Alright, here are a bunch of details on how the notable power system works (as of beta 1.5.1) just to shed some light on it.
First of all, there is a universal power decay modifier for all notables each day depending on current power level. The more powerful the notable, the greater the daily decay. The lower bound of this decay is 100 power. Under 100 power they will gain power each day. (This is actually inaccurate. They changed it so it only affects notables with > 100 power, so there is no gain).
The exact equation for this decay is: [-1 x ((hero.Power - 100) / 500)] while notable power is > 100.
Some notable types also have a separate baseline daily power gain to counteract the daily decay, and some have additional losses. Merchants get +0.3 power per day. Both types of village notables get +0.1. Gang leaders actually lose an extra -0.6 power per day. Artisans also lose an extra -1 per day (presumably because they own the Artisan workshop).
There are also a variety of other ways that notables can gain or lose power. The most familiar will probably be the flat power gains/losses as a reward/consequence of completing or failing quests. On top of this, if a notable has certain unsolved issues/quests they will also lose 1 power each day the quest remains unsolved (this includes the time while companions are sent on the mission, so there are extra drawbacks to sending companions).
Npc lords can also "complete" quests under certain conditions by entering a settlement that has an outstanding issue. The npc must be the leader of the clan that owns the settlement. Each time they enter, they have a 10% chance of completing a random quest in towns and villages, and a 30% chance in villages (edit: hotfix changed the village chance). I don't believe they receive any rewards for this. Edit: Issues also expire after some time if the player doesn't accept them. The time to expire varies depending on the issue.
Notables will gain 1 power each day if they are a supporter of the clan who owns the settlement (check their tooltip). This effect is huge, and is enough to overcome the daily decay until power climbs very high. This effect is what is responsible for certain notables having more than 500 power. Village notables that don't get this boost are usually the ones who quickly disappear.
If a notable has gold in excess of 10150 at the end of the day, the amount of gold over 10k will be converted into power according to the equation [(hero.Gold - 10000) / 150] and their gold will be set back to 10k. If a notable has less than 4850 gold at the end of the day, gold is set back to 5k, and power is removed according to the equation [(5000 - hero.Gold) / 150]. Workshops and caravans are notables' main sources of income.
Merchant notables can only own 1 caravan at a time, which will bring in money for them (which then gets converted into power). If their caravan is destroyed, they will lose a flat 30 power upon creating a new one. They also always pay the wages for the caravan out of pocket.
Workshops can be owned by any of the urban notables (except Artisans), and will gain them power through converted gold. If a workshop's capital ever runs out, a notable will declare bankruptcy, and the workshop is sold to another notable and its type is randomly changed. This is rare, but does happen.
Gang leaders own properties called "common areas" (e.g. waterfront, clearing). They earn 0.1 power per day for each owned common area. Gang leaders can lose control of common areas in behind-the-scenes "alley fights." Owing a common area also earns a gang leader 30 gold per day per area. I'd have to double check, but I think they pay wages for thugs occupying the common area (edit: nope). These common areas also have "productions" of their own (such as extortion), but I'd have to look into it more to see if it produces any other income (edit: They don't generate income as of right now. The production is cleared each week without having any effect). There is a lot of interesting stuff associated with criminal enterprises in the code though.
Notables in a village will each lose 5 power when their village gets fully raided.
As noted by others above, notables have a chance of disappearing each day if they are below 100 power and do not own any workshops, caravans, or common areas. This chance increases the lower their power falls. The % chance is determined by the equation [((100 - hero.Power) / 100) * 2].
The whole point of the system is that individual notables will equalize at certain power levels depending on their specific circumstances. My guess as to why notables can disappear is to get rid of "failed" notables that don't have the right conditions to survive, and to give the player some ability to manipulate a settlement's notables. It definitely still needs additional balancing.
So with all that in mind, what are some other conditions that you guys can think of that should cause notables to gain or lose power without being too redundant? For instance, currently the gold that is used to recruit troops just vanishes, but maybe it should go to the notable instead to boost the power of notables that are recruited from frequently (might be too powerful).
