# Arrow's impossibility theorem facts for kids

**Arrow's impossibility theorem**, **Arrow's theorem**, or **Arrow's paradox** is a statement from social choice theory, named after economist Kenneth Arrow, who first described it in 1950: Suppose there is a vote, and voters have at least three different options to choose from. Each voter will then rank the options according to his or her preference. Arrow said, that in such a case, there is no way to convert these rankings into a community-wide complete and transitive ranking while also meeting certain criteria.

Arrow demonstrated the theorem in his doctoral thesis. He popularized it in his 1951 book *Social Choice and Individual Values*. The original paper was titled "A Difficulty in the Concept of Social Welfare".

In short, the theorem states that no rank-order electoral system can be designed that always satisfies these three "fairness" criteria:

- If every voter prefers alternative X over alternative Y, then the group prefers X over Y.
- If every voter's preference between X and Y remains unchanged, then the group's preference between X and Y will also remain unchanged (even if voters' preferences between other pairs like X and Z, Y and Z, or Z and W change).
- There is no "dictator": no single voter possesses the power to always determine the group's preference.

*Kiddle Encyclopedia.*