Economist and philosopher Amartya Sen posited that no social system could guarantee:

1. A minimal sense of freedom in social choice
2. Pareto efficiency

In his original motivating example, he gave an example of two people faced with a scandalous book. One person thinks it's hot garbage and would prefer no one should read it, but would rather put themselves through the book than see the other person read it and enjoy it. The second person, while preferring to read the book than it be destroyed with no one reading it, would think it'd be hilarious if the first person were forced to read it.

In this scenario, suppose you let each person have some degree of choice in the matter of who ends up reading this book. So the social planner will consider whether each person would rather they themselves read the book, or throw it away. Their choices will be directly put into the social planner's preferences.

So the social planner will therefore have the preferences:

$$\text{P2 reads} \succ \text{no one reads} \succ \text{P1 reads}$$

And the social planner will have the second person read the book. This is not a Pareto optimal result! Both people would rather the first person be made to read the book.

There are a few ways out of the paradox:

• Let the two people make a contract to bargain their way to a better result.
• Let them express their "preferences" sequentially, as a game.
• Lighten the restriction on needing Pareto efficiency specifically
• Only care about societies where everyone respects each others' choices and don't create weird externalities (societies that don't do this are the only ones that have this paradox).

So my general questions are:

• Are there other solutions to the Liberal paradox?
• Beyond abstract ideas of social justice, what practical implications could the paradox have on markets?
• The social planner has very strange preferences. In your explanation of the story the persons have preferences over collective actions that are much more refined than their preferences over their individual choices. I don't see why the social planner would construct her preferences based on their individual choice preferences. It is like she does not consider externalities but that is one of the most important roles of social planners. Jun 11 '16 at 7:05
• @denesp Don't shoot the messenger. ¯_(ツ)_/¯ Rankings are perhaps a better word. The social planner's rankings are decided by a pretty simplistic rule, I agree. But then what rule would you propose? Maybe this question would be better with Sen's formal formulation of the problem? (That would be rather long though.) Jun 11 '16 at 7:13
• "There are a few ways out of the paradox: Let the two people make a contract to bargain their way to a better result." Does this not preclude this situation occurring in markets?
– user7935
Jun 12 '16 at 8:01
• That's exactly the reasoning some people use to counter Sen's criticism of laissez-faire econ. Jun 12 '16 at 16:34