The Coase "Theorem" in Real Life ...
But let's embrace Barro's conceit. Two problems:
(1) The good Mr. Barro assumes well-defined property rights here. (actually, he mistakenly asserts that they are well defined.) As the reclined upon, I am not just "bothered" by his reclining. I arguably have purchased a property right to the space my lower extremities occupy. And his reclining infringes my property right. (Here I am just stating the converse of Barro's claim that he has a property right to the recline function.)
At this point I'd almost be willing to pay Barro to zip it! If you are going to pose as social science literate, please at least try to get things right.