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/
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