Doesn't consistency imply participation?
I can't see how participation and consistency are different. Participation says that adding extra votes that all rank A>B shouldn't cause the social choice function to switch from A>B to B>A. Consistency says adding the votes from a constituency with A>B shouldn't cause the function to switch from A>B to B>A. Unless we're not assuming Pareto, doesn't that mean consistency implies participation? Closed Limelike Curves (talk) 03:17, 8 February 2024 (UTC)
- There seem to be two types of consistency, and we should clear up which is meant. Wikipedia says that consistency means that whenever A>B in both districts, A>B in the two combined. But this page only says that if A wins in both separately, then A should win the combined election, i.e. it says nothing about lower preferences.
- If consistency is about all pairwise preferences, then as far as I can see, you're right that consistency implies participation. But if it's only winners, then it's possible for a method to fail lower preference participation yet pass consistency. E.g. an added ballot of the type B>A>C to an election where A is already winning could harm A even though the method passes (winner) consistency.
- In any case, participation is different than consistency in the other direction. You can have participation without consistency. Kristomun (talk) 22:02, 14 February 2024 (UTC)