[EM] Delegate cascade and proportional representation

[Michael Allan]

Raph Frank wrote:
> Michael Allan <mike at zelea.com> wrote:
> > Except that all candidates are formally equal.  Their inputs (votes
> > received) all flood out to the same level (pool), giving them equal
> > measures of assent from the voters.  Without additional information,
> > there is no fair way to choose among them.
> 
> In your cyclic cycle example,
> http://zelea.com/project/votorola/d/theory.xht
> you show one node holding more votes.


                (1)

             6 /   \ 6
              /     \
      1
 (0) ----> (1)       (1)

            ^         |
          5 |         | 6
            |         v

           (2)       (1)
        *                   
             \      /
            6 \    / 6

                (1)            

 
Yes, at bottom left.  But the caption to my original diagram is
misleading.  It's the votes one *receives* that are the measure of
assent, not the votes one *holds*.  (Votes held are an artifact of the
model, with no actual meaning.)
 
> Actually, my visualisation of the method was slightly off.
> 
> I thought a vote was credited to every node along which it passes (but
> couldn't credit a node more than once).
> 
> So, in that example, all on the members of the loop would hold 7 votes
> and the other node would hold 1 vote.

This sounds very close to my model.  Here its 6 for the members of the
loop, and zero for the outsider.  No node can receive the same vote
twice, nor can it receive its own vote.  Votes are deposited around
the ring (held), at points where they can flow no further.

> Maybe the rule would be to break the weakest link of the strongest loop.
> 
> In that example, the links are all 6's and one 5, so the 5 link would be broken.
> 
> Ofc, there could also be a tie for that too, if there are 2 entry
> points into the loop.
> 
> Breaking at the 5 link would mean that members of the loop get
> priority over non-members when assigning seats.
> 
> If you had a loop of 8 and only 5 seats for that loop, I am not sure
> how to manage that.
> 
> This may lead to strategic problems.  The node that is the
> 'entry-point' into a loop for a large number of votes has an incentive
> to abstain in order to be sure of getting a seat.
> 
> This means that a better rule might be to break the link after the
> member of the loop who received the most votes from outside the loop.
> In the example on your page, that would break the loop after the node
> on the left-top.  This is the node who benefited the loop the most and
> rightly should get the first call on any seats that the loop receives.

I like that rule better, because it factors out the loop - the one
thing shared by all of its members.  I guess it's still not fair,
because it assumes that the loop is meaningless (that assent is not
really uniform within it), or that it was intended to be unravelled in
this manner.  In another sub-thread, I've discovered a case in which a
loop is intended to be unravelled:

 http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-August/022280.html

Here the central delegates withdraw their votes from an incumbent
office holder (root), in order to form a loop with each other.  Kind
of like bees swarming to decide on a new hive, except here they're
swarming to decide on a new candidate for office.  It will be a loop
like above, but with a massive inflow of votes entering from all
member nodes.  By common agreement, the weakest of the contributors
will be ejected from the loop, one by one - only to become the
kingmakers, as they re-direct their votes back in.  So the delegates
will be applying your rule, but in reverse - ejecting the weakest
first.  They'll also be ejecting any reluctant ones, at their own
request; and any ill-disciplined ones, who happen to break the rules
of the decision game.

I imagine it would be a very slow game, played out over a period of
months.  The voters would have time to respond to every move.  Could
it work, do you think?

-- 
Michael Allan

Toronto, 647-436-4521
http://zelea.com/