whether to read books or not for himself.

I think the classic example gets in the way a bit, so let’s reformulate it. Let’s say we’re in a situation where Prude and Lewd are in line to receive an award, and they both agree that Prude is the more deserving recipient. Prude would prefer not to accept it because he thinks that accepting it will harm the internal workings of the organization to which they belong, as it makes it public that Prude is more deserving than Lewd. However, Lewd believes that it is important that someone from their organization accept the award since this is likely to bring their ogranization prestige. So, Lewd will accept the award if Prude will not. This is a clearer example for me, because it leaves Prude and Lewd individually free to decide whether to accept an award, and it further doesn’t seem artificial that there should only be one such reward to receive.

Alright, that in mind, it’s not a coincidence that the pareto optimal solution is the one that would result from compromise between the two. Lewd can make clear to Prude that he intends to accept the award if Prude will not, and then Prude can weigh his desire to avoid having anyone accept the award against his preference that Lewd not get it.

This encapsulates the two main objections that people have raised to the supposed "paradox:" (1) that Sen’s concept of minimal liberalism ignores the right of Prude and Lewd to reach an agreement and (2) that if you order the choices (i.e. let one choose before the other), a pareto optimal outcome can always be reached.

If Lewd chooses first (whether it’s the book or the award), he will choose to accept the award (or read the book), since he has no control over what Prude does. Prude then chooses to accept the award (or read the book) instead – and we get pareto optimal outcome P. If Prude goes first, we also get P, because he will choose to accept the award to prevent Lewd from so choosing.

And in turn, that demonstrates the real reason why Sen’s supposed "paradox" is a deeply contrived way of looking at things: because it imagines a world where people have preferences over how other people act in which they can’t interact with each other. It’s a precise inversion of what liberalism actually is, really. In liberalism, we all have prerogatives and interests, but we have to share the world with other people. So, we’re trying to find a system where everyone’s interests are least-damaged, and the idea in making sure that no one is finally decisive on every outcome (i.e. the minimal liberalism constraint from before) is precisely to ensure that everyone gets to represent their interests.

Sen’s "paradox" has been interpreted as a death knell for liberalism by supposedly showing that it is incompatible with pareto efficiency. IN fact, it shows just the opposite. In fact it shows that dictatorial systems are pareto efficient or not at the behest of the dictator – a fact so trivial as to not be worth mentioning. Because either one of Prude and Lewd is the dictator, and we can guarantee a pareto efficient system, or the responsibility for making it pareto efficient falls on the third party doling out preference prerogatives – i.e. on the central authority – who either doles them out in the right way or doesn’t. It’s basically like saying that non-interactive systems are either pareto efficient or not. Gee.

Interactive systems where everyone has equal rights and prerogatives, by contrast, will tend to pareto efficiency. Which is, you know, what we classical liberals call a happy result.

So I’m truly sorry, maybe I’m missing something, but the "liberal paradox" just reads like academic fraud to me. It’s set up in such a way to get a desired result, but that result only obtains if you buy the setup, and the setup just happens to assume the conclusion it is (or at least seems to be) trying to draw. It tries to expose a flaw in liberalism by setting up a model of liberalism that’s something like the opposite of liberalism. I’m underwhelmed.

One thought on “The Liberal Paradox is Neither Liberal nor a Paradox

  1. Yes indeed, you missed something. You have confused an academic insight, a counter-example to be pondered when thinking in the abstract about whole systems, with a particular silly example meant to open your eyes, not to be resolved so you can close your mind as you have.

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