[EM] Notes on a few Later-no-harm methods

[Kristofer Munsterhjelm]

On 22.05.2022 22:24, Richard Lung wrote:
> 
> BSTV does not handle equal preferences ("ilections") on principle. I
> just don't want to go there for the purpose of elections, (choosing-out).
> 
> BSTV handles both all preferences filled and missing rankings.
> 
> Help and Harm are both made possible to the Election count by the
> Exclusion count, but they are based on the preference information, and
> not on some assumption or guess about voters wishes. Thus a candidate
> who does not land an exclusion quota is helped to consolidate the
> election quota. Whereas an exclusion quota (with surplus exclusions)
> will harm the candidates election prospects.

Later-no-harm is defined like this for single-winner:

Suppose that candidate A wins. Then a voter who provides an incomplete
ballot (e.g. A>B) can not make A lose by filling in the remaining ranks
(below those already provided) in some way.

Later-no-help is analogously defined that if some other candidate B
wins, a voter who provides an incomplete ballot can not make A *win* by
ranking additional candidates below A.

Ordinary STV passes both criteria. Are you saying that BSTV passes both
as well? Just making sure I read you right!

In any case, neither criterion requires equal-rank to be supported
(that's why I said that example wasn't important, though I was curious
how it would work). They do, however, require truncation to be
supported. So although I'm not sure what you mean by missing rankings, I
take it that you mean truncation.

> That 3-candidate example was rudimentary, as maybe was my assessment of it!

That's a fair point. The main thing I was going for was trying to
understand how last preferences would be counted for exclusion counts
when there's truncation. Thus I just made up some numbers that would
give an answer to the question (or at least let me distinguish between
common ways of doing it) just by seeing the keep and exclude values. It
was pretty clear that C was going to win, but just how would've let me
understand the method better.

So if I could ask for one more, it would be this more decisive example,
from which I can learn something by just knowing who won:

19600: A
39366: A>C>B
38957: B>C>A

although I would very much like to know the keep and exclude values too.

-km