Jonathan Lundell wrote:
On Sep 3, 2008, at 12:28 AM, Juho wrote:
I hope this speculation provided something useful. And I hope I got
the Meek's method dynamics right.
Meek completely fixes Woodall free riding. That strategy takes advantage
of the fact that most STV methods (to the extent we're in a STV/Meek/etc
context) are sensitive to elimination order in how they distribute
surpluses. In most other STV methods, if I vote for my first and second
preferences AB first, and A has a surplus, then only a fraction of my
vote (or a probabilistic whole) transfers to B. But if I rank hopeless
candidate Z first: ZAB, then (hopefully) A gets elected before Z is
eliminated, and my whole vote goes to B. If Z gets eliminated first, no
harm done, I'm left with AB. The hazard, of course, is that so many
voters do this that Z gets elected and/or AB eliminated.
Meek cures this entirely via its principle that when Z is eliminated,
the ballots are counted *as if Z had never run*. There's no advantage to
me in ranking Z first.
In general then, any method that acts like Z had never run (when Z is
eliminated) would be resistant to Woodall free-riding.
Hylland is another kettle of fish. Here, I vote BA instead of my sincere
AB, because I "know" that A will be elected without my help, and I can
afford to spend my entire vote on B.
This is only useful, of course, if I'm competing with other A supporters
who have some second choice, say AC voters. They will have only a
fraction of their votes transfer to C, while I will have my entire vote
counted for B because I didn't bother to rank A first, even though A is
my first choice (I'd better be very confident).
There's a risk to the Hylland strategy, of course, if I make a mistake
in judging that A will be elected without my help. Other than that,
though, I don't offhand see a way of defending against Hylland free riding.
Hmm.. what could be done here? We could try to find out methods that
resist Hylland free-riding, or find methods where there are few honest
reasons to use the vote management version.
For the latter, I think PR methods that deal with equally ranked
candidates as if they were symmetrically completed would have an
advantage. For a party that expects very few personal votes, equal
ranking would spread the voting power to a much larger extent than they
could by running a vote management strategy. For instance, for a 6
candidate case, there's no way the party could arrange 720 different
pseudo-bailiwicks. Hopefully, parties that say "don't equal rank" would
appear dishonest. There's nothing stopping them from doing so,
technically, though, and the equal-rank property would make it easier
for those who actually want to do vote management to do so, as they can
get the majority to equal rank and then just have a small subgroup vote
opposite the ordering of the personal voters.
For the former, I think that Approval methods would have some inherent
safety against this (simply because you can't reorder the candidates). I
might be wrong (I don't know enough about it), since Plurality doesn't
let you reorder the candidates either, but SNTV basically requires
vote-management to work at all.
One could also have a PR method that uses relative information about the
ranking of strong winners as little as possible. Schulze's STV is one
example of such a method. Perhaps one could make a method based on DSC
or DAC in a similar vein (but not PSC-CLE, it scores badly in my
simulations), since DAC/DSC works based on sets of candidates.
A final option would be to have a method where either not running a vote
management scheme is a stable equilibrium, or where the risks when
performing vote management are too high. The latter would probably deter
individual voters more than parties, since parties can coordinate; but
parties can't perfectly manage votes either.
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