Sen's Liberal Paradox Economist and philosopher Amartya Sen posited that no social system could guarantee:


A minimal sense of freedom in social choice
Pareto efficiency


His original article can be found here.

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.


Person 1 prefers not reading the book to reading it.
Person 2 prefers reading the book to not reading it.


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?
Another solution can arise if you allow for uncertainty and for the planner to provide private information to each player. See Bergemann and Morris, 2018 for a survey in what is called information design. In that way, it is not hard to see how each player can be convinced that the social allocation is its most preferred outcome with high probability such that from the ex-ante perspective, the outcome is Pareto-optimal. 

Of course, I'm throwing a lot of details under the rug, but having asymmetric information seems like another solution to this conundrum.