# [EM] Fwd: “Monotonic” Binomial STV

Richard Lung voting at ukscientists.com
Fri Mar 4 13:47:51 PST 2022

```Yes, Kristofer,

the standard statistical test, I use, is a “hypothesis”. Elections are
hypotheses ( - they are not absolutely determined). This is the song I
have been chirruping all along: All elections are a statistic or
statistical distribution. And their representation is no better than a
good estimate. (This is in keeping with the theorem of the Impossibility
of determinate election results.)

At least, binomial STV knows it is a statistic. It is an explicitly
statistical method. I even had cause to invent a statistical quota: the
harmonic mean quota. This is one of the four averages of FAB STV.

So, it is quite reasonable to use a statistical test to verify (highly
probably) the achievement of a quota.

I do not know whether that would be required, in practise.

Regards,

Richard Lung.

On 02/03/2022 23:02, Kristofer Munsterhjelm wrote:
> On 28.02.2022 19:17, Richard Lung wrote:
>> 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.
> Of course. But if the STV election method is used as part of a partisan
> system, then the STV elections will be partisan.
> For instance, the Australian Senate STV ballots explicitly list the
> party membership of the candidates who are up for election. See
> In my example, the voters don't directly vote for the A party and then
> the B party. They vote for the candidates associated with those parties,
> and the candidates who run are listed on the ballot as being members of
> their respective parties; or they are not, but the voters know what
> parties they are part of.
>
> Even in a nonpartisan environment, I think something analogous to the
> example I provided can be used as long as the candidates mainly identify
> themselves along a single axis (say economic left versus right, or
> unitary state vs confederation). Then the voters close to one side of
> the axis (say those preferring a unitary state) will correspond to the A
> voters, and the voters close to the other (say those preferring
> confederation) will correspond to the B voters. No explicit party line
> needs to be instated as long as the voting is sufficiently strongly
> single issue.
>
> So I was trying to give at least a not too unrealistic example to show
> that the majority failure can be induced in at least somewhat a
> realistic setting.
>
>> 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.
> Yes. When I respond to claims about the method, I am certainly not
> objecting to you as a person. I am using "naive" here in the sense of
> applying a simple mechanism (here, statistical hypothesis testing) in a
> context it's not well suited for without modification.
>
> I argued that using significance testing in a straightforward matter
> could lead to strange outcomes. So either the method should use
> something else than hypothesis testing, or it needs a (more
> sophisticated) model that incorporates the knowledge that "200 voters,
> 100 of which vote this way" is the same thing as "2000 voters, 1000 of
> which vote this way".
>
>> 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.)
> That's true, but some of the things you say about Binomial STV applies
> to it as a winner method: for instance, a claim that it's monotone means
> that ranking candidates lower don't help them and ranking them higher
> don't hurt them.
>
> Even proportionality, in the STV context, usually means Droop
> proportionality, which is a property that can be tested and disproven --
> or mathematically proven.
>
> A method may be only a minor part of a greater democratic system, but it
> still deserves to be examined. And particularly when claims about the
> method involve combinations of properties that are rarely found in other
> methods, I think it's important that they can be verified.
>
> About single districts: I've been limiting myself to single-winner
> because that's what Forest's example was. If you'd do a similar
> explanation for electing two winners out of three using the same
> example, I could probably check that too.
>
>> 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.
> I'm not sure what you mean here. Ordinary STV also works essentially the
> same way for single- and multi-winner. Surplus redistribution just
> doesn't happen because the election is over before it's necessary.
>
> The same thing goes for CPO-STV and Schulze STV: both of the latter
> methods naturally reduce to a Condorcet method when there's a single
> winner, without the election officials having to switch to a separate
> method for single-winner constituencies.
>
>> 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.
> That sounds right. I don't know multi-winner Binomial STV, but what
> you've shown passes homogeneity/scale invariance because it's
> essentially electing the candidate with the maximum value of (first
> preferences)/(last preferences); and multiplying the total number of
> voters multiplies both the denominator and numerator by the same
> constant, which cancels out.
>
> -km
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