[EM] Fwd: “Monotonic” Binomial STV

[Richard Lung]

Kristofer,

STV makes no assumptions about parties or outside bodies. To do so, you 
have to make the candidates into party candidates, voted on certain 
party lines. This happens, of course, but existing elections commonly 
are not systems of personal choice, that STV is, and which can transcend 
party divisions with a transferabe vote, to express unity, thru freely 
personal ranked choice, as well as party or faction division. Division 
is all party list systems, or single member systems (most of Europe and 
America between them) can do.

The object of attaining a quota cannot simply be ignored because, at 
least in theory, best average keep values can be obtained without 
achieving a quota. It was probably a short-coming on my part, not to 
fully appreciate a need for rule priorities.

I would not wish to bother you. You may have, perhaps justifiably, had 
enough of binomial stv, but that does not justify your depreciating it. 
I take the criticism of what is only standard statistical testing, as 
"naive" as a criticism of statistics, rather than personal criticism. To 
suggest this old man needs to finish the new stv system is inevitably 
true. It is also less than just. Most of FAB STV has not even been 
touched upon - only hand count first order binomial stv, in single 
districts. Binomial STV develops a democratic system, not merely a 
winner system. They are different games, over which we appear to be at 
odds. Politicians are  more interested in the latter: The main thing is 
to win! (That led to the riot on Capitol Hill.)

Binomial stv can work essentially the same way for both single and 
multi-member constituencies, thru its keep value averaging. It doesn't 
have to be AV/IRV and STV/Hare system. So it does not lack consistency 
compared to other systems.

What I called IIA might indeed be better called something else -- 
perhaps "scale invariance"? At any rate, the order of keep values 
remains constant, whatever the size of the quota, which is, in effect, a 
change of constant.

Regards,

Richard Lung.


On 28/02/2022 11:20, Kristofer Munsterhjelm wrote:
> 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.