Arrow's Impossibility Theorem
A theorem that illustrates the difficulty of designing ways of aggregating preferences
(Dwayne Benjamin, PPG 1002)
Arrow’s impossibility theorem states that if a social decision mechanism satisfies the following three properties, then it must be a dictatorship:
- Given any set of complete, reflexive, and transitive individual preferences, the social decision mechanism should result in social preferences that satisfy the same properties.
- If everyone prefers alternative x to alternative y, then the social preferences should rank x ahead of y.
- The preferences between x and y should depend only on how people rank x versus y, and not on how they rank other alternatives.
Arrow’s theorem shows us the difficulty of designing ways of aggregating preferences. Despite the fact that all three of these conditions are plausible and desirable features of a social decision making mechanism, together they are incompatible with democracy. Arrow’s theorem illustrates the fact that there is no perfect way to “aggregate” individual preferences to make one social preference. In order to find a way to form social preferences, we will have to give up at least one of the properties of a social decision mechanism described in Arrow’s theorem.