[seneca]

> None of it would address the question of justice.

I'm probably misunderstanding your point, but this is a question of justice. Specifically, it's a question of Distributive Justice, which is "[concerned with] the socially just allocation of resources". Saying "What would we need to change about our absurd arm-wrestling-based distribution system in order for it to be just" is squarely a question of distributive justice.

Are you saying that nothing that determines who gets to be Lord can be tweaked to reach a just distribution because of the winner-take-all nature of the rewards? Further, are you suggesting that the current (American, I assume) system of distribution is equally unjust in distriubtion?

https://en.wikipedia.org/wiki/Distributive_justice