[Election-Methods] delegate cascade

Tue Jul 22 12:49:57 PDT 2008

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.)

What is btw the reason that there were no arrows forward from the two  
leading candidates in the election snapshot picture in the references  
page? Did they abstain or were their votes (not even their own vote)  
not cascaded forward for some other reason?

>
>> 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?"

The behaviour of voter A in the example above may be quite "sincere".  
He likes B. If B forwards his votes to some candidate that A  
considers to be worse than C then A may vote for C directly.

>
>> 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 expect the cycles in opinions to potentially cause repeated changes  
in the cast votes (but since I don't know yet exactly how the voter  
will be cascaded I will not attempt to describe the details yet).

>   (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

Could you explain what happened in Figure 9? What are the rules that  
keep one vote at five of the candidates (red numbers) but forward  
some of the votes to the next candidate in the ring? I.e. why not  
forward all votes or keep all votes?

Juho

>
> -- 
> Michael Allan
>
> Toronto, 647-436-4521
> http://zelea.com/
>
> ----
> Election-Methods mailing list - see http://electorama.com/em for  
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