[EM] immunity to burying

[Jameson Quinn]

2011/2/20 Kristofer Munsterhjelm <km-elmet at broadpark.no>

> 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.
>>
>
To me, the term "burial" implies burying under something. So, I'd propose:
If w is winner when votes are sincere, and voters who prefer q to w change
their ballots only by giving w an inferior ranking, or by improving the
rating of x, then the winner cannot change fro w to q.

Why is this better than the first definition, why bring x into it? There is
nothing a priori wrong with reducing w's rating leading to w not winning.
The problem is when you start using third parties to game the system -
because of the inherent risk of misfired strategy leading to unqualified x
winning.


>
>> 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.


First off, I don't call myself a Bucklin advocate, for precisely this
reason; the limited version of Bucklin you propose is silly. That's why I
say MCA - aside from being more descriptive, the Majority Choice Approval
name clearly does not refer to your limited Bucklin.

Second, both of those arguments are true, and are what I think voters would
do in reality. But under my criterion definition, they're irrelevant -
nonblack noncrows. The relevant move would be for B>A>C voters to move to
B>A=C, which does not change the winner. (Or, if you add an empty second
rank to all ballots, such that the original vote is B>...>A>C, the same can
be said of B>C>A>...). So that's why I'd argue that MCA does pass (my
definition of) burial immunity, or at least that I think it does and no
counterexample has been given.

>
>
>  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.


Interesting.

>
>
>  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.


I'd use a symmetrical modification of the definition for compromising
immunity. I haven't worked this out at all, but initially, I don't see why
MCA wouldn't meet that criterion.

JQ

>
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