Insightful method of categorisation, upvoted.
I would suggest that the reason mighty/conflict seems underrepresented here is because most of the obvious candidates for that kind of thinking have been tabooed from the site.
I was thinking about ways people "do good" (or otherwise achieve their values) and it occurred to me that it makes sense to organize these along two axes: humble/mighty and cooperation/conflict.
Whenever you organize things into categories, you open yourself up to people questioning whether these are the "right" categories, whether they carve reality at the joints; I don't have statistical evidence that these are good categories, only salient examples and a general sense that this "fits." If you don't think it fits, say so, and I'll have learned something new.
Four Quadrants
Quadrant 1: Help
The humble/cooperation quadrant refers to small acts of helpfulness. The prototypical action is giving to charity, or comforting a friend. The mindset in this quadrant is an attitude of kindness, gentleness, or benevolence, with great attention to not being presumptuous and accidentally doing more harm than good. The humble/cooperation attitude doesn't expect great victories, but a lifetime of dedication. The humble/cooperative person isn't interested in antagonism, but tries to listen to others and understand their point of view.
Quadrant 2: Invent
The mighty/cooperation quadrant refers to creating brilliant, win/win solutions. The prototypical mighty/cooperation action is inventing a hugely beneficial new technology, or negotiating a mutually beneficial agreement. The mindset in this quadrant is a an attitude of can-do, creativity, and innovation; it's associated with exchange, trade, and collaboration. This attitude does expect great victories. It's focused on fixing problems instead of managing them.1 The mighty/cooperative person thinks antagonism is mostly unnecessary if you come up with good enough solutions.
Quadrant 3: Fight
The mighty/conflict quadrant refers to fighting malicious opponents. The prototypical mighty/conflict action is, of course, fighting in a war or defending yourself against attack, but it can also refer to non-violent actions: a moderator who bans a troll, for instance, or someone who speaks out against a bully. The salient point is that this is a way of doing good by stopping the people who mean to do harm. The mindset in this quadrant is determination, courage, and will to win. The mighty/conflict person thinks that evil (or at least dangerous) people exist, and that it's absolutely necessary to defeat them, and deluded to try to cooperate with them.
Quadrant 4: Doubt
The humble/conflict quadrant refers to recognizing flaws and fallacies. The prototypical humble/conflict action is warning people that a proposal will fail or have horrible unintended consequences. The humble/conflict mindset sees human beings as fallible, flawed, and over-confident -- it is a cynical, or at least guarded, attitude. Through vigilant attention, we can avert the real catastrophes that result from fallacious thinking. The humble/conflict person sees it as his duty to oppose naive bad ideas, inaccuracies, and hypocrisies; he thinks cooperation is often less feasible than people imagine.
Four Fallacies
Each of these ways of doing good can become a fallacy if it's assumed to be the only way to do good.
Universalized humble/cooperation leads to the assumption that it's always the best choice to be more generous or altruistic. But sometimes, this is bad game theory and won't work.
Universalized mighty/cooperation leads to the assumption that all problems come with win/win solutions or structural fixes. But they don't; some games are zero-sum, some issues aren't really "problems" to "solve," and it's very common to mistakenly assume you have a brilliant solution when you engage in wishful thinking.
Universalized mighty/conflict leads to the assumption that when something's wrong there's always an evildoer to fight. Sometimes things go badly when there's no malice at all; sometimes your enemies are not innately evil; sometimes the most productive thing to do has nothing to do with defeating the bad guys.
Universalized humble/conflict leads to the assumption that the best thing to do is always to look for flaws and fallacies. This can let the perfect be the enemy of the good. It can have a chilling, demotivating effect and stop people from being as generous, innovative, or brave as they'd otherwise be.
LessWrong and the Ways to Do Good
LessWrong seems to have a high percent of ideas that fall into the humble/conflict quadrant; after all, that's part of its mission. Understanding cognitive fallacies and preparing for major risks is the special purview of the humble/conflict quadrant. And humble/conflict viewpoints seem underrepresented in the general public, so building a community around that specific perspective is potentially a good idea. But you also see ideas on here that belong to the other quadrants; there have been several posts about charity, which falls under humble/cooperation, and there was Alicorn's "A Suite of Pragmatic Considerations in Favor of Niceness," which also falls under humble/cooperation. Some of the writing about Friendly AI seems to fall under mighty/cooperation. I can't think of an example of mighty/conflict writing on LW -- it seems to be a much less common mindset here than in the general population.
Specialization and the Ways to Do Good
Differences in temperaments, skills, and professions probably mean that individual people are more likely to focus on one of the four quadrants more than the others. Sometimes one perspective just seems more natural or more feasible. It's dangerous to universalize (to assume there's only one way to do good) but it's probably okay to specialize. Some people thrive on conflict and some people hate it. If you happen to have a "type," it's probably best to regard your polar opposite "type" as an ally. Humble/cooperative people need mighty/conflict types to remind them that sometimes you have truly determined opponents; mighty/conflict types need humble/cooperative types to remind them that not everything is a battlefield. Mighty/cooperative types need humble/conflict types to remind them that you can't "fix" everything; humble/conflict types need mighty/cooperative types to remind them that ingenious successes do exist.
1This is a distinction I read about from The Hacker's Diet. The idea is that managers manage a problem, taking care of it on an ongoing basis, while engineers fix a problem, making a structural change to get rid of it once and for all. Which approach is best depends on the problem. Which approach you prefer depends on whether you're a manager or an engineer.