for most of the lords you must have a reputaion of at least 20 with them.
otherwise they reject to talk to you in private.
sometimes you will find lords that are VERY unhappy with ther current king and are willing to talk to you even when your reputation is at 0.
but it is still very hard to convince them convert into your kingdome.
i dont know whether its random or a "2 out auf 3" decission, but the lords have 3 "arguments" like military power, kingdom politics, other lords already in your kingdom and your "promise" you gave them.
yes i know that are 4 but they "choose" only 3 of them when you talk to them...
i noticed, that when 2 or even 3 of the 3 arguments are "good" (ie they like your point of view) they will convert to your faction.
otherwise they will reject it!
oh and your reputation to the lord also increases the chance that they will convert... but it does not garantee it.
i had a lord @75 reputation and he refused to convert to my kingdom.
it is VERY frustrating the first months after you founded your own kingdom. later on it is getting better because the more honor and reknown you gain the higher your reputation with other lords get without having to do 100000 quests again and again...
another trick/tipp for the beginning:
take a look at the "nobility table": http://strategywiki.org/wiki/Mount%26Blade/Companions
some heroes are nobles.
you can give fiefs to those noble heroes WITHOUT messing up your reputation with other lords not in your kingdom!
you can recruit those noble heroes and then make them to your vassal even if you have heroes in your team that dont like that "vassal hero".
this helps a lot to establish your own kingdom and defend the borders until you are able to convince other lords to join your faction
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