On Sep 3, 2008, at 18:06 , 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.
Meek's approach to treat all votes in the same way can simply be said
to be fair.
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.
I note that you describe Hylland as raking the favourite candidate at
second place instead of omitting it completely.
Additional free riding scenarios that I tried to cover include also
e.g. swapping of second and third candidates. The point was really
that the ordering of all the candidates should be re-evaluated based
on the estimated probabilities and utilities. Meek like systems will
give different probabilities than those that allow also Woodall style
free riding.
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.
One simple approach would be to follow a candidate given inheritance
order (=> trees or explicit candidate given inheritance lists)
instead of multiple voter given inheritance orders. That would not be
really STV any more, but at least a reference point to compare with
(and maybe to start finding some intermediate solutions with optimal
properties from both sides).
Juho
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