[EM] Fwd: “Monotonic” Binomial STV

[Kristofer Munsterhjelm]

On 28.02.2022 11:50, Richard Lung wrote:
> 
> postscript.
> 
> Actually that example of splitting B into Bo and Be wouldnt be possible
> with STV, of any stripe, which is only concerned with individual
> candidates. They may form into parties, making the analysis of internal
> and cross party support possible. But STV is not of parties splitting
> into smaller parties.

I'm not saying that the party itself is splitting into smaller parties.
I'm just saying that the extremist faction has enough clout with the
leadership to convince it to run two candidates under its auspices,
instead of one.

As the example shows, such a strategy benefits the party as a whole,
because the shift leads to a B candidate getting elected instead of an A
candidate. While the B party might stumble upon this strategy by
internal disagreement, it would thus soon realize that the strategy pays
off even when there's no factionalism within the party, and would then
decide to run multiple candidates to override majority rule.

> There are good philosophical reasons for this. But
> the afore-mentioned analysis is perhaps the most pertinent.
> Never the less, a main interest of seeing real examples of binomial stv,
> (with enough voters to form a binomial distribution) is to see whether
> best keep values sometimes have to be over-ruled by the distance of
> their total candidates vote from the quota, in standard deviations.

Another property that just about every election method passes is called
homogeneity or scalar invariance. This means that if you multiply every
group of voters by the same constant, the outcome should be the same.
For instance, the outcome should be the same if you have

36: A>B>C
34: B>C>A
30: C>A>B

and

360000: A>B>C
340000: B>C>A
300000: C>A>B

But from what I remember from statistical significance testing, say, a
coin that is flipped twice and gives heads twice provides much less
significant evidence that the coin is unfair than if the coin is flipped
ten thousand times and gives heads every time. So a method that naively
depends on significance testing may fail scale invariance.

In any case, since you say "whether best keep values sometimes have to
be over-ruled by the distance...", it sounds to me that you haven't
completely finalized Binomial STV yet. If that's right, then I don't
think you can meaningfully state whether the final version will be, say,
monotone, or pass Droop proportionality, until you have finished its
construction.

Finally, about Forest's election example:

> 35 A>B>C
> 33 B>C>A
> 32 C>A>B

you said that A wins. But you also said, in another post, that

> Binomial STV has “Independence of Irrelevant Alternatives.” For
> instance, it makes no difference what level the quota is set, to the
> order of the candidates keep values, their order of election. It is just
> that bigger quotas raise the threshold of election.

If by "independence of irrelevant alternatives" you mean, as Arrow
defined it, that removing a candidate who doesn't win can't change the
outcome, then Forest's election example shows that Binomial STV fails IIA.

Elimnate B (who is an irrelevant candidate) and you get:

35: A>C
65: C>A

And C wins by majority rule. So eliminating B changes who won.[1]

If you mean another concept of IIA, you should probably call it
something else so it doesn't get confused for Arrow's :-)

-km

[1] Forest's example can be used to show IIA failure no matter who is
elected, as long as the two-candidate election is majority rule. This is
due to Arrow's impossibility theorem.