February 21, 2022

# Arrow’s Impossibility Theorem

If there are 3 or more options, it’s impossible to produce a collective ‘best to worst’ ordering of choices while satisfying all of these intuitively desirable properties:

- Nondictatorship: The wishes of multiple voters should be taken into consideration.
- Pareto Efficiency: Unanimous individual preferences must be respected: If every voter prefers candidate A over candidate B, candidate A should win.
- Independence of Irrelevant Alternatives: If a choice is removed, then the others’ order should not change: If candidate A ranks ahead of candidate B, candidate A should still be ahead of candidate B, even if a third candidate, candidate C, is removed from participation.
- Unrestricted Domain: Voting must account for all individual preferences.
- Social Ordering: Each individual should be able to order the choices in any way and indicate ties.