My findings were surprising. The choice of post-invasion resolutions had no effect on the cultural penalty percentage (in this case 50%), but occupation led to a lower loyalty percentage because the absolute number of the population resisting was higher than under extermination, understandably since taking the same percentage of a bigger number will result in a bigger number. Post-invasion resolution results on cultural penalty stayed true even after several turns, suggesting unrest does not have an effect on cultural penalty (since unrest will fall over the short run and if they were corrolated both would fall together).
The demolition of culturally foreign buildings alone has ZERO effect on cultural penalty, even after several turns. So if you demolish everything in the city, there will be no reduction in cultural penalty. Only with the construction of your own religious building will cultural penalty be reduced, in this case by 5%. Some have suggested that importing population from your region (i.e. peasant dumping) will reduce cultural penalty as the Julii city will have more people like yourself and thus the cultural penalty will fall. After the invasion, I went ahead and disbanded my entire army except the two generals and a unit of iberian infantry, infusing 1000 souls into the city. The impact of this population surge on the cultural penalty was ZERO, and interestingly enough a couple of turns later I had a riot in which 600 were killed. On a population of 6000 (5000 post invasion + 1000 Carthoginians) a death of 600 should reduce the cultural penalty by at least 10% right? The real result was that there was NO impact on the cultural penalty.
Given a time constraint (primarily sleep) I wasn't able to test the cultural penalty penalty in the long run (perhaps over time the population is replaced by Carthoginians?) I'll explore this matter further, perhaps in my older campaigns where I can see a fall/no change in cultural penalty over the long haul. So in the short run, just destroy the foreign religious building, build your own, and exterminate the population. Over the long run, ideally the cultural penalty will fall as the population is replaced with the dominant ethnic populace (your people). Or you can just garrison the city with 20 units of peasants and hope the trade income covers the upkeep cost (> [This message has been edited by ttnguyen05 (edited 03-21-2005 @ 02:23 AM).]