On Apr 12, 2010, at 10:59 PM, Abd ul-Rahman Lomax wrote:
At 05:04 AM 4/12/2010, Juho wrote:
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).
Factions in an election are quite likely to follow the public
recommendations of their candidate. Nader claimed that Gore and Bush
were Tweedledum and Tweedledee. Did his supporters follow that idea
to its conclusion?
One point should be made clear: any candidate who recommends that
voters not vote sincerely is probably shooting himself or herself in
the foot. It isn't a winning strategy, generally, it really looks
bad (even if the strategy makes some sense.)
Yes, I believe this is true in most societies (and for most parties).
So if B is, say, leading C, but these candidates are really close in
preference for the set of B,C supporters, if B attacks C, B will
quite likely reduce his or her own support. There will be C
supporters who don't like that!
Yes, this is important. If the overall attitude is against strategic
plotting then election methods need less defence against such
behaviour. (Note however that this doesn't stop strategic voting - it
just reduces the public side of it (both at party and individual
level).)
I believe I just showed that WV, if it elects B in the scenario
given, and assuming that the votes are sincere, is low-performing. I
don't know if the scenario was reasonably possible, and, indeed, it
wasn't realistic.
I don't think we want to reform voting to use systems that produce
poor results if people vote sincerely!
Yes, that is important. (One may also need make some compromises to
eliminate some strategic threats.)
It is enough that a system does not reward preference reversal, and
approval/range systems don't do that. They do reward suppressing
minor preferences, while expressing major ones.
It is not enough to solve one problem only. One needs a balanced
approach where all identified vulnerabilities are analyzed and
appropriate fixes are implemented where needed and where possible
(often no action is needed; often there are no good fixes). All
Condorcet methods are vulnerable to preference reversal but in real
life elections it is quite difficult to implement any strategies that
would make use of that vulnerability. The discussed example (or one
explanation of the vote set) addressed one potential problem of WV
(where only truncation was used, not reversal). I'd say that is a
vulnerability. Note however that WV based methods have been used in
academic circles for a while without problems. So far that
vulnerability has thus not been a vulnerability in real life elections.
Even if the vulnerabilities are quite clear on paper, as in the given
WV example, in real life the environment is much noisier, and
controlled strategic voting is not very easy to implement. You also
mentioned the important point that often strategists may lose more
support because of their plots than they win as a result of a
successful implementation of a strategy (not to mention failed
strategic attempts). In WV I am maybe more worried about the
performance of WV with sincere votes (also a property that you
mentioned above) than about strategies.
Note also that Approval and Range do have very similar vulnerabilities
(probably more difficult to handle) when people suppress some of their
preferences and exaggerate some others, and they do not provide ideal
results if voters don't indicate their sincere preferences but some
strategically exaggerated ones. The discussed WV example where we have
two competing left wing candidates is a typical and difficult problem
scenario in Approval and Range.
Juho
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