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In every characters data, you can see his/her conviction in the faction he/she belongs (a number in brackets). I think that certain titles can shift their allegiance (eg "tribune of the soldiers" to the military).
What DesertSnow said, except as of 2.1 minor titles no longer give conviction by themselves; they only give conviction for that job if the character had it as an objective.
For example, a character with the ambition to be a Military Tribune gets +2 Military Conviction if he is given that title. A character wanting to be a Legate gets +5, etc.