[Election-Methods] delegate cascade

[Michael Allan]

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.

> 2) Let's say that the preferences of voter A are A>B>C>D>E. At some point 
> he decides to vote for his second preference (B) instead of himself. B's 
> preferences are B>D>etc. At some (later) point B decides to vote for his 
> second preference D. A is however not happy with that the vote now goes 
> directly to D (instead of C that was better). He changes his vote and votes 
> for C. The point here is that it may be that many voters will vote directly 
> the leading candidates instead of letting the voters in longer chains 
> (according to their own preferences) determine where the vote ends at. The 
> reason may be as above or maybe the voter simply prefers to vote directly 
> for the leading/best candidates instead of being at the long branches of 
> the tree (away from the main streams close to the root of the trees where 
> the decision making appears to take place). Controlling one's own vote may 
> also give the voter some additional negotiating power. The end result may 
> be that the cascade chains may tend to be short rather than long. The same 
> question here. Is this ok and how do you expect the method to behave?

The proportion of voters who preferred to vote for the "stars" would
act as a dead weight in the electoral system - a kind of irrational
ballast.  To the extent they were fickle, they would act as a shifting
cargo on a rolling ship.  Some factors that might reduce this:

  * it can be detected and filtered from the results (as irrational
    dross)

  * it will be boring, there's less scope to interact with a star
    candidate, because a single vote has relatively little worth to
    her, so:

     - the voter's questions, and attempts to enter into dialogue are
       likely to go unanswered

     - the voter's freedom to shift the vote will confer no leverage,
       no input to the candidate's behaviour

  * the star voter will be open to criticism from better informed
    peers, because the vote placements are public information

     - "I see you're voting for a star.  If you want to waste your
        vote like that, why not waste it on me?"

> 3) In theory the method may also end up in a loop. There could be three 
> voters (A, B, C) with opinions A: A>B>C, B: B>C>A and C: C>A>B. If A votes 
> for A, B votes for B and C votes for A, then B has an incentive to change 
> his vote to C in the hope that also C will vote for himself after this 
> move. That would improve the result from B's (as well as C's) point of view 
> (from A to C). But as a result now A has a similar incentive to vote for B 
> that is to him better than C. And the story might continue forever. This 
> kind of loops would probably be rare. But do you think this is acceptable 
> or should there be some limitations that would eliminate or slow down 
> possible continuous changes in the votes? In this looped case is possible 
> that when the voters note the loop they are capable of negotiating some 
> compromise solution (e.g. A and C agree that C will get something in return 
> if he sticks to voting for A).

Maybe the rule of vote flow (1) will prevent that, since self-votes
are null?  (I have to look at this one again in the morning.)  There's
a little more detail on cycles here:

  http://zelea.com/project/votorola/d/theory.xht#cascade-cyclic

-- 
Michael Allan

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