[EM] Trying to out-do... a result! pt 2

[Kristofer Munsterhjelm]

Kevin Venzke wrote:
> Hi Kristofer,
> 
> --- En date de : Lun 21.2.11, Kristofer Munsterhjelm <km-elmet at broadpark.no> 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.