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

[Joshua Boehme]

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.