There are several challenging parts of this:
1) Determining what behavior to be rewarded
2) Determining how to measure that behavior
3) Devising bonuses to apply to reward it
First, what do you consider to be proper behavior? Someone who sits in their capital not doing any game mechanics actions can still be a great player and asset to the realm with the sum of their knowledge, contacts, diplomatic skills, letters, rps, etc. Someone who follows every order and keeps their region in top notch condition can still be someone who contributes little or nothing to the game. Ask several people about a specific character's behavior, and you'll get several different answers. A lot of this comes down to individual play style preferences. Causing chaos may be fun for some people, but does it provide the largest amount of fun across the player base as a whole?
A way to narrow this down may be to focus on things related to position holders. It's not really a big deal if a character holding no position at all is a hermit who squats the capital. A duke/margrave/marshal who does that is causing a lot of missed opportunities.
Second, how do you measure it? The real challenge comes in making meaningful measurements that filter out the noise. You can't just count the number of messages sent. As Anaris says, copy/pasting reports of police/civil/court work is meaningless, or even counter-productive. Message length is easily spoofed by copy/pasting long amounts of text, like those people that copy/paste their unit stats. Or people that frequently quote other people's messages in their replies, or forward many messages between groups.
Third, how do you apply these bonuses? The bonuses should apply to things directly associated to the character being rewarded, and preferably related to the behavior being measured. Obvious things include their unit and their region. For higher level characters, the bonus can be applied more widely, perhaps to duchy and even realm.
One possibility: Fighting battles is usually considered a good thing. So why not do some sort of Glory for characters? Like the old stat we used to have for realms, but applied at the character level.
* A region whose lord has a high glory could have a morale boost.
* Every time a lord is involved in a battle, their region gets a loyalty boost as well.
* Perhaps the above two bonuses can be applied at the duchy level for dukes, at reduced rates.
* Units led by nobles with high glory could have training and morale bonuses.
* Perhaps the above bonus can be applied to entire armies led by high glory marshals, at reduced rates.
* Perhaps this could be extended to entire realms for high glory generals, at further reduced rates.
* This metric should not reward victory. We don't want to encourage ganging up on realms, or cause a positive feedback loop. We're rewarding participation.
* Members of the hierarchy who have high glory, and participate in battles could provide temporary bonuses to the troops of their realm for that battle. A high glory ruler could provide a morale bonus. A high glory general could provide a training bonus. Maybe the same for the marshal/VM. Higher glory gives higher bonuses.
This obviously rewards characters who participate in battles, and not things like religion or diplomacy. But then we are extremely war-focused.
Any other ideas that could be used to reward other desirable behavior, that is not necessarily directly derived from combat?