Deliberation and Agreement

TL;DR: For example, the authors showed that pairwise majority voting fails to generate a consistent "popular will" in a group of voters with radically different preferences, i.e., a majority preference for one option over another.

Abstract: A central problem of democracy is decision making among individuals with conflicting preferences or judgments. Democracy is sometimes thought to be about finding ‘the will of the people’, but if different individuals have radically different ‘wills’, it may be hard to extract from these ‘individual wills’ a consistent ‘popular will’. To illustrate, imagine a group of people in which a third prefers option x to option y to option z, a second third prefers option y to option z to option x, and the last third prefers option z to option x to option y. Then a majority prefers x to y, a majority prefers y to z, and a majority prefers z to x — a ‘cyclical’ majority preference. So the plausible democratic procedure of pairwise majority voting fails to generate a consistent ‘popular will’ here. This is Condorcet’s paradox.