[EM] Easy fix to Alaska's ranked-choice voting

[Richard, the VoteFair guy]

On 11/9/2022 12:05 AM, Forest Simmons wrote:

 > A candidate is uncovered iff it has a beatpath of
 > only two steps to each candidate (if any) that beats it.

Should the "only two steps" be interpreted as "two or fewer steps?" or 
"two or more steps?" or "exactly two steps?"

I'm still trying to understand the "uncovered" (and "covered") concept. 
Especially, what is its relationship to the Smith set?

Thanks,

Richard Fobes


On 11/9/2022 12:05 AM, Forest Simmons wrote:
> In this context the most relevant question is what do we mean by 
> "uncovered", since that's the word used in the method definition ...
> 
> Repeatedly eliminate the (remaining) candidate with fewest votes until 
> there remains only one uncovered candidate to elect.
> 
> No need to know what covering means, although you can figure it out 
> indirectly from the definition of "uncovered:"
> 
> A candidate is uncovered iff it has a beatpath of only two steps to each 
> candidate (if any) that beats it.
> 
> Any candidate X who complains that they should have won because they 
> beat the winner W pairwise will get this truthful and obviously relevant 
> rejoinder:
> 
> When you were eliminated, you had fewer transferred votes than I.
> 
> I fact, I beat every candidate pairwise that was not already eliminated 
> (like you) on the basis of two few (transferred) votes.
> 
> It is very easy to discern if some candidate X is uncovered:
> 
> Just check each candidate Y that beats it (X) to see if it has a two 
> step beatpath via some Z, back to Y:
> 
> X beats Z beats Y
> 
> Only Smith candidates can be uncovered because only Smith candidates 
> have beatpaths back to the candidates that beat them. So the candidates 
> you have to check are the Smith candidates ... at most three, and rarely 
> more than one, in a public election.
> 
> If you want, you can run IRV all the way through ... then if the IRV 
> winner is uncovered, you are done. If not, back up until you cone to an 
> uncovered candidate ... that's your winner!
> 
> It's just a matter of doing regular IRV, and backing up (if necessary) 
> until you get to an uncovered candidate.
> 
> Forest
> 
> 
> On Tue, Nov 8, 2022, 11:18 AM Kristofer Munsterhjelm 
> <km_elmet at t-online.de <mailto:km_elmet at t-online.de>> wrote:
> 
>     On 08.11.2022 18:02, Richard, the VoteFair guy wrote:
>      > Forest, what do you mean by "covered"?  Is there a Wikipedia or
>      > Electowiki article (or section of an article) that explains it? 
>     Or is
>      > there a dictionary reference you can point to?
>      >
>      > Yes, you've used the words "covered" and "uncovered" many times
>     but I
>      > don't recall ever seeing a clear explanation of what you mean.  I
>      > presume it involves pairwise counts, but that's as far as I can
>     guess.
> 
>     The short answer is: A covers B if A pairwise beats everybody B
>     pairwise
>     beats and then some.
> 
>     An uncovered candidate is someone who is not covered by anyone else.
> 
>     This definition works when there are no pairwise ties. Things get
>     trickier with pairwise ties, as I found out when generalizing Friendly
>     Cover.
> 
>     -km
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