Let's say I have a swarm. It takes 50% additional damage from area effects. Let's say this swarm is also vulnerable to fire. Takes 50% additional damage from effects that deal fire damage. These stack, right, meaning if I hit that sucker with a fireball it takes double (100% additional) damage?
Yes. Sum all the percentages (and count any doublings as +100%) and then apply them all at once.
So in your case +100% damage, not +125% damage (that would be applying serially instead of all at once).
That sounds right to me, but I can't think where to find it in the rules. Pointer?
I guess, more generally, the question I am asking is, indeed, whether and in what way vulnerabilities stack. I also think Ascalaphus' reasoning sounds right.
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I'm not sure if you'll find a clear outright statement explaining it; but take a look at how multiple sources of double damage are handled elsewhere.
For example, Spirited Charge.
Normally, you'd be doing double damage with it on amounted charge. And without it, double damage with a lance on a mounted charge. But together they do triple, not quadruple damage.
This demonstrates that the extra damage is more akin to adding +100% damage per "reason" than doubling per reason, one after the other.
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Another way to look at it is to say that each of those things causes double damage compared to the original tally; not compared to the damage after the other thing.
Likewise, fire vulnerability would cause half again as much damage as the original, and swarm/AoE would also cause half again as much damage as the original. Together, that's 2x +50%.
I'm not sure if you'll find a clear outright statement explaining it; but take a look at how multiple sources of double damage are handled elsewhere.
For example, Spirited Charge.
Normally, you'd be doing double damage with it on amounted charge. And without it, double damage with a lance on a mounted charge. But together they do triple, not quadruple damage.
This demonstrates that the extra damage is more akin to adding +100% damage per "reason" than doubling per reason, one after the other.
This is correct. It's a function of the ordinary rule on multiplying: you multiply the base damage only, unless told otherwise.
Multiplying Damage: Sometimes you multiply damage by some factor, such as on a critical hit. Roll the damage (with all modifiers) multiple times and total the results.
Note: When you multiply damage more than once, each multiplier works off the original, unmultiplied damage. So if you are asked to double the damage twice, the end result is three times the normal damage.
EDIT: Ninjas! Ninjas everywhere! (That's what I get for not refreshing ...)
...wait. I'm bad at math. Everything you guys are writing seems right, but all this still means that "50% additional damage" applied twice results in "100% additional damage", yes? It doesn't become "75% additional damage" or something? The "if you are asked to apply a ×2 multiplier twice, the result would be ×3, not ×4" line is confusing me a bit in this context.
Yes, +50% (i.e. x1.5) twice equals +100% (i.e. x2).
Applying a x2 (+100%) multiplier twice gets you x3 (+200%). If you always turn it into +X% and +Y% you'll always get +(X+Y)%, but the rules often speak in terms of multipliers, especially when doubling, so the rule is often stated as "two doublings is a tripling (etc)."
Aha! That clears that up. Much obliged. :)