Constructing Majority Paths Between Arbitrary Points: General Methods of Solution for Quasi-Concave Preferences

A series of recent articles has established that in continuous alternative spaces where voter preferences are representable by continuous utility functions, there generally exist majority paths between any two points in the space. In this paper, the problem of constructing such paths is dealt with. It is shown that if the dimensionality of the underlying alternative space is at least three, the problem can be decomposed into a series of smaller, limited horizon problems. These smaller problems can then be formulated as several independent convex programming problems, which could be solved by standard methods.