[EM] immunity to burying

[James Green-Armytage]

Dear election methods fans,


After reading the last few messages on this topic, my feeling is that  
immunity to burying should be its own criterion. I?m not quite sure  
what the relationship is to later-no-help and later-no-harm, but it  
doesn?t seem like it?s quite equivalent to either of them.

Here?s a definition:
If w is winner when votes are sincere, and voters who prefer q to w  
change their ballots only by giving w an inferior rating or ranking,  
then w must still be the winner.

The methods that I know of that pass this are things like plurality,  
runoff, and IRV. They pass it because q needs to be eliminated before  
any later preferences matter.


Bucklin definitely fails this criterion. Here?s a simple example,  
which I think applies to most Bucklin variants as well, though you can  
correct me if I?m wrong about this.

4: A>B>C
3: B>A>C
2: C>A>B
The initial winner is A, but if the B>A>C voters switch to B>C>A, the  
winner changes to B.


Descending solid coalitions (DSC) fails this criterion as well,  
assuming that I understand the method correctly. I wasn?t familiar  
with it, so I looked it up on electowiki (thank you for posting the  
definition there!), and eventually resorted to writing a computer  
program to generate burying vulnerability examples. Here?s a modified  
version of the first example it came up with:

40: A>B>C
41: B>A>C
10: C>A>B
The initial winner is B, but if the A>B>C voters switch to A>C>B, the  
winner changes to A.


By the way, immunity to compromising should be its own criterion as  
well. (Instead of ?giving w an inferior ranking or rating?, write  
?giving q a superior ranking or rating? in the definition above.) The  
methods that I know of that pass this are things like anti-plurality,  
and Coombs... basically, the mirror images of plurality and IRV. I?ve  
found that these methods are highly vulnerable to burying, and more  
vulnerable to strategy overall than their counterparts.

my best,
James