Money is Power
In the Empire, political power is often connected to economic prosperity. There is perhaps no group or organization that has a greater effect on economic prosperity across state borders than the Merchant's Guild, the rumours being that many of the Elector themselves are on their payroll.
Using your gravitas, it may be possible to arrange 'favours' for the patrons of the Merchant's Guild - such as loosened regulations for or tax cuts, in addition to more personal furtherances - in return for their help in advancing your political standing, all at a considerable cost of course.
Arrange Favours: -1000 Prestige, +1 Imperial Authority
Do Nothing: +200 Prestige