Hello!

Ascension book presents a guideline for GMs on how much Influence he should give as a reward. It states that +1 to Influence per 1000 XP. My question is - is this 'average' XP, that each player earns, or TOTAL?

So, assume 3 players recieve 1000 XP at the end of adventure. How much Influence (using this guideline) should GM give to the group? +1 or +3?

P.S. Yes, I understand that it depends. But I'm talking about this guideline and nothing else.

That's not only "it depends", but "whatever you as a GM want" as well. Should a group of three PCs gain +30 influence after adventures worth 10000 XP? Then yes. The table gives you some examples for what influence level represents which kind of person.

Personally, I'd assume the bonus is per group - larger groups already have the benefit of being able to exert their influence in multiple places at once.