Good question. I'm really not sure what LEP is. I know what it's supposed to be, but it fails miserably to achieve it's aims and it's removal is a good thing in every possible way. The best description would be that it's the ghost of bad ideas past.
To give some details:
LEP is a -0.2 happiness penalty applied by every planet in your empire, to every planet in your empire. So if you have 10 planets you get -2 happiness on every planet. This is applied before any % bonuses to approval, so even if you have +200000% happiness, once you have enough planets to cancel out your additive approval bonuses, you will end up with 0% approval. This is, of course, a completely insane implementation, which Paul indicated wasn't what he intended about 4 months ago and then did nothing to change.
But even if he had, using Approval to limit both 'tall' (high-pop) empires and 'wide' (many planet) empires simply doesn't work (Civ 5 was the first to implement the idea, and it didn't work there either). Here's the basic happiness equation:
((Base happiness + flat happiness bonuses - LEP) * Multiplier bonuses)/population = Happiness.
The problem with this is that the bit where happiness is divided by population is far more powerful than the flat negative, so you're always better off splitting the population over more planets. So, say I have 10 population, and my base happiness is 5:
If I have 1 planet, I have 4.8/10 = 48% happiness.
If I have 2 planets. each has 4.6/5 = 96% happiness.
If I have 3 planets, each has 3.3/4.4 = 100% happiness.
etc.
The entire happiness mechanic is set up to prevent you focusing too much production on a single build queue. That's what Happiness has ALWAYS been for in 4x games, all the way back to Civ 1. If you have a city/colony/whatever with a very high population, then they are less efficient than population spread across multiple build queues. This is a good mechanic, as it makes it harder to have 1 build queue that can produce anything it likes in 1 turn. It encourages the player to expand his empire into multiple weaker build queues.Unfortunately, given that the entire point of the approval mechanic is to encourage expansion, it is beyond insane to try and use the same mechanism to discourage expansion.
The mechanic used to discourage expansion in 4Xes has varied over the last twenty years. Initially, 4Xes used 'corruption', which simply made additional planets less effective after a certain arbitrary point. There were variations - some based corruption on the distance from the capital, some allowed you to eliminate corruption penalties based on governments etc. But corruption was ineffectual, since you could not completely eliminate output from a build queue; as a result, it was ALWAYS better to keep expanding, because even if a city/colony/whatever was reduced to producing 1 industry per turn, that was 1 industry you otherwise wouldn't have. The result is what Civ players called 'Infinite City Sprawl', or ICS.
Civ 4 changed this by using maintenance to punish the player for expanding. Every city added an exponential increase in maintenance costs (you can see similar things in a number of GC3 mods, including my own, and can mod the effect in yourself very easily). This was generally brutal for newer players, who often spent their first 4-5 games bankrupting themselves, but but had the advantage that a new colony needed to be supported financially until it could develop and begin turning a profit - and the amount of time needed for it to reach profit was higher for every new planet. Each new colony became an investment, and your empire could only support a limited number of fledgeling colonies at any time without running into financial trouble. This leads to a mechanic which allows the player to grow very big, but forces him to do so slowly - ideal for 4X gameplay.
In recent years, following Civ 5, many 4Xes have switched to using a global happiness modifier. This is less painful on new players, since they build few cities, develop them slowly and take a while to bump into the penalty. Unfortunately, once the player understands how to manipulate his production, global happiness modifiers do not discourage rapid expansion. If I keep my colonies small, I can have hundreds of them, and more colonies are inherently better than fewer because the most valuable resource in any 4X game isn't science, or gold, or iron or whatever - it's build queues. So it encourages the player to build as many colonies as quickly as he can and keep all of them severely under-developed.
This problem is further compounded by other bad design decisions - charging maintenance for buildings makes not developing cities more attractive (remember how high-level Civ 5 MP basically involved no-one ever building a building for many months after release). The penalties on happiness are pretty laughable; two of them have almost no discernible effect, and the two that do are pretty minor, particularly if you have very small undeveloped planets anyway; the free production from the colony capitals means they're equivalent to 5 free population on their own, and can comfortably build the colony up for you even if there's no population; coupled with the fact that a colony ship can successfully found a colony with 0.1 population on it, this makes churning out useless colonies easy and gives you a far greater return on investment than anything else that you can build in the game.
The problem has diminished a little with the introduction of maintenance on colony hubs. But that makes the point of LEP itself rather questionable; if the main thing keeping me from endlessly expanding is the maintenance cost rather than the happiness penalty, what's the point of the happiness penalty anymore? You could argue it's not to punish growth, but just to punish empires for being very big... but since the exact same penalties are applied if you build your population up too much, it also punishes you for staying small and building up the population of individual planets, so there's no way you can match a larger empire without suffering the exact same penalty, only worse. And since after you have about 30 planets, it simply ceases to be worth building happiness buildings, any 'wide' player who doesn't either mod LEP out or use the Patriotic trait so that it doesn't effect him will simply ignore happiness altogether and take the minor production hit.
So yeah, LEP can go die in a hole. It never did what it was meant to do, it was a bad design, poorly implemented, and it's purpose is already being fulfilled better by other mechanisms. It also breaks the AI (which couldn't hack it at all and ended up stopping colonization when it hit 0 approval) and because it didn't scale in any way at all, it broke larger map sizes because the player would almost inevitably trigger absurd amounts of it in the course of game play. There was extensive discussion about the problem on this forum about 4 months ago, eventually leading to more or less universal acknowledgement that it just didn't work and needed to be rethought from the ground up.
