Some notes Pathfinder makes on Archons, which in Pathfinder are the Lawful Good Celestials. For the record, Please remember that because they are celestials, the description of them will be the extreme form of the alignment:
Archon:
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...These warriors of Law act honorably, even to their foes, but are not foolish or without passion, and little in the multiverse dares stand against the rage of heaven.
Although Archons are champions of good, they have little patience for those who do not follow strict traditions and patterns of goodness.
While a Cruel Dictatorship might legitimate enemy of the Archon, rebellion and riot is not the proper way to address such an inequality. Justice and law must not be abandoned in the constant struggle for peace and good, for in such anarchic actions one often promotes further harm and mayhem, even if unintentionally.
The laws of Heaven exist to minimize collateral damage and unwanted pain, and while adhering to these laws often results in longer campaigns, Archons point out that their victories are lasting triumphs as a result.
Because of this strong adherence to tradition and law, Archons often find themselves the unwilling enemies of Chaotic Good creatures, particularly the Azatas.
To an Archon, an Azata's nature seems whimsical and impatient-- in striking swiftly against an enemy without bothering to think through the implications of their sudden act, its possible to do more harm than good.
Still, while opposing the chaos of an Azata is a necessary step, the Archon takes no pleasure in such opposition, and does its best to minimize the length of such a conflict.
Unfortunately, the capricious and emotional Azatas are legendary among the Archons for their ability to hold grudges, so for many Archons the best Policy is to be brief, succinct, and firm.
Remembering that Archons are an extreme example, they
do tend to show signs of some of the aspects I tend to complain about when it comes to Lawful good. Edit: scratch that, what i say next makes that invalid, by giving several strategies that would actually work and maintain order.
The main one is that of the dictator. (Why do we have to keep coming back to that?) where it says that Riot and rebellion is not the way to deal with him. In which case I can see two or three options for them that would fulfill their objectives swiftly; they work because one notes that the "laws of heaven" are not the laws of the king, so they need not follow his laws, but need follow their own.
1. March up to the king and apprehend him; using a force of strong men. Preferably not an entire army, but strong enough to deal with the guards. Leading to the kings possible execution.
2. Assassination... not much to say there. May require some level of justification in their code of good first though.
3. A "Non-Rebellion uprising". Where rather than becoming a disorganized mess of chaos, they organize the oppressed into a legitimate army, that can take down the Dictator while maintaining Lawful Good order.
Remember that not not all Lawful Good characters are going to be as extreme as an Archon, and that many may have minor lapses in order for the sake of good, but will ultimately return to trying to maintain order; as they believe that order is... better than chaos.
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Hopefully I haven't mangled both sides of the argument at this point.
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Personally, I think the Archons could be rubbing the Azatas the wrong way by being "firm". Its bound to rub them the wrong way.
Think about it. Chaotic Good hates it when people tell them, or anyone what to do. And unless its just to get their attention, this strategy is bound to cause problems.
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I'm not really sure which I'm arguing for at this point. All I know is that I prefer Chaotic Good.
Sure, a Lawful Good way of running the world is probably better. But, I just find A Chaotic Good approach to individual people will always work better.
Imagine a lawful Good conversation, I imagine it would go like this:
Paladin 1: So, are the troops ready?
Paladin 2: Mostly, all we need is more weapons for the musketeers.
Paladin 1: The next shipment should arrive in the morning.
Paladin 2: I just hope we don't get ambushed.
Paladin 1: Those daemon scum are likely to pull such a trick. Make sure the Turret operators can stay awake, and get me those stim' packs, I don't want to fall asleep before they do.
Paladin 2:Yes sir. I presume the cigar form is good? It's all we've got left.
Paladin 1: It will do, for now.
I feel like that kind of conversation isn't exactly the kind that is going to be considered the most endearing. Its good for a grim setting, but I've rarely met someone who talked to others that way outside of a military setting. Its not particularly endearing.
Now let's try Chaotic Good:
Barbarian: Hey kid, Do the guys out there look ready to you?
Rogue: They look like they're riled up enough. But something seems missing.
Barbarian: Oh?
Rogue: Weapons. Seriously, not all of them can fight barehanded you know.
Barbarian: Don't worry, I sent the Knight to go grab some. He'll be back tomorrow, I just hope he didn't cut back on the Rum supplies to do it.
Rogue: I'm more worried about nightfall, the Daemons are likely to catch us of guard if we aren't careful. You seen some of them? Last time, I swore I saw one that looked like a drowned child.
Barbarian: Just load everyone who's on watch with stim' packs. That will do the trick. Which reminds me, mind if I have some? I have no intention of giving the Daemons the satisfaction of seeing me fall asleep before my men.
Rogue: Eh, I would, but all we've got left is those damn cigars the gunslingers brought in. I have discovered a more palatable method of using them though. They're filled with some kind of dried bean like stuff that when crushed and strained with hot water makes quite a nice drink. A bit bitter, but I just mixed in some of the Milk and sugar rations and it makes it taste divine.
Barbarian: Sound tasty, I'll take it. What do you call it?
Rogue: I've been thinking of calling it "coffee", I thought it was appropriate considering most people who try cigars get into coughing fits the first time.
Barbarian: You sly little- I'd hug you if you weren't so fragile.
I find that one slightly better.
Now note that I was doing both examples off the top of my head. So take that as you will.
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Apart from that, I hate tradition. Lawful Good values Tradition according to most cases. And- yeah, you know what that means.