ABSTRACT
Condorcet's famous paradox captures some of these problems. If there are three individuals, where one prefers option x to option y to option z, the second prefers option y to option z to option x, and the third prefers option z to option x to option y, then there exist a majority for x against y, a majority for y against z, and a majority for z against x. This means that, if pairwise majority voting is the method for aggregating individual preferences into collective ones, or more grandly, for extracting 'the will of the people', then the resulting collective preferences can be cyclical and thus useless for reaching consistent collective outcomes.
