On Jul 23, 2008, at 10:59 , Michael Allan wrote:
(ii) Otherwise, A is a mosquito voting for an elephant!
You seem to assume that there is a hierarchy of voters that is used
for communication in the political process, and that this hierarchy
is determined (maybe even formally) by the voting behaviour, and that
direct links between mosquitos and elephants are not the best working
solution.
Should I read this so that if a person has voted for a candidate that
has then (surprisingly) become popular, and this voter doesn't have
many indirect votes to carry from the other voters, then it would be
better for this voter to change his vote and vote for some less
popular (mouse size) intermediate candidate whose votes will cascade
to the original most preferred candidate? If this is true then the
voting process is quite strongly a communication hierarchy building
process. I.e. voters do not vote their favourites but candidates that
they think would be good enough, and right size contact points for
them, and whose votes would cascade to the right candidate.
I understood that the votes are public, so the candidates would know
who their voters are. I understood it would be acceptable for a
mosquito to vote for an elephant, but the mosquito could then assume
that the elephant would not have much time to discuss with him (worth
one vote only).
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
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...
Let's say that in Figure 9 there are three candidates that are
interested in getting lots of votes. They could be the very top
candidate (T), the bottom left candidate (L) and the bottom right
candidate (R). Candidate T prefers R to L. Candidate R prefers L to
T. Candidate L prefers T to R.
Voting will start by all voting for their favourite candidate. The
result is as in Figure 9.
Then candidate T abstains. As a result he will get lots of votes.
Candidate L reacts to this by abstaining. As a result of this
candidate L will get the highest number of votes.
Now candidate T realizes that he needs to vote again (as in Figure 9)
in order to avoid electing L. Candidate L still has most votes. But
now candidate R can (and will) abstain, and will get more votes than L.
Now candidate L is in the same position as candidate T was few
moments ago. Candidate L votes again and thereby opens up the option
for candidate T to abstain again and become the leader.
Next it is candidate R's turn to do the same tricks and allow
candidate L to become the leader.
These cyclic changes could in principle continue forever.
The point here is that group opinions may contain cycles (this is not
dependent on what election method is used). Methods that allow votes
to be changed continuously may end up in loops like this. If cycles
are expected to cause problems (when they exist) one could develop
some tricks that could slow down the cyclic changes or even ban them
somehow.
Juho
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