[Election-Methods] delegate cascade

[Michael Allan]

Juho wrote:
>
> 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?

  http://zelea.com/project/votorola/d/outline.xht#delegate-cascade

They abstained.

> 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.

So A has good reason to vote for C, even though C (suppose) is a star
having many times - thousands of times - more votes.  The reason might
be:

  i)   A knows C personally or professionally

  ii)  C is recommended by A's favourite talk-show host

(i) If communication channels (personal or professional) give A
influence over C, and not just knowledge (in other words, if the
channels are 2-way) then A may be voting rationally, in the sense of
effectively.

(ii) Otherwise, A is a mosquito voting for an elephant!  It's probably
not rational.  It would be better to vote for a mouse (the talk-show
host, M), assuming that M *is* actually voting (directly or
indirectly) for C.  Then the direct effect on C would be the same -
she'd still be receiving A's vote.  But now A would have gained an
open, 2-way communication channel to C, via M.

Or A could band together with other, like-minded mosquitoes (perhaps
by soliciting their votes) and vote en-masse for C.  Then C would be
more likely to pay attention to their demands etc.

> 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).
>
>>   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?

[The vote flow volumes (black) were wrong.  I've corrected them.]

The votes flow individually.  Although received votes (black inbound)
are normally carried back out along with the delegate's own vote
(black outbound), there is one exception: if carriage of a vote would
result in a cycle (the vote being received a second time), then that
vote stops.  The stopped vote is held where it is (red), and the other
votes continue on their way.  That's why the held votes deposit
themselves evenly around the ring.  (The exception in the figure is
the one vote injected from outside of the ring.)

As a consequence, casting a vote has no effect on votes received.  If
any one of the voters in figure 9 withdraws her vote (black out), it
will not affect her received votes (black in).  And since electoral
standing is determined by votes received, and not by votes held (red),
the casting of a vote can never increase ones standing.

I doubt Figure 9 will ever occur in a real election - it's very much
an edge case - but if it does, it shouldn't cause any instability.
Unless I've overlooked something...

-- 
Michael Allan

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