Nobel laureate Amartya Sen wrote about the liberal paradox in “The Impossibility of a Paretian Liberal.” The paradox appears when we ask a social rule to satisfy three reasonable conditions at once.

Roughly speaking, we want a rule that respects personal freedom, follows what everyone agrees is better (Pareto optimal), and works no matter how people rank the choices. Each condition sounds reasonable. Together, they lead to a contradiction.

I like examples, lets illustrate this with an example:

Put yourself in the shoes of a social planner for a fictional town called Paretia. Paretia has only two citizens, named Prude and Lewd. Paretia suffers with exactly one social issue: what to do with a copy of the sexually explicit novel Lady Chatterley’s Lover.

Prude thinks the book is indecent and should be disposed of unread. If someone must read it, however, Prude would rather suffer personally than let Lewd read and enjoy it. Prude believes reading such a text in suffering is better than reading it in joy.

Opposed to this, Lewd enjoys this sort of reading and would rather read the book than dispose of it. But Lewd would enjoy it even more if Prude were forced to read it. Lewd is a disruptor and wants the society to normalize such texts.

Let the three outcomes be:

• P mean Prude reads.
• L mean Lewd reads.
• N mean nobody reads.

Their preferences are:

You have to decide whether to give the book to Lewd, give it to Prude, or dispose of it. How would you rank these outcomes?

Let’s say you value individual freedom. Each person should decide whether they themselves will read the book.

Lewd controls the choice between L and N. Lewd prefers reading, so:

L > N

Prude controls the choice between P and N. Prude prefers that nobody read, so:

N > P

Combining the two, by transitivity:

L > N > P and therefore L > P

The planner therefore chooses: Give the book to Lewd!

But ask yourself: would either citizen agree?

Is Prude's top choice giving the book to Lewd? Is Lewd's top choice giving the book to themself? The answer it no! for both. In fact, they both would rather give the book to Prude than to Lewd. As a social planner maximizing personal freedom, you are making both Prude and Lewd unhappier than they need be.

The Pareto condition (socially optimal for everyone) requires P > L. Personal freedom require L > P.

And that is the paradox.

You cannot guarantee both personal freedom and unanimous welfare across every possible set of preferences. Therefore, never ask: “How do I maximize freedom and welfare simultaneously?” Instead ask: “Which value am I willing to sacrifice when they conflict?”

I would call this Sen's liberal tradeoff, not a paradox.

Speaking of tradeoffs, here is another one: the CAP theorem.

Systems engineers are well versed in the CAP theorem. It concerns three properties of a distributed system:

1. Consistency: Every node presents the same, up-to-date data.
2. Availability: Every request receives a response.
3. Partition tolerance: The system continues operating when parts of the network cannot communicate.

A distributed system must be prepared for network partitions. When one occurs, the engineer must choose between consistency and availability. A banking ledger leans toward consistency. The Instagram feed optimizes availability. During a partition, no system can guarantee both.

The CAP theorem does not tell an engineer what to choose. It tells them that a choice exists and cannot be wished away. Once engineers understand this, they make more informed decisions. The liberal paradox (read: tradeoff) can do the same for our political ideologies. It does not tell us what to value. It forces us to see what we are sacrificing. It makes the trade-offs obvious and easy to identify people (read politicians and big corp) selling snake oil. The world does not become better through wishing. It becomes better through voting, reading, debating, discussing, and influencing.

Awareness of CAP theorem and the trade-off between consistency and availability renders all debates of extremes moot. Yet, the trade-off between welfare state and individual freedom is often either not acknowledged or discussed in gross extremes. I believe the awareness of Sen's liberal paradox will greatly benefit everyone discussing social policies.

Science is easier when its claims are verifiable and quantifiable. Social science, even with humanity’s most advanced tools, remains elusive. Lack of data, poor statistics, unrealistic simulations, unverifiable results, seeming impossibility of proving causality over correlation are some of the evil complexities of social science.

Consider a more statistically well-behaved science: psychology. One can argue social science is an aggregate of psychology over many individuals interacting with other (chaotic) environment variables. Even for psychology performing a well defined controlled study is prone to many follies of lacking statistical rigor. Scaling this rigor to social science seems impossibly hard.

Many people are aware of the impossibilities of social science as an exact science. Therefore they treat all of social science as the work of charlatans. This, in my opinion, is too pessimistic, myopic and often disrespectful. I do not claim to know how to make the study of social science better, but I refuse to dismiss it as a whole. For starters, the modern definition of exact science needs to be revised.

All of us benefit from social structures that have existed before us. We owe it to ourselves to keep those structures alive. And if we criticize them, the duty is even greater: we must change them. When was the last time you dreamt for a change? Talk about it more! We need to keep the culture of social science alive.

Finally, you are in it whether you like it or not. You are born with rights. You exchange currency for goods. You own objects and property. You are socio-politically active by default and there is no way to opt out. There is no such thing as an apolitical human. Being apolitical is itself a political choice. It is the politics of ignorance, and it is more often a burden than bliss.