[EM] Fwd: “Monotonic” Binomial STV

[Kristofer Munsterhjelm]

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
https://upload.wikimedia.org/wikipedia/commons/a/aa/Victorian-senate-paper-folded-01.png.
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