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In a traditional MMORPG, you run around picking up quests and doing the quests. A quest asks you to kill ten rats or go talk to some particular NPC or go kill some particular boss or whatever. One problem with this approach is that some of the quests are bugged. You need to kill a boss that won't spawn. You need to give something to an NPC who won't respond to you. You do what a quest said to do and it mysteriously won't give you credit. You need to escort an NPC who finds creative ways to die. (Actually, that last one might be working as intended, but it's still really annoying.)
Guild Wars 2 fixed that problem and we didn't even notice. Sure, some of the dynamic events are buggy. But those are more a replacement for the public quests that a few games have dabbled in, and not the traditional exclamation mark over the head quests. I like dynamic events, but that's not what this thread is about.
Rather, renown hearts are Guild Wars 2's replacement for traditional quests. What makes renown hearts different is that rather than having to do one particular thing that might be broken or scaled to be unreasonably difficult, you get your choice of several different things that might be broken or scaled to be unreasonably difficult. Why is this such a good thing? Because if you have four choices, of which one is broken and three work fine, then you can ignore the broken one and do the other three. The odds that all four will independently be broken are very slim.