On Apr 12, 2010, at 3:57 AM, I wrote:
On Apr 11, 2010, at 7:25 PM, Kevin Venzke wrote:
49 A
5 B
19 B>C
27 C>B
It remains bad. I can't see what criticism would
remain of this, other
than saying that in a real election we might be lucky
enough to have
some A voters vote A>B and accidentally give the
election away.
I'm not quite sure that B should win with this set of
votes. Note e.g. that the sincere opinion of the five "B"
voters could be "B>C", and then this example says that
with WV it is ok if those five voters truncate strategically
and B wins instead of C.
Yes, it is okay, because B voters should hardly be able to expect
that
they will get full support from C.
In this scenario I'd use another explanation. B and C are from left
wing parties that always support each others and rank the right wing
candidates (A) last. This time the election will be arranged using
WV. B supporters note that they can win by not supporting C any
more. C supporters do not have the same incentive since they are
about to win. Truncation is also useless as a counter strategy. In a
large public election it is probable that also others than B
supporters will know about this strategic opportunity and plan.
Candidate B could recommend sincere voting to his/her supporters, or
maybe not. But many B supporters might vote strategically anyway. C
supporters could truncate but that would be just a revenge that
could elect A instead of B. The dilemma is thus that B and C could
agree before the election that they will recommend sincere voting
and the candidate with more support would win (if left has more
votes than right), but they can not control the most eager B
supporters, and also B might be happy if some of the supporters will
truncate. The situation is unstable. If B wins the election with the
help of the truncating voters, what can we do before the next
election? Maybe change the method. Maybe try to convince all voters
that sincere voting is the best approach for all.
Here's one addition to the story. WV has been defended by saying that
it is a benefit of WV that defensive truncation is possible. In this
example the C supporters could spread word that they plan to truncate
in any case (and vote 27: C). This approach would make the strategy of
B voters useless in the sense that the risk that truncation of the B
voters (5: B instead of sincere 5: B>C) would elect A increases. This
approach has however some problems like requiring C voters to be
strategic (and also in a way vote against their closest ally). The end
result is also very unstable if B and C are about equally strong since
then both could claim to be the leading candidate within the left wing
and both recommend truncation (=> A may win). Some supporters of both
of them may truncate for any of the reasons (attack, defence, revenge).
Juho
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