Majority judgment over a convex candidate space

Most voting methods can only deal with a finite number of candidates. In practice, there are important voting applications where the candidate space is continuous. We describe a new voting method by extending the Majority Judgment voting and ranking method to handle a continuous candidate space which is modeled as a convex set. We characterize the structure of the winner determination problem and present a practical iterative voting procedure for finding a (or the) winner when voter preferences are unknown.