Let’s start with legalism vs. Confucianism. Legalism believed that human nature was selfish and hedonistic (similar to the attitudes of, say Machiavelli or Hobbes) and that strict laws, harshly imposed, was necessary to restrict human nature and enable civilization to progress. Confucianism was a bit more optimistic about human nature, and believed that by inculcating the correct values at all levels of society, from the family up to the nation, you could get people to choose virtuous behavior of their own accord.
In terms of Stannis as a legalist, I’d say the following things are key commonalities:
- Belief in a powerful unitary authority to impose law. The legalists believed that the ruler needed to be a hegemonic power in order to ensure that the law could be enforced. Stannis believes that “It is all one. One realm, for one king to rule alone.“
- Belief in a public and predictable law that treats all equally in how it rewards those who obey and punishes those who break the law. A big part of the reason why the legalists stressed the necessity for hegemony was that they wanted to enforce the law against the nobility as well as the common folk, because they felt privilege led to corruption and civil war. Stannis stresses that “I shall bring justice to Westeros … Every man shall reap what he has sown, from the highest lord to the lowest gutter rat. And some will lose more than the tips off their fingers, I promise you. They have made my kingdom bleed, and I do not forget that.” And he believes utterly that “a good act does not wash out the bad, nor a bad act the good. Each should have its own reward.”
- Ministers should be evaluated solely on the basis of meritorious action, so that enforcing the law is the only route to promotion. Here the concern of the legalists is that the ruler needs to be able to monitor his ministers to ensure that they’re carrying out his will and not subverting the state, but also the need to restrain corruption. Stannis believes that “to be lordly is to be false,” and promotes Davos for loyal service, saying “we will make new lords.“
- The rule of law should be govern the state, not the whims of a ruler. In this fashion, the legalists hoped to avoid both weak monarchs and tyrants, by ensuring that the rules would always be enforced and the system would function even without the king. Likewise, Stannis believes “"My duty is to the realm… we must do our duty, no? Great or small, we must do our duty…It is not a question of wanting. The throne is mine, as Robert’s heir. That is law. After me, it must pass to my daughter… I am king. Wants do not enter into it. I have a duty to my daughter. To the realm. Even to Robert." Similarly, Stannis keeps Davos in his service when Davos disobeys him over Edric Storm because Davos reminds him of his duty to all of his subjects, and follows Davos’ rebuke that he ought to put his duty above his rights by coming to the aid of the Night’s Watch.