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... do they increase their effectiveness (I assume so) and if so, by what rate? Are their effects simply multiplied or is there some sort of ratio of reduced effect per structure.
PS. apologies of rthe nooby nature of the question. I did search but found not answer.
Broadcast stations stack up. Each one provides the same benefit in the sector, so two is 2x better then one... I think. I do know they stack, so more is better. 
The thing is that the culture spread from a broadcast center decreases as you move away from it. Putting four at one planet will do a lot there, but won't do much of anything a few hops away (one station one hop away is better then three stations three hops away).
Yeah, Tridus is right on the broadcast centers. It's a linear stack (the same with trade ports) so each one adds the same amount as the previous, there are no diminishing returns.
Shield generators, however, do not stack 
Oh, wishful thinking I guess.
I was more generally wondering if structures that can be built in multiples generally follow the rule of 'linier multiplication' or increase their effectiveness 'logarithmically' (inverse exponential) ... or indeed exponential. It seems from your answers that linier multiplication is the norm.
I was prompted to ask after I tried a couple of broadcast stations and it didn't seem to quite double its effectiveness - but I'm fairly new to the game and may have just miss perceived things.
Each broadcast centre provides 10 culture/sec without research, and this is divided evenly according to how many phase lanes radiate from that gravity well. Not sure if this relationship holds for spread coming from gravity wells your culture has reached.
Shield Generators already provide 30%/50%/80% planet bombing mitigation depending on researched level, so stacking would have diminished returns if it was possible.
Trade Ports also stack linearly - the only way to increase income rate of each trade port is by lengthening the longest chain of these ports in your empire, or research cargo hold upgrades to your trade vessels (2nd option available only to TEC and Vasari).
well, what I know is that four broadcast centers beats three. either way, it works, and we know that spread out centers are more effective over range than concentrated ones.
Number of towers definitely increases the speed that your culture spreads and pushes enemy culture back more easily so if you're dealing with an annoying turtler or you'd prefer they come to your turtle, buildling 8 culture structures on a fully developed neighboring arid world should get their attention rather quickly.
I'm not sure multiple towers will actually enhance the distance unchallenged culture travels though. Population might have something to do with that. I'm pretty sure one tower will always spread culture one phase lane away when unchallenged though.
One thing I am certain is that multiple cultures travelling through a choke point will kick the crap out of whatever is on the other end. Try an AI game of centrifuge with the Advent. Take the inner worlds only and build a ton of culture buildings and lots of defenses. It's over pretty quick since everybody's homeworld is only two phase lanes away from every culture structure you build. Even the AI seems to get pissed off at the strategy.
My general approach is to build one tower on every non asteroid world and multiple towers where needed. Culture isn't necessarily a great offensive weapon but it can be a great way to force your opponents to attack you on more favorable ground.
If the enemy has cap's at that world it will be very hard to *take it over*. But tbh you may be right, culture mecanics either need an overhaul or someone needs to explain whay 99% of us are missing. it dossent really seem all that important and, at least to me, feels like something that was thought up during development but never really resived and real work or thought.
given equal skill a tec vs tec game (just an example) will simply mean that the defender will have higer AM regen it seems a bit lackluster imo.
it should affect diplomacy for instance. Implement secondary alligience --> controling player 45% alligience-> 2'nd player has 30% alligience 3'rd player has 25% the last to don't have media hubs in range so screw them ^^ that would mean a substantial amount of your empire's population would support the views of competing empires. that in turn could have grave implications if you deside to declare war against a culture that has substantial support in your empire. there are many ways to do this quick sullution make it give an aditional production penelty equal to the support the enemy culture has on your planet as the try and work aganins the war effort ( think US during the vietnam war and the peace movement)
wassent sure anyway yes culture seems to be an aspect of the game that realy needs an overhaul.
Culture already provides faction-specific bonuses...
Rate of change for allegiance is always capped at +/- 0.07% per second, regardless of the spread rate of culture (the rate of decrease, however can be -0.10% if your culture completely dominates a planet and that player's empire does not have a capital). This seems to be influenced by how many phase lanes your culture is reaching the target planet (approaching from 2 lanes causes the rate that allegiance is lost to be higher than from 1) and if hostile culture is also influencing that planet and from how many phase lanes.
Given this, culture can more easily overthrow the fringes of a hostile empire, but have more difficulty overthrowing core planets. Culture wasn't intended to be a way to victory on its own, but more of a supplement to your empire and to a lesser extent, your fleet.
all true, but it still feels like it is an underdeveloped part of the game.
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