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

[Kristofer Munsterhjelm]

On 2025-01-31 02:56, Joshua Boehme wrote:
> 
> 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.

Yes; my hunch is that the problem arises from ties at the top or bottom 
adding too many constraints, and they can't all be satisfied.

E.g. having A=B>C>D means that, in addition to the bottom-end removal of 
D, we must preserve the order both when A is removed and when B is 
removed. But if the tie is broken beforehand, it only needs to stay 
consistent with removing one of the candidates on the top end, not both 
at once.

This could have more serious theoretical implications based on what's 
possible to do with tiebreakers. For instance, I don't know if there 
exists a summable cloneproof LIIA tiebreaker. The "random voter 
hierarchy" tiebreaker is, as far as I know, not summable. Strictly 
speaking, that means full ranked pairs isn't summable either (at least 
when using RVH).

In practice, I don't think it's going to cause too much trouble for LIIA 
methods, since large elections would probably have distinct counts for 
every pairwise contest, so they'll be decisive. But it's a bit annoying.

It would be nice to have proof of whether a LIIA cloneproof tiebreaker 
could be constructed, but I don't know where I would begin :-)

-km