Arrow's Paradox

In voting systems, Arrow’s impossibility theorem, or Arrow’s paradox, demonstrates that no voting system based on ranked preferences can possibly meet a certain set of reasonable criteria when there are three or more options to choose from. These criteria are called unrestricted domain, non-imposition, non-dictatorship, monotonicity, and independence of irrelevant alternatives, and are defined below.

The theorem is named after economist Kenneth Arrow, who demonstrated the theorem in his Ph.D. thesis and popularized it in his 1951 book Social Choice and Individual Values. The original paper was entitled "A Difficulty in the Concept of Social Welfare" and can be found in The Journal of Political Economy, Volume 58, Issue 4 (August, 1950), pp. 328–346. Arrow was a co-recipient of the 1972 Nobel Prize in Economics.