[EM] Are LIIA, majority, determinism, and neutrality incompatible?

[Joshua Boehme]

As a post-script, I realized at the last minute that you mentioned 
determinism in the subject. The fact that my counterexample relies on a 
distribution might actually be another piece of evidence in favor of 
your argument.


On 1/30/25 8:51 PM, Joshua Boehme wrote:
> 
> The centrifugal margins solutions to this election seem like a 
> reasonable counterexample to me.
> 
> These are distributions over potential orderings. Alternatively, you can 
> think of these as if the method sometimes returns tied orderings it was 
> indifferent between and throws the decision to the tiebreaking mechanism 
> (in other words, the tiebreaking becomes external to the method instead 
> of internal).
> 
> {A, B, C}: 50% A > C > B, 50% C > B > A
> {A, B}:    50% A > B,     50% B > A
> {A, C}:    50% A > C,     50% C > A
> {B, C}:    100% C > B
> 
> 
> Centrifugal margins satisfies majority and Smith (the latter in the 
> "successive Smith set" way that ranked pairs does). I'm not sure whether 
> or not it always satisfies LIIA, though.
> 
> 
> On 1/23/25 08:32, Kristofer Munsterhjelm wrote:
>  > Someone check my reasoning here, because I might have found out why 
> LIIA methods like ranked pairs are so intertwined with their tiebreakers.
>  >
>  > Suppose we have a method that passes majority and also LIIA. (It thus 
> has to pass Smith and ISDA.) Consider the following election:
>  >
>  > 4: A > B > C
>  > 5: A > C > B
>  > 1: B > A > C
>  > 4: B > C > A
>  > 1: C > A > B
>  > 5: C > B > A
>  >
>  > A ties both B and C pairwise, and C beats B: A=B, A=C, C>B.
> 
>