I mentioned this idea a while ago, and I'm not sure, I think it's even not mine originally, but I can't remember where I picked it up. I've been thinking about it for a while, and I'm very close to solving how it can actually be done even without any tweaks to the servers and rulesets.
The basics:
Every player runs a nation for a limited period of time. Then he, as a ruler, "dies", takes over some other nation, while his nation is taken over by someone else. What counts is the progress he has made during his rule.
The details:
After the game starts, the clock starts ticking. Let's say you have 20 turns (number can be discussed) to rule uninterrupted, but then the probability starts to increase that the next turn will be your last. Eventually the dice are cast and you're done with this nation. You sit on the bench waiting for the next ruler to "die" to take over his spot. Your previous nation is taken by the player who was sitting on the bench previously.
Variant:
All players switch nations at the same time.
The score:
I haven't checked full math, but as a first approximation this model sounds reasonable. For this, the in-game score must be known from the beginning. During the first segment, when you "die", your score is calculated and normalised for total score of all players. (If all players combined have score 200 and yours is 20, you hold 10%) During your second segment/rule, what counts is the difference between the Normalised Score at the beginning and the end of your rule. If you start your nation with 12% and end with 14%, 2% is added to your initial Normalised Score. So, in each segment, you gain or lose % depending on how you ruled.
The mechanics:
"Blank" players are created on LT.net. They can be given any names, maybe it's best to tie them to nations. Then standard, live human players are delegated into those nations. When the segment/rule period is over, the delegation is simply changed by the LT admin.
When to switch:
One model for the probability of transition could be 1% for turn 20-25, 2% for turn 25-30 and then the probability increases for 2% every turn. So, theoretically, a player can run his nation for a maximum of 80 days total, but it is most likely it will last maybe 40 days. (Not 50, probabilities multiply, they don't add.) Of course, this is only one model. Probabilities can be modeled according to anything that is agreed on. Of course, this is just the example model, anything else can be agreed.
As always, comments are welcome.