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

[Kristofer Munsterhjelm]

On 03/15/2016 02:39 AM, robert bristow-johnson wrote:
> maybe it was because i wasn't paying attention, but i hadn't even heard
> of this until looking into elections for moderators at Stack Exchange.

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".

> also, are Jeff O'Neill and/or Chuck Sipos of OpaVote.com on this EM
> mailing list?  would you be willing to discuss here the ideas your
> website promotes regarding the "Best way to elect..."?
> 
> http://blog.opavote.com/2015/11/electing-single-person.html
> 
> http://blog.opavote.com/2016/02/best-methods-for-electing-group-of.html

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.

> also, what to others on this list think of Meek STV?  i would love to
> hear pros and cons?

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.

> and can we discuss Condorcet methods for multi-winner elections?

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.