On 03/15/2016 02:39 AM, robert bristow-johnson wrote:

I suppose it is because Meek is a clearly defined method we know a lot
about, so there's not that much to discuss. When it's mentioned, it's
usually in the context of some other method, e.g. "this method is
impervious to Woodall vote management, like Meek, but doesn't require
Meek's iterative approximation algorithm".

I know O'Neill has posted on here before, e.g. this message from
December:
http://permalink.gmane.org/gmane.politics.election-methods/25070.
However, he doesn't post all that often; that was his only post in all
of 2015.

Consider a complexity line for STV. On the very left is the simplest
possible STV method, which goes something like this:

1. Create n piles, one for each candidate.
2. Place each ballot in the pile corresponding to the candidate it ranks
   first.
3. As long as there's any pile has more ballots in it than the Droop
   quota Q:
   3.1. Elect the candidate that pile belongs to.
   3.2. Eliminate that candidate from the count.
   3.3. Let the number of ballots in the pile be n. Draw n-Q ballots at
   random from this pile and place the ballots in piles according to their
   first uneliminated preference.
4. Eliminate the unelected uneliminated candidate with the least votes
   (thinnest pile) and redistribute the ballots in that pile according to
   their first uneliminated preference.
5. Repeat from 3 until all candidates are either eliminated or elected.

This is only approximately fair because of the random component, and is
also vulnerable to Woodall free riding (where you vote for candidates
who have no chance so that you don't get stuck early in an elected pile).

You can then go further to the right by transferring every ballot at a
fractional weight rather than a random subset at full weight in step
3.3. That's not very practical in the real world, but simple enough for
an algorithm to do.

So as you go to the right, the method gets more complex but also more
fair. Meek, in particular, deals with two things: first, it acts like a
method that restarts the count whenever a candidate is eliminated (i.e.
no candidates are considered elected and they're back in the running).
This makes Meek impervious to Woodall vote management. Second, it tries
to be more fair with votes that transfer to someone who is already
elected. E.g. suppose we have a ballot
X>Y>Z
where Y was elected earlier on and we're transferring away from X
(either because X is eliminated or because he's elected). Simpler rules
would give that ballot to Z. But that means that this ballot isn't
subjected to the redistribution that every ballot that got Y elected is.

Meek fixes that problem by giving each candidate a weight between 0 and
1 (or 0 and 100%). If candidate X has a weight of 80%, then a ballot
voting for X first will give 80% of a vote to X, and 20% to whichever
candidates come after X on that ballot (recursively, e.g. if the second
ranked candidate is Y with weight 70%, the ballot would give 20% * 70% =
10% to Y and so on).
If a candidate X ends up with more than a Droop quota, his weight is
adjusted downwards. In turn, that may cause other candidates to get more
than a Droop quota as more ballot weight flows past X to others, so the
process is repeated with them. The method eventually converges, but it
can take a long time.

So in short, Meek is a more complex but more fair type of STV. It isn't
fundamentally different from other types of STV, since its single-winner
version is still IRV. But it treats ballots more equally and so is
better than the manual methods if you can handle the complexity.

If you mean on this list, then sure. I've done so before (e.g.
http://comments.gmane.org/gmane.politics.election-methods/24486) , and I
think Schulze has talked about Schulze STV before too.

A problem with multiwinner Condorcet methods is that they're generally
very complex. It's hard to come up with a multiwinner analog to the
Condorcet criterion, so usually what the methods do (like Schulze STV)
is compare assemblies as if they were candidates in a Condorcet method
(e.g. "elect A, B, and C" beats "elect B, C, and E" pairwise). But since
there are up to (numcands choose numseats) of these assemblies, it can
get unwieldy fast.

Hello Robert,

The reply from Kristofer seems a fair description of Meek STV. That is
so far as I understand the usual technical language used on this list.
The thing about Meek method is that it seems to offer only a marginal
improvement in fairness on traditional STV, at a great cost in extra
complexity. It has to be computer-counted, after all.
But this is deceptive. Meek method introduces a new and key concept: the
re-adjustable keep value.

As I have explained before, on this list, this idea made possible my
system of Binomial STV, which extends keep values to candidates in
deficit, as well as in surplus of a quota. When every candidate has a
quantified keep value irrespective of being elected or not, in a given
count, that means a candidate only needs to have a keep value that is
elective, as an average of more than one count.
The bi- in Binomial STV means there are two basic kinds of count: the
usual election count of preference votes, and a new rational exclusion
count of voters preferences in reverse order. Exclusion keep values are
inverted to make them comparable and averagable with election keep values.

This proper exclusion count, in its own right, does away with the
problem of premature exclusion of candidates, and sets the system apart
from all the worlds present electoral systems, which rely on arbitrary
exclusions of candidates or parties.
This theoretical improvement has its most dramatic impact on single
vacancy elections, where premature exclusion of candidates is at its
grossest.

The simplest (first order) Binomial STV procedure consists of averaging
one election count with one exclusion count.

In order for the exclusion count not to be given undue importance,
compared to the election count, (abstentions-inclusive keep-value
averaged) Binomial STV counts all preferences, including abstentions,
which if they reach a quota, leave a seat unfilled.
Kristofer recently supplied an artificially simple STV election for me
to show how the system would work. And I have previously posted the link:
http://www.voting.ukscientists.com/Binomial_STV.html

I would like to persuade some organisation to do preliminary trials on
Binomial STV.
It would need to be coded, from where the Meek STV computer program
leaves off. Unlike Meek method, there would be no successive reduction
of the Droop quota, as the preferences run out with each round. This
obviously follows from the fact that Binomial STV counts all
preferences, including abstentions, maximising (preference) information,
a basic goal of scientific progress.

from
Richard Lung.

On 15/03/2016 01:39, robert bristow-johnson wrote:

--
Richard Lung.

E-books (mostly available free or reader-sets-price)
http://www.voting.ukscientists.com/colverse.html
Includes the series of books on:
Democracy Science (starting with electoral reform and research);
Commentaries (literature and liberty; science and democracy);
Collected verse (in five books).

---------------------------- Original Message ----------------------------

Subject: Re: [EM] how come i hadn't heard about "Meek STV" before on this list?

From: "Kristofer Munsterhjelm" km_elmet@t-online.de

Date: Tue, March 15, 2016 11:21 am

To: rbj@audioimagination.com

election-methods@electorama.com

it's unbelievably complex in my judgement. �i can't believe it gets as much traction as it does (as i found out at Stack Exchange).
�

why?

1. start with NumRemainingCandidates = NumCandidates and NumRemainingSeats = NumSeats .
2. compute the "Defeat Matrix" like you would for single winner Condorcet, which i still think should be triangular in shape and not rectangular.
   �everything else is determined solely from that Defeat Matrix.
3. determine whom the top-preferred candidate is (using whatever variant of Condorcet you like best, Schulze, RP, minmax, margins, winning votes, whatever to resolve any cycle).
4. elect that person and eliminate that
   person from the set of candidates. �decrement both NumRemaningCandiates and NumRemainingSeats by 1.
5. with the set of remaining candidates, if NumRemainingSeats > 0 go to step 3. �else end and pack up the ballots into the ballot bag and seal it.
   how hard is
   that??
   �
   and here is what we tell voters how the system works. �first this is what we tell them for single winner:
   "If more voters prefer Candidate A over Candidate B than vise versa, then do not elect Candidate B."
   with �multiwinner races, simply add
   four words at the end getting
   "If more voters prefer Candidate A over Candidate B than vise versa, then do not elect Candidate B before electing Candidate A."
   who can argue with that?
   even with the need to resolve cycles, it's a far simpler, more meaningful, ostensibly
   fair and democratic (majoritarian) rule or principle than any way you can explain any STV which, even at it's simplest, is a�kabuki dance of transferred votes that will make a lot of people suspicious that you're trying to pull something over on them. �Meek seems like it's trying to be
   fair and proportional, but it's complicated and, like other STV, has contrivances (totally opaque to second ranked votes until the first choice is eliminated) and i am sure goofy pathologies like single-winner IRV has.
   �

i don't see why it would have to.
sorry to sound like a Condorcet partisan, but i am that. �especially after our experience in Burlington Vermont in 2009 and 2010.
�
thanks for replying, Kristofer.
BTW, if i may share a fun little fact:
i am an elected Inspector of Election for Ward 7 in Burlington Vermont ( https://www.burlingtonvt.gov/CT/Ward-Clerks-and-Inspectors-of-Election�). �a certain very cool U.S. presidential candidate lives in Ward 7 and i got to greet him and his wife when they voted last March 1 (Super
Tuesday). �my sister told me on facebook that she saw me on the Today Show that morning.

--
r b-j � � � � � � � � �rbj@audioimagination.com
"Imagination is more important than knowledge."

�

On 03/15/2016 10:12 PM, robert bristow-johnson wrote:

[snip]

I think it gets the traction it does because it's relatively simple for
a proportional candidate-based method, and like IRV, its logic seems
reasonable at first glance: you say each Droop quota's worth of voters
is entitled to one winner (no more and no less), and then you split up
the ballots into piles to enforce that.

Of course, if you consider IRV a chaotic kabuki dance (as you put it),
then the initial impression won't hold.

I get the impression that quite a few IRV advocates focus on the
workings of the method rather than on the results: not what the method
accomplishes, but how it does it. That may to some extent hold for STV
as well, although the proportionality criterion it passes limits how
weird results you can get much more than in IRV's case, since the
criterion gets tighter the more seats there are.

Suppose we replace Plurality per constituency with a repeated election
method that goes like this: first, conduct a Plurality election for the
whole state, then elect the winner and redo the election. Do so until
you've filled as many seats as you need.

If there's a coherent majority that supports a particular party P, the
method  will amplify majority into unanimity. The majority first votes
for say, P1. By the majority criterion, it gets P1. In the second round,
the majority votes for P2. It gets P2. And so on until every seat is filled.

Every method would amplify majority into unanimity in that manner,
including the Condorcet extension you've described. For Condorcet, it is
actually worse. If the method is cloneproof (and it should be), then if
the winner is part of party A, and no voter votes across party lines
(e.g. first candidate A1, then candidate B1, then candidate A5), then
party A would fill the whole assembly.

If the method is Plurality, Plurality behaves about as unpredictably as
you'd expect, and the result is you get kinda-sorta proportional
representation  as long as all the voters use the right strategy. But
for more well-behaved single-winner methods, the effect is kind of like
replacing single member Plurality with bloc voting: it hurts minority
representation. A cloneproof method will rank every clone of the winner
in order after the winner before it gets to a non-clone.

The usual way to deal with that kind of problem is to use single-winner
districts. If, say, the state is 40% right-wing and 60% left-wing, the
distribution may end up so that 40% of the districts have a right-wing
majority and 60% have a left-wing majority, and then the single-winner
method works properly in each district and you get a balanced assembly.

But through either bad luck or malice (gerrymandering), the statistical
assumption may not hold. Then the reasoning fails and groups of voters
may fail to be represented at all, or may conversely be represented far
in excess of their real support. Condorcet is better than Plurality here
because it handles situations with no single majority faction better,
but Condorcet also implies the majority criterion, so incorrect
representation can still happen.

Multiwinner methods like STV try to directly infer from the ballots what
sort of groups exist and then give each of their candidate groups
representation proportional to their support. You could say that they
try to find the optimal gerrymander from the point of view of all the
voters.

And that's why they're generally much more complex than their equivalent
single-winner methods: they have to do two things at once. First, they
have to elect good winners from the point of view of the voters as a
whole. Second, they have to give different groups their fair share of
the seats. These objectives pull in opposite directions; e.g. say a
significant number of left-wing voters like a candidate who the rest of
the voters loathe. How wide support inside the group balances out how
much general loathing?

It can be hard to know what kind of winners STV will pick in general,
since it shares IRV's logic, but in a similar way to how all Condorcet
methods pass the Condorcet criterion, usually there's one criterion one
considers the method to have to pass to be proportional in the STV
sense; and STV passes it. The criterion is the Droop proportionality
criterion: if more than k * 100/(s+1) % of the voters rank a certain
group of candidates before everybody else (not necessarily in the same
order), then at least k of those candidates should be elected.

Ordinary STV decides which of the candidates in the group should be
elected by, in essence, IRV within the group, so it's not all that good.
Schulze STV also passes the same criterion, but is Condorcet-based. It
is also very complex.

It may not have to - there may exist Condorcet methods that extend the
Condorcet logic to multiwinner while obeying some proportionality
criterion. Comparing assemblies is just the most intuitive way to extend
the Condorcet logic. Matrix-based Condorcet methods could be seen as
comparing pairs of propositions (i.e. "Elect A" vs "Elect B") and
determining which proposition wins every hypothetical runoff.
Assembly-comparison methods makes the propositions into "The assembly
shall consist of A, B, C", "The assembly shall consist of B, C, and E"
and so on.

I think the problem is that we don't have a good proportional extension
of the Condorcet criterion for multiwinner systems. So most Condorcet
multiwinner methods are constructed to follow these properties:

• The method should reduce to some kind of Condorcet method when the
  size of the assembly is one (i.e. single-winner) and be well-behaved in
  this case (monotone, cloneproof, whatever).
• The method should pass some proportionality criterion (usually the
  Droop proportionality criterion) in the multiwinner case.
• The method might also pass other multiwinner criteria (e.g. resistance
  to vote management for Schulze STV).

Assembly-comparison is just a relatively easy way to pass multiwinner
criteria as if they were singlewinner criteria, or to make use of a base
method's single-winner criterion compliance for multiwinner purposes.

I have an idea of a computationally simpler Condorcet multiwinner method
based on MAM/RP, but I'm kind of stuck on a particular point. Perhaps I
can mention it later in case others can see how to fix it.

But in the absence of such, I'd suggest that Condorcet methods be used
in single-winner districts rather than multiwinner "en bloc".
Redistricting then becomes an issue, so I'd suggest either an
independent redistricting commission, or some kind of MMP/biproportional
system to even out imbalances.

Bloc Condorcet voting might be useful for preventing kingmaker scenarios
in proportional representation assemblies. Suppose a 2% party can decide
which coalition wins by deciding which to support. That 2% party then
has undue power. But if 2% of the representatives are elected by
Condorcet based on a large area, these would be broad support winners
(due to how Condorcet works) and the strategy wouldn't work. Something
like Accurate Democracy's ensemble councils
(http://www.accuratedemocracy.com/e_intro.htm), but on a larger scale. A
similar effect could be had by doing single-member district voting with
much larger districts for the balancing seats, though.