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

[Richard Lung]

The snag is that these and other criteria were invented for what amounts to uninomial elections, that is elections that don't have both, or either, a rational election count and a rational exclusion count. Together they make possible the application of the binomial theorem, to higher order counts. My binomial STV hand count is just a first order binomial count of one election count and one exclusion count. 
I am not aware of any untoward effects of tactical voting on the bstv system. I am aware of it doing away with residual irrationalities to traditional stv, including Meek method. Tho I accept that traditional stv (zero-order stv in relation to binomial stv) is a robust system, in practise, as the Hare system of at-large stv/pr.

BSTV counts require values for all preference positions, which are equal to the number of candidates. Any preference position may be an abstention. A citizen who never voted but made an exception of their dislike for Donald or Hilary could abstain on their first preference but vote for either on their second preference, effecting an exclusion, because there is only one vacancy.
That is the theory of it. I don't know how well it would work in practise, because there never has been a practise.
But I do know that democracy is minimised, and evidently works badly, based on single vacancies, in the Anglo-American systems.
Fully fledged binomial stv, FAB STV, does not work on less than 4 or 5 member constituencies, the minimum requirement for a democracy of all the people being represented by their choices.

Thank you for your examples. They have helped clarify my thinking -- somewhat!
According to my (accident-prone) working, A wins on a keep value of  38957/58966.
B also has a less than unity keep value of 38957/39366. The difference is that one can say A has been elected on a quota of 48961.5, with 58966 first preferences.
But B has not reached the elective quota. Tho B has not reached the exclusion quota, that only says B has not been excluded.

Regards,
Richard Lung.




On 23 May 2022, at 6:19 pm, Kristofer Munsterhjelm <km_elmet at t-online.de> wrote:

> 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