Influence and Happiness, V2

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Vezzra
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Re: Slowing down expansion, economics

#61 Post by Vezzra »

Geoff the Medio wrote:
Vezzra wrote:...the first implementation TheSilentOne has provided so far has a costs-per-colony factor. I'd rather see a pop based factor instead of that.
This makes no sense to me. What is the purpose of population-dependent influence cost for planets? To make players have lower total population?
No, of course not, the idea is simply to slow down expansion by making the player pay maintenance for his colonies. To avoid favoring large planets even more than they already are, I thought basing these maintenance costs on pop instead of colonies would be the better approach.

As I already mentioned in other replies, I've reconsidered my position after some mulling over what you said here:
It seems like the real issue that needs to be addressed is that there are too many large population-dependent bonuses to resource output, particularly in the later stages of the tech tree. Why not just change a bunch of them to reasonable-sized population-independent (but generally location-specific) bonuses.
I'm probably getting old, but it took me some time to realize what you're suggesting here (and thereby also understanding what Morlic probably was trying to get at). Instead of nerfing the flat boni and putting all the emphasis on the pop-dependent boni, and then addressing the issue of making small planets not too worthless by basing empire influence costs primarily on pop like I suggested, do it exactly the other way round: introduce more pop-independent flat boni (which will bring back the small planets into business) and base empire influence costs on colonies (or, given the current consensus on system based influence costs, make colony based IP costs an additional factor) to counter-balance the grab-every-planet-you-can-approach favored by this (which is what Morlic argued). To address the current unbalanced, overpowered NAI and AA techs, we need to rebalance them, and probably move them in the tech tree.

If we get the balance between pop-based and flat boni right (flat boni lower, but faster available because pop-independent, pop-based boni higher but slower available because dependent on pop, which has to grow first), this will provide the player with two options: either colonize as much as you can and go for the flat boni to make the most out of your many colonies, or concentrate your colonization efforts on a few large (more valuable) planets and go for the pop-based boni. The first will give you more resource output in less time, so short term you're going to have the higher resource output. Long term you'll have the higher influence maintenance costs per PP/RP produced, which means lower resource output.

The second will give you less resource output for a longer time, so short term you're going to have the lesser resource output. Long term you'll have the lower influence maintenance costs per PP/RP produced, which means higher resource output.

The first option will give you a head start in the crucrial early game, but might cost you in the long run, the second will leave you behind in that critical stage, but might pay off in the long run. Which option is the better will very likely depend on the situation you find yourself at game start. If you have enough larger planets within reach, option 2 might be more viable, if you only have smaller planets in the near vicinity, option 1 might better suit you. I have to admit, I really like that idea.

Getting the balance right so that this actually works won't be easy. Especially when adding new techs/specials/whatever that provides resource output boosts, we need to keep the whole picture in mind. Adding a new few new flat boosts without also adding some new pop-based ones (or vice-versa) will then very likely tip the scales to much in favor of one option. Still, I think it's worth it, we should pursue this approach.

However, I'm not at all sure that this will go well together with this other suggestion you brought up, "Spending PP on Industry Meter Growth". IMO that will impact the flat-boni many colonies approach too strongly to keep it a viable option.

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Re: Slowing down expansion, economics

#62 Post by Vezzra »

Cpeosphoros wrote:One thing I should say is that when I made the referred post, I was way greener at FO as I'm now. I've changed some of my opinions since.
No problem. After all, it was me taking over a month to reply... ;)
The main point which make I feel like that is exactly the simplification of not having to bounce around a lot of screens to manage the game. That's why I made the statement you just quoted. Avoiding undoing that simplification seems to me a very sensible design choice, which is also clearly stated in the wiki's pages on game design.
Absolutely. We have to carefully consider each additional screen/queue we want to introduce.

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Re: Slowing down expansion, economics

#63 Post by Vezzra »

Cpeosphoros wrote:Also very nice, but would require some kind of adjustment on how new colonies/conquered colonies start their happiness meter. Otherwise, every new colony would start in riot.
Ah yes, good point.
Maybe some combination of actual happiness and target happiness could be used. I don't know.
I think the simplest solution to that would be to just start new colonies with sufficient happiness (no hard rule to start all meters at 0). Conquered planets are a different story, there it actually makes very much sense to start with low happiness and being in riot (I mean, in reality you also can't just withdraw your troops after successful conquest, you need to keep a strong military presence to keep things under control). However, that requires mechanics that enable the player to deploy more troops to rioting planets, which are not in place currently. So, for the first implementation, I suggest to start conquered colonies at the bare min happiness level required for no riot. The happiness level required to build ships/be a source for colonists can be raised accordingly.

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Re: Slowing down expansion, economics

#64 Post by AndrewW »

Vezzra wrote:The probem I see with Cpeosphoros' approach is that if you put too high a price tag on using new technologies, you might end up rendering the investment necessary to get them not worth it. I mean, better techs are supposed to give you more benefits for the same costs. If you try to balance e.g. the more powerful weapons (you get by researching the higher weapon tiers) by making them more expensive to produce (PP) and to maintain (IP) so that their advantage over the lower tech, but cheaper weapons gets too small, why bother investing RP to get them? Currently more powerful ship parts are usually already more expensive to produce, if you make them more expensive to maintain too, I think this will be too much.
Investing in them can still be worthwhile when you factor in shields. But agreed. Though my feeling is a flat per part model, rather then per hull, gives some incentive for not filling all the slots.

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Re: Slowing down expansion, economics

#65 Post by Geoff the Medio »

Vezzra wrote:...mechanics that enable the player to deploy more troops to rioting planets, which are not in place currently.
The defensive focus wouldn't work?

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Re: Slowing down expansion, economics

#66 Post by Vezzra »

Geoff the Medio wrote:The defensive focus wouldn't work?
The defensive focus only increases the target troop meter, not the amount the current troop meter raises each turn, so I'd expect the defensive focus to have no effect. Because even if I set the defensive focus right after an invasion, only if the rebel troop meter is lower or equal to the rate the current troop meter increases each turn the current troop meter won't drop, regardless of how high the target troop meter is.

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Re: Slowing down expansion, economics

#67 Post by Geoff the Medio »

Vezzra wrote:The defensive focus only increases the target troop meter, not the amount the current troop meter raises each turn, so I'd expect the defensive focus to have no effect.
It would not be difficult to add a suitably-sized bonus to troop regeneration while in defensive focus. Or to add a "Rebel Suppression" focus that does something more specific for that purpose...

But I think it's a bit beside the point... What the intended rebellion mechanism and problem perceived?

Assuming a planet is invaded by an empire its populace dislikes, and it starts with sufficiently low happiness to generate some rebel troops, the initial invasion will probably leave some extra invader troops on the planet, which the rebel troops would have to fight through over several turns. These could be reinforced by using more troop ships on the planet (only allowed while a planet has active rebels on it, or is owned by another empire).

No loss of control of the planet back to its original empire would happen while there are the new owner's troops on it, so it could / would take several turns for anything like that to happen. During that time, the invader's influence effects could allow the planet's happiness to start increasing, eventually getting high enough enough to stop the rebel troops from being generated, or at least to fall low enough that whatever mechanism generates or transfers ground troops to the planet is providing more troops per turn than there are rebels.

To that end, there could also be a mechanism to transfer troops to a planet from other planets of the same empire, if the source and sink are supply-connected. This might be a focus setting.

Also, presumably a planet would need to be supply-connected to another empire to revolt and (re)join it. (Leaders might provide an exception to this, though...) So, keeping an armed fleet in the system with the rebellious conquest planet could prevent it from revolting. The planet would be effectively useless to the invader while it has uncontrolled rebels on it, but it couldn't revolt back if space-blockaded. For neutral planets that have never been owned by another empire, and wouldn't want to join any empire, they could be kept by keeping armed fleets over them. They would probably be mostly useless, until they could be made happy / non-rebellious, and could revolt back to neutral if left unguarded with rebel troops being generated in numbers enough to overcome the invader troops.

So, to successfully capture and control a planet, you'd have several options...
-Made the populace like you enough that they are happy to be liberated by you (vs. invaded) and the planet doesn't generate rebel troops
-Repeatedly drop troops, or initiate troop transfers from supply-connected planets, to combat the ongoing rebellion
-Drop enough troops to keep the planet rebellion controlled short term, and then wait for influence or other effects to get the happiness high enough to stop rebel troop generation
-Not bother controlling the rebellion, and just keep the planet pacified and unable to revolt with a space fleet... Might be some limited benefits from having such a planet
-Bombard the planet and recolonize with your own populace, who aren't rebellious

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Re: Slowing down expansion, economics

#68 Post by MatGB »

For what it's worth, my thoughts about switching to a parts used approach was based around the existing fleet upkeep paradigm where I'm certain it would be better, however given Influence is basically untried I don't have a strong opinion and doing it this way is definitely simpler, and I quite like that I can balance various hulls by doing stuff with their influence costs (Organic Hull line underpowered you say, OK, well, they cost virtually no influence whereas Titans cost loads).

Ergo, I'm happy to go with this and see, we can always (I assume) add influence costs to specific parts if we think it's necessary for balance.
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Re: Slowing down expansion, economics

#69 Post by Geoff the Medio »

MatGB wrote:...we can always (I assume) add influence costs to specific parts if we think it's necessary for balance.
As with buildings, in specific cases, it might make sense to give parts influence costs regardless of whether parts in general have them.

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Re: Slowing down expansion, economics

#70 Post by The Silent One »

To sum up the discussion up to this point:
What can influence be spent on?
"empire upkeep":
- per star system, increasing cost (maybe by distance); take into account: distance of system to capitol, or to nearest colony?
- per colony, flat cost
- not per population
- per number of different species in the empire, multiplyied by colony number?

"fleet upkeep"
- per hull-type, and maybe in specific cases for ship parts

"building upkeep" -> LATER
- not in general, only for specific buildings (space elecator?).
- influence cost may vary depending on context

What happens if there is not enough influence available?
- malus on happiness or
- influence "stabilises" the colonies happiness, if insufficient influence is available, colonies may become unhappy
- low happiness leads to ships and/or colonies going rogue
- cap on surplus influence?
So, I believe we have so far consensus on: an influence cost per star system combined with an influence cost per colony, and no influence cost for population. Vezzra favors a "distance of system to capitol" over "distance to nearest colony", which I will try to talk him out of below ;)

We agree that the count of species in the empire should be reflected by an influence cost, but not exactly how.
Fleet upkeep will for now be calculated by a hull-based influence cost, specific ship parts may also have an influence cost. An influence upkeep for buildings may follow later.
Vezzra wrote:What do you think about my suggestion earlier, to just make system upkeep dependent on distance to capitol? E.g. 3x jumps to capitol, this would result in system influence costs of 9 for a system 3 jumps away.
I think this would promote circlish empires around the capitol, and not offer strategic choice. "Distance to nearest colony" would allow the player to expand in a main direction (without the need to relocate its capitol, which would be deadly for a circlish empire anyway). Only for valuable systems the player would deviate from his main direction. Or he would make the strategic decision to expand in two or three directions. Also, I would find it counter-intuitive to have to "pay" the full distance cost for each colony again; I've already "paid the supply cost" to the nearest system.
Krikkitone wrote:.. each species costs "# colonies of all Other species in the empire" x "# colonies of This species"
Could you explain more why you think this would be a good approach? It seems too complicated to me. I would probably do it like Vezzra suggested, a linearly increasing cost per species in the empire multiplied by the number of owned colonies.
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Re: Slowing down expansion, economics

#71 Post by Vezzra »

Geoff the Medio wrote:Rather than a penalty to happiness when there is insufficient influence, I think it should be expressed as a bonus to happiness when there is extra influence available.

Most planets would be substantially unhappy by default, and then by having surplus influence available, the empire would increase those planets' happiness. Use up too much influence on other stuff, an the planets' happiness drops gradually.
I've been mulling over this repeatedly in the last days, but I don't know how exactly you intend that to work, or how that approach is better than having negative effects on happiness when the influence costs aren't met. Specifically I have these questions:
  • What exactly is "extra influence available"? The amount of IP not consumed by things other than the various influence maintenance costs (influence projects?)?
  • What exactly is "substantially unhappy by default"? Happiness = 0? Happiness = some fixed (low) value? Happiness = pop/2? What happens when a colony stays at the default, "substantially unhappy" happiness level?
  • Would new colonies start out at that default "substantially unhappy" happiness level, or something higher which would decrease unless sufficient "extra influence" is available?
  • How exactly does "extra influence" translate into increased happiness?
The main issue I'm concerned about is that this approach sounds like it is more complicated and less transparent for the player what is going on. The currently proposed approach works by determining a certain IP maintenance cost per system/colony and ships (details still under discussion). If the total IP maintenance costs aren't met, this will negatively impact the happiness of your colonies (formula/numbers tbd), if the shortage of IP is too severe/lasts too long, happiness will drop too low, and your colonies are going to suffer certain consequences (rebel troops, not being able to build ships anymore, details still under discussion). But what makes that approach transparent and easy is that the player gets a simple number he has to meet - the total maintenance costs. If he fails to do that, things will start to go bad.

With your approach, I get the impression that you don't have this number anymore. It's just "the more extra influence, the better", but no clear, simple limit to meet. You have no clear, easy to understand "feedback" what the "sufficient" amount of extra influence needs to be for your empire to function smoothly. But maybe I'm misunderstanding what you try to get at, hence my questions above.
Also, some of those population-dependent resource output bonuses could depend on happiness. Make getting the biggest (population-dependent) bonuses require maintaining a high influence output. (Non-happiness dependent alternatives could also exist and be usable as a strategy...)
Hm, the ideas you've been coming up recently surprise me - IIRC you used to be wary about such more complicated approaches, e.g. like this one, which make resource output dependent on more than one meter? Or make two distinct meters serve a too similar purpose (I recall Bigjoes attempt to base resource output on pop and infra). You always argued (convincingly IMO) that the different meters should serve distinctly different purposes.

IMO we should stick to that design philosophy, which is why I'm wary of this idea. I think having the happiness meter influence things like rebel troops, ability to build ships etc. is the far better approach.
Also, rather than happiness a sort of %-like value, where 20 happiness is "content", 10 is "restless", 5 is "angry", and 0 is "revolting", consider having it be more Civ-like, where you need 8 happiness to pacify / satisfy a population of 8, and anything below that starts to have negative effects, such as for the population-dependent resource meter effects only adding the lesser of population or happiness, or the number of rebel troops generated (eg. rebels_per_turn = (happiness - population)/3 with a substantial penalty to happiness on recently-conquered planets, and dependent on species tendencies and opinion of the empire).
This. I like that idea very much. It's simple, straightforward, easy to understand, and elegantly takes care of factoring in the population level. Having to invest more to make a high pop planet happy than a low pop one makes much sense to me. As far as the negative effects are concerned, as I said above, I'd prefer the rebel troop alternative, and not being able to build ships, and things like that.

Species "tendencies", species-empire relations etc. need to be in place before we can factor them in, but once that's the case, we definitely should do this. I'm very much in favor of these ideas.
That not being effectively a population-dependent influence cost for a colony would require a population-dependent happiness bonus, likely dependent on species preferences and relevant historical events.
Can you elaborate? If we determine the basic IP maintenance costs for a system/colony independent of pop, paying those costs should keep the target happiness meter (at least) at the pop level. So, no pop based influence costs you need to counter. It just takes a high pop planet longer to reach the target happiness level.
I would attempt to implement things like a penalty for more species using such species tendencies and opinions. If a species doesn't like some other species that is in the same empire or that lives on a nearby planet, then give that planet a penalty to happiness.
Absolutely. But until those are in place, we need stop-gap solutions, and the formulas I suggested are merely meant as such, and definitely not as something final.

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Re: Slowing down expansion, economics

#72 Post by Vezzra »

Krikkitone wrote:I think the problem is the idea that happiness can simply be bought.
Why is that a problem? Isn't that the basic idea behind that whole influence/happiness mechanic? That you have to "pay" with influence to "buy" enough happiness so your empire doesn't fall apart?
Essentially your system would work if "total population of empire" was a negative for happiness (as in civ)..and additional unhappiness/happiness for a planet based on local factors.
When you put it that way, that sounds very much like this will lead to almost purely pop-based influence costs (happiness directly dependent on pop, influence required to buy happiness).
Someone had a good idea for a system based on that you had
local happiness->target was species allegiance + "local" factors (including total empire population)
Species allegiance->target was the average happiness of all worlds with that species in your empire
(there would also be one time effects to species allegiance+happiness based on things like atrocities, etc.)

So if the "local factors" for all the worlds of a species were an average negative, then happiness would continually fall for all worlds of that species, the most unhappy ones would revolt first, allowing you to bring the average up. (and also removing some pop from your empire bringing happiness up for everyone)
IIRC something like that has been brought up in the Happiness, Influence, & Allegiance thread. I'm wary of designing game mechanics like this, where you have kind of cyclic dependencies (basically happiness influences allegiance, allegiance influences happiness). Such things tend to get complicated, difficult to balance (screw up the involved factors a bit, and you risk to quickly get dramatic snowball effects, which aren't necessarily much fun), and the dynamics they create in-game are likely difficult for the player to understand.
also I would far rather have revolts than production penalties....
Production penalties are what you get when you plan ahead (switch productive planets to making influence for happiness).
Yep, exactly.
each species costs "# colonies of all Other species in the empire" x "# colonies of This species"*
Like TheSilentOne already said, I think that is too complicated, however:
so having 1 dominant species at 90% and 9 minor ones at 1.1% won't cause much problems... but having 10 species at 10% each would have big problems.
...this is a valid point, good catch, didn't think of that when coming up with my formula. Having only one tiny planet with another species than all your other colonies shouldn't increase your empire influence costs as much as when your pop is split 50/50.

Maybe factor in the number of species when calculating the colony based IP costs? The smaller a species pop in an empire is relative to the total pop (or number of colonies of a species relative to total number of colonies), the higher the IP costs for the colonies of that species. This will raise the IP costs for that one tiny colony with Ourbools drastically, but only for this one colony - the IP costs for the rest of your colonies will only marginally raise (assuming that you only have one other species in your empire).

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Re: Slowing down expansion, economics

#73 Post by Vezzra »

Geoff the Medio wrote:It would not be difficult to add a suitably-sized bonus to troop regeneration while in defensive focus. Or to add a "Rebel Suppression" focus that does something more specific for that purpose...
Of course. But in both cases the defence focus in its current form isn't sufficient. We'd either need to raise troop regeneration for the DF, or add a new focus like you suggested.
Assuming a planet is invaded by an empire its populace dislikes, and it starts with sufficiently low happiness to generate some rebel troops, the initial invasion will probably leave some extra invader troops on the planet, which the rebel troops would have to fight through over several turns.
This would be the most basic option, which probably wouldn't even require any additional coding. The player would have to calculate in advance how long it will take to get the happiness up to a level where rebel troops stop, and calculate the extra amount of troops he needs to drop during invasion accordingly.
These could be reinforced by using more troop ships on the planet (only allowed while a planet has active rebels on it, or is owned by another empire).
That would be another simple and straightforward solution, amending the above one. Disadvantage: once you've more large scale wars going on, it can get micromanagement heavy to keep track of how much troops you need to send to which recently invaded planets.
No loss of control of the planet back to its original empire would happen while there are the new owner's troops on it, so it could / would take several turns for anything like that to happen. During that time, the invader's influence effects could allow the planet's happiness to start increasing, eventually getting high enough enough to stop the rebel troops from being generated, or at least to fall low enough that whatever mechanism generates or transfers ground troops to the planet is providing more troops per turn than there are rebels.
Yes, that's a very reasonable basic approach, actually exactly what I had in mind too. I've been pondering pretty much the same ideas as you so far :D
To that end, there could also be a mechanism to transfer troops to a planet from other planets of the same empire, if the source and sink are supply-connected. This might be a focus setting.
Yep, I've been mulling over very similar ideas. The source could be specified by a focus setting or a building ("Troop Training Center" or somesuch), the sink by a focus setting (like the "Rebel Suppression" you suggested).

Or only have the source determined by a focus setting, which will distribute the troop generated on that source colony to all planets with rebel troops. There are several alternatives how such a mechanic can work.
Also, presumably a planet would need to be supply-connected to another empire to revolt and (re)join it. (Leaders might provide an exception to this, though...) So, keeping an armed fleet in the system with the rebellious conquest planet could prevent it from revolting. The planet would be effectively useless to the invader while it has uncontrolled rebels on it, but it couldn't revolt back if space-blockaded. For neutral planets that have never been owned by another empire, and wouldn't want to join any empire, they could be kept by keeping armed fleets over them. They would probably be mostly useless, until they could be made happy / non-rebellious, and could revolt back to neutral if left unguarded with rebel troops being generated in numbers enough to overcome the invader troops.
I don't know... the idea certainly has something, however, I also like the idea that a planet will revolt to independence/join another empire once the rebel troops defeat the regular garrison. Being able to keep a planet from actually breaking from your control just by having armed ships in the system sounds a bit too easy.

That said, being supply connected to another empire (the planet would like to join of course) could significantly increase the rebel troops.
-Made the populace like you enough that they are happy to be liberated by you (vs. invaded) and the planet doesn't generate rebel troops
That should definitely be an option, should be an influence project. I'd even go so far as to have an influence project that allows to take over a planet completely peacefully, without any troop operation at all. That would represent convincing a planetary government to join my empire by negotiations.

Advantage: species of planets thus taken over like my empire much more as when invaded (naturally), disadvantage: more costly and time-consuming.
-Bombard the planet and recolonize with your own populace, who aren't rebellious
Well, yeah, of course ;) Or invade and build CCs to depopulate the planet.

Of course, several of the above ideas will require to have species-empire relation mechanics in place to work. But once they are, they definitely should play a crucrial role in all those mechanics.

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Re: Slowing down expansion, economics

#74 Post by Vezzra »

MatGB wrote:Ergo, I'm happy to go with this and see, we can always (I assume) add influence costs to specific parts if we think it's necessary for balance.
Agreed, I think that's a good compromise for now.

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Re: Slowing down expansion, economics

#75 Post by Vezzra »

The Silent One wrote:To sum up the discussion up to this point...
Ok, this is slowly getting a bit hard to keep track of. Personally I'd prefer if we could put up some kind of "design document" with everything we've agreed on so far, what is still under consideration, what alternatives for things under consideration are on the table, etc. Preferably on the wiki - I made a proposal to reintroduce design documents for that purpose, see here.
We agree that the count of species in the empire should be reflected by an influence cost, but not exactly how.
See my suggestion regarding this in my post above.
I think this would promote circlish empires around the capitol, and not offer strategic choice. "Distance to nearest colony" would allow the player to expand in a main direction (without the need to relocate its capitol, which would be deadly for a circlish empire anyway). Only for valuable systems the player would deviate from his main direction. Or he would make the strategic decision to expand in two or three directions.
My main concerns with that approach are:
  • It basically only scales linearly with the size of the empire (assuming most colonies are more or less within a certain "range of distances" apart from each other), so you need to introduce an additional factor into the formula to achieve the desired exponential increase in empire influence costs. Which makes the whole formula more complex.
  • Basically, as soon as you have two systems sufficiently close to each other, the distance to the rest of your empire becomes completely irrelevant, as each of them counts as the "nearest" to the other. Then, to avoid exploits like colonizing an additional planet nearby a colony that is far removed from the rest of your empire to drastically cut down it's influence costs, we'll need to introduce something that counters that. Which will further complicate the formula (most likely significantly so, as I don't know how to do that in a simple and clear way).
  • It becomes more difficult/confusing for the player to understand/trace the influence costs for his empire, and to juggle it. Distance to the capitol can be comparatively easily seen on the map. Try to comprehend the influence costs for most of your systems by just glancing on the map when those costs depend on distance to nearest system. I expect that to be impossible once your empire has reached a certain size. Even more so if we take into account whatever we need to come up with to address the point above.
The second point is the most problematic one, that alone defeats the distance-to-nearest-colony approach IMO.

That the distance-to-capitol approach favors circlish empires is certainly something we need to keep in mind, but I don't see that as an only negative thing. Why not? I see that as a nice balance against empires which start in the corner/at the edge of a map. They have the strategic advantage of having fewer fronts they need to concentrate on, now they would have to deal with a disadvantage that comes with that (higher empire influence costs). Empires in the middle of the map can expand more evenly in all directions, so expand more "influence-cost-efficiently", but have to deal with the fact that they will find enemies all around.

If we get the numbers right, having not an exactly disc shaped empire shouldn't be that much of a disadvantage, and moving the capitol doesn't need to be something that kills your empire. You'd do that only if you expect to reduce your empire influence costs anyway. I don't see the need to do that if you want to continue a certain path of expansion as something negative, on the contrary - it offers an interesting decision the player must make. What's so bad about having to consider the option of moving your capitol in certain situations?

And if it turns out to be too restrictive to have a solely distance-to-capitol based system IP cost, we can introduce some elements that can help the player to alleviate the more dire situations. We can e.g. introduce "Sector Capital" buildings, and calculate the distance costs to the Imperial Palace or nearest Sector Captial, whichever is nearer. Or make the sector capital a focus setting.
Also, I would find it counter-intuitive to have to "pay" the full distance cost for each colony again; I've already "paid the supply cost" to the nearest system.
Because you perceive this costs differently than I do. I see those costs as an abstraction for the fact that the farther away a part of your empire is from the central seat of government, the more difficult it is to keep it in line/under control. Maybe it's more intuitive for you to imagine it so that the jumps from the nearest system (that is closer to the capitol) are more expensive than the jumps of that nearest system to the capitol (basically, each additional jump costs more). But in order to keep the formula simpler, we just base the costs on distance-to-capitol, which, for simple abstraction, should works well enough.

The concept that parts of an empire farther away from the central seat of government are more independent, more difficult to keep under control is actually quite common in SF stories. Think "outer rim" systems etc. ;)

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