[Election-Methods] delegate cascade

[Kristofer Munsterhjelm]

Juho wrote:
> On Jul 22, 2008, at 14:26 , Michael Allan wrote:
> 
>> I'm grateful I was directed to this list.  You're clearly experts.  I
>> wish I could reply more completely right away (I should know better
>> than to start 2 separate threads).  I'll just reply to Juho's
>> questions today, and tomorrow I'll look at Abd's work.  (You've been
>> thinking about this longer than I have, Abd, and I need to catch up.)
>>
>>> 1) All voters are candidates and it is possible that all voters consider
>>> themselves to be the best candidate. Therefore the method may start from
>>> all candidates having one vote each (their own vote). Maybe only 
>>> after some
>>> candidates have numerous votes and the voter himself has only one vote
>>> still, then the voter gives up voting for himself and gives his vote to
>>> some of the frontrunners. How do you expect the method to behave from 
>>> this
>>> point of view?
>>
>> The basic rule of vote flow is: a vote stops *before* it encounters a
>> voter for a second time, and it remains held where it is.  A vote is
>> always considered to have "encountered" its original caster
>> beforehand.  So it is not possible to vote for oneself.  It is
>> permitted, but the vote stops before it is even cast - there is no
>> effect.
> 
> Ok, not allowing voters to vote for themselves may to some extent solve 
> the problem. (Some voters may however decide to abstain for a while.)

This is a bit offtopic (again), but another idea that might be less 
prone to strategy in the case of cyclical proxy candidacy occurred to 
me: use eigenvector or Markov-based methods to distribute the deferred 
power "smoothly" over the candidates in the cycle.

At this point, the method looks similar to the original PageRank used to 
"vote" on web pages, where various web pages vote for the importance of 
each other - and such voting chains may be cyclical.