More information on the Politics system is available here:
http://leaguefactions.net/politics-system/A faction can select up to one petition to support or oppose. They roll against Difficulty 100. Then, take half of the margin of success (if any) and add to / subtract from the target’s roll as appropriate. If the target’s roll succeeds despite their opposition, or fails despite their support, 5 Favor is lost.
Only options above 50% will be picked, if multiple ones are above 50%, then the highest percentage wins. You may only support or oppose one thing.