Only the last revision to the timeline counts
In the world of Primer, only the final iteration of time travel truly matters. This concept is crucial to understanding the film's complex narrative and resolving apparent paradoxes.
Let's start with a key piece of narration from Aaron-2 (the hooded Aaron) about Aaron-3 (white jumper Aaron) (emphasis mine):
Aaron-2: I can tell you with certainty what I did that night when it was my turn.
But I think it would do little good, because what the world remembers, the actuality, the last revision is what counts, apparently.
So how many times did it take Aaron as he cycled through the same conversations lip-synching trivia over and over?
How many times would it take before he got it right? Three? Four? Twenty?
[...]
And eventually he must have got it perfect and it must have been beautiful with all the praise and adoration he had coming.
He had probably saved lives, after all.
Who knows what would have happened if he hadn't been there?
This narration suggests that while we might see multiple timelines in the film, only the final revision of events ultimately "counts." The Primer universe allows for timeline modifications in later iterations, effectively overwriting previous attempts.
Resolving the paradox: clones only appear when a time-traveler is prevented from making their journey
Now, let's tackle the paradox you mentioned about multiple versions of Aaron and Abe appearing at the party:
In order to go back after a failed attempt (or just an observation) they must have a box running. But when they go back in time, in the new timeline their doubles are also going to the party to have their attempt . Suppose the originals convince the doubles not to go, and let the originals go instead, since they have more experience. If they fail again this time, why would the doubles agree to stay in this timeline, where the party goes wrong?
The key here is that clones only appear when a time-traveler is prevented from making their journey. We see this when Abe-2 drugs Abe-1, and Aaron-2 drugs Aaron-1.
Remember the physical confrontation between Aaron-2 and Aaron-3? It resulted in Aaron-2 leaving town instead of using the time machine again. Aaron-2 explains (emphasis mine):
Aaron-2 [speaking as the narrator ]: And that's where I would have entered the story. Or exited, depending on your reference.
Because when Aaron came back the second time, it wasn't so easy.
He wasn't expecting me to put up a fight. And by that time, he was too exhausted to take me.
But for reasons that are only evident to me now, I understood that he simply wanted it more. That he just had more invested. So I left.
He had already performed the task, as I had intended to... of recording the conversations of the day just in case.
Through that earpiece he had a three-second lead on the world.
This scenario demonstrates how the film avoids the "sum of series" paradox you mentioned. Since the timeline is overwritten by the last revision, the doubles won't be going to the party in the final iteration. The last Aaron (Aaron-3) can simply repeat his actions to stop his doubles – drugging one and convincing the other to leave.
The concept of overwriting timelines is further hinted at in Aaron's conversation with Abe at the gas station:
The worst thing in the world is to know that the moment you are experiencing has already been defined, that this is the second or third time through, or whatever.
And do you ever feel like... maybe things aren't right, like maybe your life is in disarray or just not what you would like and you start to wonder what caused this. How did things get like this?
[...]
What if you knew for sure this is not the way things are supposed to be?
This dialogue suggests Aaron's awareness that their current timeline might be altered by future iterations.
Shane Carruth, the film's writer, director, and actor who played Aaron, offered some relevant insights into this aspect of the film (emphasis mine):
Question: Where did the title come from?
Carruth: First thing, I saw these guys as scientifically accomplished but ethically, morons. They never had any reasons before to have ethical questions. So when they’re hit with this device they’re blindsided by it. The first thing they do is make money with it. They’re not talking about the ethics of altering your former self. So to me, they’re kids, they’re like prep school kids basically. To call it a primer or a lesson was the easy way to go. And then there’s also this power they have in using the device is something almost worse than death. To put someone else in the position where they’re not sure they’re in control of anything. They’re not in the front of the line anymore and they’re living in someone’s past, to be secondary in that world. The thing that is most important is to feel like you’re at the front of the line, to be prime or primer. I definitely never wanted to say that in the film, but that’s where it comes from.
Source: DVD RE-RUN INTERVIEW: Shane Carruth on “Primer”; The Lessons of a First-Timer — IndieWire