James Green-Armytage wrote:
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.
Those methods pass both LNHelp and LNHarm. Do you think those criteria,
in combination, imply immunity to burial? I'm pretty sure they do, but
I'll think about it a bit more.
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.
Bucklin advocates might say that you could just vote B > (empty) > A >
C, or for that matter, truncate. But if we limit ourselves to ordinary
rank ballots (i.e. no empties), and ties are broken by excess (how much
above majority each candidate is), then that example shows burial works.
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.
That's interesting, because DAC and DSC are equal when there's no
partial or equal rank. Therefore, your example works both for DAC (which
passes LNHelp) and DSC (which passes LNHarm), showing that either by
itself isn't enough. That's kind of what you're saying, but this makes
it very clear.
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.
Doing a Smith constraint seems to limit compromising pretty well, even
though the method isn't immune. That's why I was focused on burial
rather than compromising :-)
Quite some time ago, Kevin Venzke talked about criteria called
"earlier-no-help" and "earlier-no-harm". If it turns out that having
both LNHelp and LNHarm immunizes a method against burial, perhaps the
same thing is the case for ENHelp and ENHarm with respect to compromising.
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