It would be so funny to watch Maedhros meet Tywin Lannister
There are enormous philosophical and moral differences between Maedhros and Tywin, which I'm pretty sure wouldn't endear Tywin to Maedhros, but there is one thing that they absolutely have in common, and that, of course, is political theory:
Maedhros summarises his view on kingship after Thingol does some posturing and bluster: “To this council came Angrod out of Doriath bearing the words of King Thingol, and their welcome seemed cold to the Noldor. The sons of Fëanor indeed were wroth thereat; and Maidros laughed, saying: ‘He is a king that can hold his own, or else his title is vain. Thingol does but grant us lands where his power does not run. Indeed Doriath only would be his realm this day, but for the coming of the Noldor. Therefore in Doriath let him reign, and be glad that he hath the sons of Finwë for neighbours, not the Orcs of Morgoth that we found. Elsewhere it shall go as seems good to us.’ [...]” (HoME XI (1994), Grey Annals, p. 33)
And funnily, here we have Tywin's view of the matter: “And any man who must say ‘I am the king’ is no true king at all.” (ASOS (2006), ch. 53, Tyrion VI)
You know, I think that a post-Angband Maedhros would do very well in Westeros.
Ok there's another thing that they'd agree on but at least with Maedhros it's not going to result in Cersei, Jaime and Tyrion.
By the way, it's hilarious how much of GoT comes straight from Tolkien. And even funnier is when people make grand pronouncements à la "GoT is Tolkien but with all that cool brutality and dragon incest added and without the booooring good vs evil morality that makes LOTR so boring", and it's just like...let me introduce you to Túrin real quick! And the rest of the First Age. And the entire Second Age.