It is not just Chivalric governors who help with happiness. Dreadful governors give the same 5% bonus for each point of dread. Although it is is not happiness, it is "fear". In any case, the best governors are ones who have EITHER high chivalry or high dread. There is no advantage to having a 'neutral' governor (or general for that matter). Chivalric governors actually have a slight disadvantage in this particular case because they also give a +0.5% growth per point of chivalry, so the settlement will grow larger and become even more unruly.
It is VERY important to note, that when you first capture a settlement, it gets a +unrest 'bonus' (visible in city details) which will decrease happiness 10-40%. It disappears after a few turns but it can be a big hassle while it lasts. The unrest depends on what action you take when you defeat the city. Occupation gives largest unrest, Sack gives medium, and Exterminate gives the lowest. Equally likely, it could be that the unrest depends on the population size, in which case Exterminate gives the lowest unrest 'bonus' simply because you only have 25% of the population left. In any case the outcome is the same in terms of happiness: Exterminated cities are easier to keep under control. I have never taken the time to figure out which one is the triggering cause.
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