@pit2001 said:

Is conquest a valid claim to the throne? Mad King conquered and so did Robert yet it appears they were both considered legitimate kings. Is fighting and stealing the throne (via conquest) a valid claim such that your children can base their claim on your conquest (Joffrey on Robert's, Danaerys on the Mad King's)?

I think Robert was also known as the Usurper. The Mad King succeeded his father to the throne. He did not conquer it.

Right of conquest establishes a dynasty which remains in power until challenged. If there's no challenge, because everyone's pretty happy, then the status quo endures.

If the challenger's unhappy and the challenger wins, there's a new dynasty.

If s/he loses, then the previous dynasty sticks around. Simple!

If the conquery deposed a bad king and proves to be a good one, the people may decide that he deserves the power, and may even be favored by the gods. On the other hand, if he spends his reign chasing women and getting drunk, like Robert, that's not good for his heirs

@CharlesTheBold said:

If the conquery deposed a bad king and proves to be a good one, the people may decide that he deserves the power, and may even be favored by the gods. On the other hand, if he spends his reign chasing women and getting drunk, like Robert, that's not good for his heirs

Don't forget bankrupting the treasury. The best anyone could say about Robert, as he himself admitted, is that he was a better king than Aerys- and would stay king because he was afraid of the kind of king Joffrey would be.