[Election-Methods] delegate cascade

[Michael Allan]

Juho wrote:

>>   http://zelea.com/project/votorola/d/theory.xht#cascade-cyclic
>
> Let's say that in Figure 9 there are three candidates that are interested 
> in getting lots of votes. They could be the very top candidate (T), the 
> bottom left candidate (L) and the bottom right candidate (R). Candidate T 
> prefers R to L. Candidate R prefers L to T. Candidate L prefers T to R.
>
> Voting will start by all voting for their favourite candidate. The result 
> is as in Figure 9.

                 T


                (1)

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

            ^         |
          5 |         | 6
            |         v

           (2)       (1)
      L                     R
             \      /
            6 \    / 6

                (1)            


Voting nodes are bracketed (H), where H is the count of votes held
(removed from flow).  Volume in/out is shown by numbers.  Vote flow is
clockwise.

For example, L (bottom left) has votes:

   6  incoming
  (2) held
   5  outgoing

T (top) has:

   6  incoming
  (1) held
   6  outgoing

> Then candidate T abstains. As a result he will get lots of votes.
> Candidate L reacts to this... These cyclic changes could in
> principle continue forever.

                 T


                (6)

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

            ^         |
          4 |         | 1
            |         v

           (0)       (0)
      L                     R
             \      /
            3 \    / 2

                (0)            

After abstaining, T has:

   6  incoming
  (6) held
   0  outgoing

Rankings are determined by votes incoming, not votes held.  This is
crucial.  (It was only decided a couple of releases ago, so there may
inconstencies in the docs.)  T's absolute standing in the election is
unchanged by the decision to abstain.  T still has the same 6 votes of
assent.  But T's *relative* standing has been increased, at the
expense of the others in the ring.

Large cycles will tend to be *structurally* un-stable - they will tend
to fall apart and not re-form.  But I doubt they will be *dynamically*
unstable.  (Smoothing might not be needed, as Kristofer suggested.
But PageRank is interesting, I'm looking at it for the first time.  I
wonder how they handled the problem of vote cycles among pages?)

>> (ii) Otherwise, A is a mosquito voting for an elephant!
>
> You seem to assume that there is a hierarchy of voters that is used for 
> communication in the political process, and that this hierarchy is 
> determined (maybe even formally) by the voting behaviour, and that direct 
> links between mosquitos and elephants are not the best working solution.

True, I expect a similar patterns of a) formal vote flow, and b)
informal communications.

> Should I read this so that if a person has voted for a candidate that has 
> then (surprisingly) become popular, and this voter doesn't have many 
> indirect votes to carry from the other voters, then it would be better for 
> this voter to change his vote and vote for some less popular (mouse size) 
> intermediate candidate whose votes will cascade to the original most 
> preferred candidate?

Yes, it would seem to be better.  So a communication choice (dialogue
with a fitting partner) determines vote placement (a informs b).
Aside from gaining an effective dialogue partner, and increased
leverage, the voter is now in a position to eavesdrop downstream.  A
whole sub-branch of the communication network is explicitly revealed,
that would otherwise have been hidden.  In it, the voter can learn
what the issues are.  He can then correlate the issues with his own
peculiar interests.

By the same token, he can easily watch for downstream vote shifts in
the assent network.  So he will learn about alternatives that might
otherwise have been hidden.  (And maybe learn too how to use his vote
as leverage.)

> If this is true then the voting process is quite strongly a
> communication hierarchy building process. I.e. voters do not vote
> their favourites but candidates that they think would be good
> enough, and right size contact points for them, and whose votes
> would cascade to the right candidate.

I've never shone much light on it.  You're pointing to a tension
between voting for competence in communication, on the one hand, and
competence in a specialty, on the other.  In an election for Municipal
Public Health Officer, for instance, a voter might choose his most
medical-minded friend (a nurse).  But then, if the nurse turned out to
be an ineffective communicator (questions going unanswered) he might
shift his vote to someone else.

I guess a similar tension will play out among candidates too - between
their roles as politicians, and as experts.  Will the politicians
cooperate with the experts somehow?  What happens if two candidates
vote for each other (tight cycle), in order to formalize a kind of
partnership between them?  Maybe one is a technical expert (doctor or
scientist) and the other a politician (communicator, consensus
builder).  Would they attract more votes that way?  More generally, to
what extent will the formal structure of the communication/voting
network (mid-election) predict the actual structure of administrative
power (post-election)?

Parallel to all of this, and in addition to it, is the pattern of text
flow in the evolution of consensus norms (such as a public health bill
- a separate election from above).  The channels by which the
legislative drafters are exchanging bits of text will tend to align
(to some extent) with the channels of discussion and discourse, and
with the patterns of vote flow.  There could be interesting synergies
among all of these.  (I hope there are no instabilities.)

-- 
Michael Allan

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