[Election-Methods] delegate cascade

Sat Jul 26 02:41:44 PDT 2008

(It occurs to me, Abd may have thoughts on this topic too.  I haven't
read all of his Wiki.  It's still down.)
http://beyondpolitics.org/wiki/

Juho wrote:
>
> I'm quite confident that the possibility of continuous cyclic changes in 
> continuous elections (due to cycles in the group opinions; A preferred over 
> B, B preferred over C and C preferred over A) exists since that is a very 
> general property of voting methods. The problem may not appear often and it 
> may be that the cyclic behaviour won't last long for other reasons, but in 
> theory that risk exists.

OK. The dynamic is complex, and hard to predict.  I'm curious to see
what happens in reality.  Marcus Pivato said there's no way to model
this stuff in vitro (simulations), we have to run it in vivo.

But thought experiments are still useful.  Aside from the voting
medium, there's also an underlying trust network for authenticating
the voter lists.  We discovered last summer - doing thought
experiments in the APSA_ITP list - that my initial design was
unstable.  I've since split it into 2 parallel networks of positive
(trust) and negative (doubt) signals, in order to prevent an unstable
mixture - escalating signal warfare among voters.  I'll post it later,
when the design is documented.  (It's already coded.)

>> What happens if two candidates vote for each other (tight cycle),
>> in order to formalize a kind of partnership between them?
>
> If the incoming votes are the ones to be counted then both will get more 
> votes. Sounds like a good strategy, except that the one with less original 
> incoming votes will now get as many incoming votes as the other one.

Which suggests a criterion:

  I. Formal vote flow ought to correspond to the actual consensus and
     will of the electorate's community.

     More technically (and assuming 100% turnout of the community),
     the overall flow of votes in any branch of the election tree
     ought to exactly reflect the current, collective decision of that
     branch's electorate, and not that of any individual or subgroup
     among them.

     So the following ought *not* to be merely the decision of A and
     B:

   (1)

    \  |       |  /
     \ |       | /

  ---  A <---> B  ---

     / |       |  \
    /  |       |   \

When A and B vote for each other, their incoming votes are pooled and
spread out to the same level on both sides.  Applying criterion (I),
how does this formal arrangement match the actual reality?
Specifically:

  i) Are A and B really a team (in mutual deference) as their pooling
     of votes would imply?

 ii) Do people want them as a team?  Can team A-B retain at least the
     level of vote flow of MAX(A,B), and maybe build on that?

(i) Maybe A and B have worked together in the past.  Or maybe they
just intend to work together in the future.  In any case, it was not a
mere accident that they voted for each other; otherwise the cycle
would immediately pull itself apart, correcting the mismatch of formal
and actual.

(ii) If A-B was a popular team in the past (like a pair of Roman
Consuls with complimentary strengths) then pooled vote flow A + B
ought to rise.

Or, if A-B is a novel union, then we ought to see an immediate,
decline in A + B, in response to the union.  But as long as it stays
above MAX(A,B), or rebounds to that level, the union should prove
stable.

On the other hand, if voters ever perceive that the union A-B is *not*
a good idea, then A + B ought to decline below MAX(A,B).  The union
would then fall apart, correcting the mismatch of formal and actual.

> Here's one more potential problem case. If some candidate receives votes 
> from too many directions then some of the voters should switch to not 
> voting this candidate directly (to make the tree structure less flat). If 
> many of them have about the same number of incoming votes they may be 
> reluctant to change their vote since they'd prefer other voters making the 
> move first and thereby letting them stay closer to the root of the tree 
> (instead of ending up close to the leaves).

Picture a simpler extreme first, a tree flattened to the densest
possible star:

   (2)

    \  |  / 
     \ | /  

  ---  C  <-- D

     / |  \ 
    /  |   \

Suppose density is higher than shown, and C has thousands of voters.
None of them is a delegate, so only C has incoming votes.  If this
were the entire election, then C would have 100% of the vote flow, and
the community would formally be expressing itself, saying, "Among us,
only C has any particular interest or competence in this issue."  This
sounds false.  Suppose the issue is the Public Health Bill mentioned
previously.  It is unlikely that the community has no interest or
competence in this issue.  Consequently, this pattern of vote flow
ought to prove unstable.

Suppose that D (who has no votes) nevertheless has an interest in this
piece of legislation.  D expresses her interest to C, requesting
specific changes in the draft bill.  But C does not listen to D; or C
decides (for whatever reason) not to make the requested changes.  What
are D's options?  D might withdraw her vote from C.  But what good
would it do?

So D starts talking with the other voters.  There's a loose halo of
them surrounding C - ripe for the picking - and D has no trouble
finding others who agree to the proposed changes.  Moreover they
respect the effort she is putting into the issue, and admire her sense
of initiative.  So feeling this way, they have everything to gain (and
nothing to lose) by expressing themselves as follows:

   (3)

    \  |  /      /
     \ | /      /

  ---  C  <-- D  ---

     / |  \     \
    /  |   \     \

Here the dense star pattern begins to unravel into a tree.  Even
though C has lost some direct votes (and no longer has 100% of the
flow) she still has most of it (thousands of votes).  Nevertheless she
is under increased pressure from D.  This is much to the advantage of
D's new voters, who are not at all unhappy at being further from the
root, and having D to fight so energetically for their interests.  C
may have trouble resisting the pressure unless she gets help from
someone who is opposed to D.

   (4)

     \      \  |  /      /         \  |  / 
      \      \ | /      /           \ | /  

   ---  E -->  C  <-- D  ---     ---  X  ---

      /      / |  \     \           / |  \ 
     /      /  |   \     \         /  |   \

Here E is expressing opposition to D.  The content of E's legislative
draft (or amendment request) opposes that of D's, and consequently E
has attracted his own voters from among C's halo - those voters who
prefer E's ideas over D's.  Note how C is at the mercy of these
upstarts.  Note also that D has a big rival X (not shown previously),
who is watching the show from the sidelines.

D and E are both supporters and rivals of C.  This puts them in a
strong position.  Nothing would prevent them from talking to X, and
offering (threatening) to move their support, provided X is more
willing to satisfy them.  In deciding whom to satisfy, both C and X
will require a clear understanding of the *basis* of their support.
But they have no way to attain that understanding except through the
rational structure of their incoming vote flow - a structure that is
beginning to emerge in D and E.  Consequently, the amorphous and
irrational halos around C and X are likely to disappear, and re-form
into more-or-less rational trees.  It will be in everybody's interest.

This is true recursively.  As D and E acquire more vote flow, the
formal stucture of the sub-branches will elaborate the finer details
of their own interest positions. (Was it Abd who called this a
fractal?)  They will then be under pressure from formal vote shifts in
these structures, shifts that reflect the dynamics of interest.  None
of the details of this can be known in advance, nor can the overall
pattern be predicted - it can only be revealed moment by moment as the
election proceeds.

-- 
Michael Allan

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