The simple process of voting leads to surprisingly counterintuitive paradoxes. For example, if three people vote for three candidates, giving the rankings A, B, C; B, C, A; and C, A, B. A majority prefers A to B, B to C, but also C to A! It is also possible to conduct a secret ballot even if the votes are sent in to a central polling station (Lipton and Widgerson, Honsberger 1985).

Arrow's paradox | ballot problem | cake cutting | May's theorem | quota system | social choice theory