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.

that you cannot achieve this with ranking. And, there’s a nobel prize, a thesis and a book behind it so it must be true!

E.g. you cannot satisfy:

  1. Non-dictatorship: The preferences of an individual should not become the group ranking without considering the preferences of others.
  2. Individual Sovereignty: each individual should be able to order the choices in any way and indicate ties
  3. Unanimity: If every individual prefers one choice to another, then the group ranking should do the same
  4. Freedom From Irrelevant Alternatives: If a choice is removed, then the others’ order should not change
  5. 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.






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