The Arrow paradox is the oldest and best-known paradox to do with voting. The American economist Kenneth Arrow (1921–2017) showed that it is impossible to devise a perfect democratic voting system. In his book Social Choice and Individual Values,1 Arrow identified five conditions that are universally regarded as essential for any system in which social decisions are based on individual voting preferences. The Arrow paradox is that these five conditions are logically inconsistent: under certain conditions, at least one of the essential conditions will be violated.
1. Arrow, Kenneth. Social Choice and Individual Values. New York: John Wiley & Sons, 1951.