Arrow's Impossibility Theorem

What is 'Arrow's Impossibility Theorem'

Arrow's impossibility theorem is a social-choice paradox illustrating the impossibility of having an ideal voting structure that is reflective of specific fairness criteria, such as Pareto efficiency. Arrow's impossibility theorem states that a clear order of preferences cannot be determined while adhering to mandatory principles of fair voting procedures.

BREAKING DOWN 'Arrow's Impossibility Theorem'

For example, the following shows the type of problem typical of an election. Consider the following example, where voters are asked to rank their preference of candidates A, B and C:

• 45 votes A > B > C (45 people prefer A over B and prefer B over C)
• 40 votes B > C > A (40 people prefer B over C and prefer C over A)
• 30 votes C > A > B (30 people prefer C over A and prefer A over B)

Candidate A has the most votes, so he/she would be the winner. However, if B was not running, C would be the winner, as more people prefer C over A. (A would have 45 votes and C would have 70). This result is a demonstration of Arrow's theorem.

Who Developed the Theorem?

Kenneth J. Arrow (1921-2017) was an American economist who had a long teaching career at Harvard University and Stanford University. Arrow's impossibility theorem, published in 1950, earned him a Nobel Prize in Economics in 1972.