[EM] Best IRV Tweak

[Daniel Carrera]

On Tue, Jul 6, 2021 at 9:58 PM Susan Simmons <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 lowest or 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.

I'm actually surprised that this isn't a well-known method already. You'd
think someone would have thought of it before.

Daniel.
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