[EM] Three-candidate failure problems

[Kevin Venzke]

Hello,

I've been looking into properties of election methods when there
are only three candidates. I'm stumped by a few things, and I wonder
if there are any comments on these three, especially the first one:

1. Does three-candidate MinMax(WV) (or alternatively Tideman, Schulze, or
Heitzig) fail Participation?

Moulin's incompatibility proof uses four candidates. Woodall claims 
MinMax(Margins) meets Participation with three candidates, and it seems 
implied that a three-candidate method meeting Plurality (as WV would), 
Condorcet, and Participation is impossible. However, I haven't been able 
to find any WV Participation failures with three candidates.

2. With three candidates and complete strict rankings, is Baldwin (i.e.
successively eliminate the candidate with the lowest Borda score)
monotonic?

I know in general Baldwin isn't. The two methods I have which are not
monotonic with three candidates (IRV and Raynaud) fail it very obviously,
on ballot types AB BC and CA. But I haven't found any problems with
Baldwin.

(Interesting side note: With ballot types AB BC and CA, Baldwin gives
the same results as Craig Carey's IFPP.)

3. With three candidates and complete strict rankings, is this method
monotonic?: "Elect the winner of the pairwise comparison between the
candidate with the fewest last-preferences, and the winner of the
pairwise comparison between the other two candidates."

This is Chris Benham's SCRIRVE method. It doesn't seem like this would
be monotonic, but as above, I haven't found any problems with it. Any
thoughts on this?


I know these questions are too obscure for me to expect any answers,
but thanks in advance anyway to anyone who would consider these.

Kevin Venzke



	

	
		
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