“Monotonic” Binomial STV
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.
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.
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
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
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