Why ranked voting doesn’t work: Arrow’s Impossibility Theorem
We’ve been talking about election reform a lot. One of the methods mooted as an alternative to First-Past-The-Post is ‘Ranked’. You give each candidate a ranking of where you would vote them.
Today I learned about Arrow’s Impossibility Theorem. In a nutshell it says that if the goals are:
- 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 neither “dictator” nor “prophet“: no single voter possesses the power or the knowledge to always determine the group’s preference.
E.g. you cannot satisfy:
- Non-dictatorship: The preferences of an individual should not become the group ranking without considering the preferences of others.
- Individual Sovereignty: each individual should be able to order the choices in any way and indicate ties
- Unanimity: If every individual prefers one choice to another, then the group ranking should do the same
- Freedom From Irrelevant Alternatives: If a choice is removed, then the others’ order should not change
- Uniqueness of Group Rank: The method should yield the same result whenever applied to a set of preferences. The group ranking should be transitive.
I guess I now have another economist other than Adam Smith to quote now.