Answer:
A common practiced used in large courts is the chance of a judge and defense attorneys allowing each clients case to be heard by a judge best perceived as most favorable for their particular cases.
I would think the author is speaking about an political event in which people vote.
Queen Anne's War, (1702–13), second in a series of wars fought between Great Britain and France in North America for control of the continent. It was contemporaneous with the War of the Spanish Succession in Europe.