[EM] Best IRV Tweak

[Kristofer Munsterhjelm]

On 07.07.2021 09:05, Daniel Carrera wrote:
> 
> On Tue, Jul 6, 2021 at 9:58 PM Susan Simmons
> <suzerainsimmons at outlook.com <mailto:suzerainsimmons at outlook.com>> wrote:
> 
>     It appears that this IRV Tweak satisfies independence from Smith
>     dominated alternatives.(ISDA)
> 
> 
> I'm really impressed. The method I was discussing a few days ago was not
> ISDA, was not independent of clones, and your method is easier to
> implement. Even for a fairly complex election anyone can quickly compute
> the winner with pencil and paper.I have no idea how to prove that a
> voting method satisfies ISDA but I've thought carefully about the
> independence of clones and I'm pretty sure I can confirm that yours is
> indeed independent of clones.
> 
> Your method naturally extends to one that produces a full ranking: The
> candidate that is removed first is the lowest rank, and so on. It seems
> to me like this ranking satisfies local independence from irrelevant
> alternatives. If you remove the lowestor highest ranked candidate, the
> order of the remaining candidates does not change.I'm not sure how to
> prove this because to me it looks self-evident, but it's weird because
> very few methods satisfy LIIA. The table on Wikipedia only lists Ranked
> Pairs and Kemeny-Young as satisfying LIIA.

Call the two first candidates to be eliminated X and Y (Y is eliminated
first), and the last one to be eliminated (i.e. the winner) A.

Suppose that Y's worst matchup is against A, but that X's worst matchup
is against someone else, and slightly worse than Y's next worst matchup.

Then eliminating A (the winner) may cause X to be eliminated first,
instead of Y. This is a violation of LIIA.

LIIA is just very hard to pass :-)

-km