I already explained why in a previous post, though the quotes were screwed up. I do wish this forum just defaulted to HTML rather than this horrible word interface. Anyway:

This was a central element in your proposed changes to LEP. There is a very, very basic logical error in this calculation.

And limiting military and colony expansion through maintenance isn't bad in any way, means shape or form.

Firstly, the game already does it - maintenance is charged on buildings as well as ships. Presently, maintenance is punishing 'Tall' empires, in that you pay more maintenance the more buildings you have - it's another of the many reasons I've outlined elsewhere why tall empires are punished in multiple ways while wide empires aren't punished at all, and is therefore another example of why using global stats to limit local problems and visa versa doesn't actually work very well.

Secondly, military size and number of colonies are both global measures, so the central problem of approval-based LEP doesn't apply - it's a false analogy.  

Thirdly, your 'no sacrifices should be made' argument is completely inconsistent with the aim of slowing down expansion. The only way to incentivize a player to not always expand is to make it a sacrifice to do so - even if that sacrifice is an opportunity cost. And this is simply an opportunity cost, you can't build a ship AND have your 30th completely under-developed colony, you have to pick. Once you've developed a few of your core worlds as econ, THEN you can have both - comfortably (unlike the present maintenance system, where you can either have a new planet and a new ship OR build up the planet). 

In short, this 'unacceptable military cost' line of your argument is simply absurd, and doesn't hold up even in the face of an improved AI that actually builds ships (which my mod also has). You are either wildly overestimating the impact that maintenance has (for most empires, it's actually lower for a well-developed planet), or have a deeply flawed understanding of basic game theory.

As to your other points:

1. The fact LEP doesn't do what it's supposed to do doesn't necessarily change the intent. The intent also doesn't mean it can actually do it, though. You want to change approval to a global stat in order to achieve it, which is downright convoluted even without the broken maths.

2. Merely because the effect of approval does the right thing does not mean that the mechanic of approval is perfectly suited. The mechanics of approval are set up to prevent individual planets getting too big, and so aren't remotely suited to it, which is why even those who support the effect think it's presently broken.

3. is basically irrelevant to the difference between maintenance and LEP, given it's only there to make up for LEP's failure.

4. I covered above.

and 4 number 2. Culture is entirely effected by economy when you actually need to devote increasing numbers of planets to cash. Every market center you have to build is a cultural center you now can't build. This directly impacts on passive cultural growth. If you have 15 planets, you're paying out 6 cash per colony (90 total) and can basically have 1 econ world. If you have 50 planets, you're paying out 13 gold per colony (650 total), and need nearly 7 times as many cash planets. Increasing the % of the empire which must be dedicated to cash directly reduces manufacturing, research, influence, hell, everything which you can use a building to produce. It is, once again, a matter of making the player pick between opportunities.

In short, most of the arguments you're putting forward are actually just a question of finding the right balance for the mechanic - unlikely LEP, which is a matter of the mechanic being unsuitable for the purpose it's being put to and therefore no amount of balance work will help, short of a complete redesign (which will, undoubtedly, ruin it's use for restricting 'tall' empires). A good feature for a mechanic for slowing growth is one where you will overcome it as the game progresses; the player gets a sense of achievement from overcoming each obstacle. A really bad feature for one is having to go back and re-assign land on all your existing planets to counter a stacking penalty; it adds lots of unfun micromanagement. Maintenance has the former, while approval has the latter.

I made a few tests modding morale curves.

I attempted keeping the LEP as it is now but modifying the morale curves reducing bonuses (restricting them to really high approval levels) and increasing maluses on an inmense Galaxy with abundant habs and 6 civs, and soaked until around turn 60, pausing every 5 or so turns to check all the colonies in god mode (I couldn't get beyond turn 80 I think with all the soak/start/stop cycles). I only used base civs and a custom I built (with no morale or LEP immunity traits)

I modded raw production and growth.

The curves had a strong malus below 40%, with a sharp cut-off below 10%. Bonuses were neutralized between 40 and 60% and only kicked in above 80% (not beyond the current maximum level)

What I found:

a ) Modifying the morale curves to increase the malus will not work unless you heavily penalize anything below 100% at higher dificulty levels :

At higher dificulty levels the AIs get a massive morale bonus that neutralizes almost all penalties. At that level, human players will get almost every time massive negative morale malus at which point building (probably rush buying) lots of morale buildings is required just to get some production. That makes almost all the planets not worthwhile (planets below class 12 are effectively not usable) and the AI still has "level" bonuses

b ) at regular difficulties (AIs without morale bonuses) the AIs just don't know what it is happening and any player building enough morale and researching the right techs will squash the AIs solely because the AIs will get colonies producing less tan 5 hammers/beakers once the morale malus kicks in.

c ) The changes on growth rate were really really massive. Some civs just stopped growing at some point (ok, growing at a really crawling pace). Around the time the AIs get to a 6-7 colony count most colonies had a nominal 2-3 pop with no growth whatsoever (and almost no production). I took over my civ and fixed the issues (it took some time but it was an easy, but boring, thing to do), the AIs just kept doing the same they would do normally very slowly (I ended the game around turn 70 with no clear indication the AI would do something to fix their morale problem)

Unfortunately all three cases make the game extremely boring: colonize, rush build 3 or 4 morale buildings (depending on bonus features) research morale techs (flat bonus specializations), upgrade the morale buildings 1 or 2 times (using rush buy) just to get to around 60% morale only to get just a slight bonus (or a reduced manageable malus)...not fun (and time consuming). Add the AI inability to counter the malus to actually do something useful...

It is also noteworthy that non-organics civs will not get the growth penalties (or at least I haven't figured it out how they work for them), but the prod penalty did affect them.

I tried a lot of curves (softening effects, adjusting maluses), but it seems the AI does not address the morale issue of having a malus (for instance Kona was producing just 0.6 hammers with a 25% morale [-60% production]) and the AI just tried to build more colonies, more factories and not a single AI did anything except the altarians (since they have their morale trait that neutralized the malus) and the ones that shall be not be named with their LEP negation trait.

In the end, I think 5 things need to happen:

a ) The moral malus should be harsh, adjusting the LEP factor perhaps. The AI needs to be modified to account for this

b ) The LEP should be size aware (hab planet count)

c ) Colony cost should be implemented, tourism should be affected

d ) Research should be affected by bad morale (I didn't find a morale/research curve to play with and the raw prod malus didn't affect much my research rate [that was another test I tried with 80 colonies with all colonies on 0% morale I was able to research my way out with adding 2 or 3 morale buildings])

e ) The patriotic trait needs to be changed (idea: multiply LEP by 0.25)

It's been kinda funny watching this debate evolve over the past couple of weeks and half a dozen threads, tbh.

Initially, we were in two camps - the 'LEP is broken' camp and the 'LEP is fine' camp. Those who played on larger maps mostly fell into the first group, those playing on smaller maps into the second. The broken group proposed things like changing how LEP was applied, or adding a map size check, and the fine group said these things were not required.

Over time, the 'LEP is fine' camp has more or less totally disappeared; everyone in it has now moved over to saying LEP is broken and needs adjustments of the kind the brokenites were originally asking for. But those who were in the 'LEP is broken' camp have now largely moved on to 'LEP cannot be fixed and should be outright replaced'. Many of us tried modding in the original proposed fixes and found them ineffective; the general proposals which remain for repairing it are now massive code changes requiring additional mechanics to be defined, drastic schema alterations, and wild conjectures on what 'might' work better. Increasingly, modders are either just flat-out removing LEP, or replacing it with other methods. Even those defending approval-based LEP are now largely only doing so because they want to keep the approval effect, rather than how the mechanic works, while more and more people are coming round to the idea that maintenance works better - even those who were originally in the 'LEP is fine' camp.

The community as a whole is, slowly but surely, becoming increasingly hostile to LEP. We've moved from debating whether it's broken at all to debating whether it's fixable at all. I wouldn't be much surprised if, three months down the line, we're all just debating what it should be completely replaced with, as the increasingly drastic attempts to keep the creaking wreckage of LEP going fail one after another.

While I am fine with continued discussions about LEP using morale, to me maintenance does seem like a more elegant mechanic:

1) Maintenance is already a global bonus/penalty. Morale could be made such but would take more work and require gameplay changes. Maintenance is ready to go.

2) Increases the importance of economy buildings/bonuses. Common feedback is that money in the game is not important enough, and as such an entire section of the infrastructure tree (economy) is mostly ignored. This change automatically fixes that problem....at least at a balk level, further refinement may be necessary for balance.

3) It works. Maintenance ultimately puts a hard stop on expansion without infrastructure. At some point, you have to stop and build up economy or your empire will not function. With approval as is, you could have an empire at 0% approval that is still functional.

Now to me, maintenance only has a few issues:

1) Its more "common". Aka you see it in other 4x games more often, so its one less way the game differentiates itself.

2) Its less newbie friendly. A newbie player could put themselves in a permanent economic hole if they are not a little bit aware of building economy. With approval that is not possible.

3) Its more exponential. Economy can grow exponentially with later game building multipliers and higher population. This would theoretically need to be countered with an exponential penalty to expansion....and that can be tricky to balance (though not impossible by any stretch). This would be a great area to adjust by game difficulty if it at possible. Beginner difficultly, very little maintenance growth. Highest difficulties, a lot more.

So while maintenance has a few issues, I think overall its a superior model to approval.

To an extent, I agree; we're never really looking to make, say, a 5-planet empire equal in power to a 500-planet empire, and I wouldn't want to. If you're a third-rate power, then you should be third-rate.

But I think there is an point where you can say that a 'tall' 25-planet empire can be made competitive with a 50-planet Wide empire. This was something Civ 4 did very well. ICS was basically eliminated by the maintenance mechanics, because wider empires ended up paying much higher maintenance per active build queue; this in turn forced them to turn a larger % of their empire to wealth production just to get the same outcome they had before adding the new city. The size a new city had to reach to break-even increased over time (where as, under the current LEP mechanics of GC3, the smaller the new colony is, the more likely it is to pay for itself - as you add buildings and population, approval goes down and maintenance cost increases).

This is largely achieved through diminishing returns. At present, there is no effective diminishing return on planets. Every new planet is worth 1 planet. Approval attempts to introduce one, but the diminishing return will eventually cap-out and thereby ceases to work - when you have 0% approval and can no longer move from that point, there is no longer any reason to stop colonizing. The mechanic effectively obsoletes itself, but does not obsolete expansion.

Maintenance is an effective a diminishing return - while you still eventually cap out, the cap works the other way. You eventually reach a point where no new planet is worth colonizing, because even if it's entirely dedicated to wealth it won't pay for itself. The mechanic obsoletes expansion rather than obsoleting itself, and the point where expansion is obsolete increases over time. 

Basically, I want to know that an empire can be roughly as effective as another empire which has twice as many planets. If they have more than twice as many as you, yes, you should be weaker. But presently, you may as well end any MP game the moment the last empty planet is colonized, because the largest empire has reached an insurmountable superiority. He has no serious disadvantage compared to an opponent half his size, and hundreds of advantages. Maintenance not only provides this key levelling device, it also introduces the slowdown effect on expansion, too. 

As to Stalker's 3 points:

1) There's a good reason why maintenance is commonly used - it works.

2) If it's correctly balanced against growth, then any such pitfalls can be largely countered through natural population expansion - I've seen quite a few 'AI recessions' in my test games, where one AI or another will over-expand early on and throw itself into enormous debt. It's economy will then automatically go 100%-econ until it has a positive balance again; they will, eventually, grow themselves out of recessions. If they're forced to sit tight for 20-30 turns, then so be it.

and 3) It turns out, 0.2/colony/colony is actually pretty well balanced anyway; as to the fact you could add this into the difficulty settings, well, that's almost a feature

Change LEP to -0.2 Money/Planet and it should solve your concern for the very very large maps.  

I figured out a way to do this.

You'd need to convert one of the existing Strategic Resources into a 'food' SR. Then you make farm buildings produce this instead of adding population. Then you add another building (housing) which consumes the food resource and adds population cap to the planet it's built on.

If we can figure out how to ADD a resource, rather than replacing one of the existing ones, then you wouldn't even need to sacrifice the other resource.

Well said.  I'd as well be most interested to hear the dev's plans, I have confidence that they have understood the problem for quite a while, but they are following their original schedule of correcting bugs and providing mission critical new features in 1.1.  Perhaps we will see something done by 1.2 or 1.3.  But hearing the details of their plan prior to 1.2 will be most re-assuring to the community.  

Do you prefer wide or tall? Would you like it slow or fast? 

I'd tried to do that before, but didn't want to sacrifice a resource so I tried to implement it another way (production/consumption of trade licenses). It makes sense because you can either sell the food internationally or move it domestically. If as an empire you've got additional trading licenses, you can import food in this fashion as well by building the import center.