The precise effect of influence bases has been debated a lot - to my knowledge there hasn't been reached a definitive answer to the inner workings of the influence algorithm, but I believe it works something like this:

Every square in the game is influenced by the IP of the different races, the race with the highest level of IP in a given sector controls it (as represented by the coloured borders). IP radiates from every colony (and to a less degree every starbase) into the surrounding sectors. If you build an influence starbase the IP level in the SB's sphere of influence is boosted by a given percentage. So if your colonies in a sector radiate a total amount of 100 IP and you build a SB with a bonus level of 50%, you will have an equivalent of 150 IP in the SB sphere of influence.

The blue resources add to your global influence bonus which is multiplied with the produced value of influence points for every colony.

Or at least this is how I think it works

Yea, there needs to be a counter to this besides building your own right next to theirs. But honestly, since we don't know how influence really works, it's hard to determine what should be done or if these are really a threat or just annoying.

I just won a cultural conquest,id say the influence star base put me over the edge and helped me win.

As close to the enemies home world as possible. The enemy must be in awe of you. If your culture surrounds their planets then,their citizens will revolt,then its a matter of time before they join up with you. Do not let up,keep building them,until you simply dominate. You must be good at diplomacy,to talk your way out of sticky situations. Also superior research helps a lot.
my settings were....
Terran Alliance
economics +30
research +20
diplomacy +20
espionage +15
logistics +6

i would suggest putting the starbases near your own border wher your influence is higher for a larger influence increase and working your way toward whoever you are trying to take over that way the starbases are more effective they protect yourself from influence and spread it out wards it is extremly expesive in producion points but generaly you are going to have only a few colonies produceing military ships unless you are under attack so you can use lower production colonies to prduce constructors and the other race will not complain as much because the starbases are in sectors that you control

I use them both to expand my influence border and to subvert the planets of other races. I have noticed that if you put them on your borders and build them up you will see your influence bulge. As far as getting planets to defect. the AI will try and counter you with planetary improvemtns and its own influnence starbases. It is a nice alternative to traditional warfare.

Influence can be a bad thing. Well, too much of it can be, at least.

On the losing path for one of the first Dread Lords missions you have to basically seduce another race into joining with you. There are a couple of other races about the place, too, and a ton of influence resources to be mined. I forget the name of it.

Anyway, I got off to a very fast start on this, managed to grab a lot of space and many of the influence resoures. Figuring that I'd be able to overwhelm them culturally I built everything up to the point where the whole damn minimap was blue.

What happened? Instead of ceding to me, one of the other races decided to start a war because I was *too* influencial. After a maybe 10 turns after that, the race I was supposed to be schmoozing up to decided they were really good pals with the ones (the Korx?) that went to war with me, and decided to declare war, also. The result: game over.

It seems odd that this would happen if I wasn't the one that started the war, and that it didn't happen the instant the other race declared war. It also seems odd that I failed when I was just doing things in what would appear to be the suggested manner - be influencial in order to gain an alliance.

I must admit that I just don't get influence at all. Too much, too little - I don't bloody know.

No race has ever seemed to do anything to me for putting up influence bases right next to their planet. But then, I've made sure that I have the highest military rating.

I really don't understand the math behind the influence at all. What's the best strategy for increasing your overall influence? I'm just not sure.