Kevin Venzke wrote:
Hi Kristofer,
--- En date de : Lun 21.2.11, Kristofer Munsterhjelm <[email protected]> a
écrit :
Now, if only we could use something more
clone-friendly than first
preferences... The tricky thing is that most other
metrics (such as
worst pairwise loss) are already vulnerable to
burial.
It would be a very strange system, but perhaps IRV. Define
the ordering so that if X is eliminated before Y, Y is
ranked ahead of X. IRV itself is cloneproof, which Plurality
isn't, so the result should at least be more
clone-friendly.
That seems possible. As clones are eliminated they would boost their
fellow clones in the order.
On the other hand (now that I'm thinking about it), clone independence
for a winner would not necessarily translate to clone independence over
the whole ranking. Consider something like Schulze where you have 51
voting Democrats first and 49 voting Republicans first, then because
Schulze is cloneproof, the number of Democratic and Republican
candidates can't affect who wins (in this case, a Democrat). However,
the ranking will list all the Democrats in order before any of the
Republicans, and adding more Democrats will list more Democratic
candidates before the ordering gets to the Republicans.
I'm not sure, but I have the feeling that the Plurality
variant would not be monotone. The IRV variant wouldn't be,
either.
I think that if you don't do the Condorcet or Smith filter at the
beginning, the Plurality version is monotone.
I forgot to say it, but I was thinking of the filtered versions. My
implied line of reasoning was probably that because you originally
defined the method for three candidates, and because a method that can
only work with three candidates or less in total is much more limiting
than one that can only work with three candidates or less in the Smith
set, I considered a filter evident.
(You might even resurrect the "sprucing up" idea from long ago, because
given certain criteria, you only need to define the base method for
three candidates or less.)
The reason I felt the Smith-constrained KH with Plurality would be
non-monotonic was because in some respect it is similar to
Smith-constrained Plurality itself (because its "internal ordering",
i.e. who starts off as king, is based on Plurality), and
Smith-constrained Plurality is not monotone.
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