[EM] "Unmanipulable Majority" strategy criterion

[Chris Benham]

Kristofer,

"...your Dominant Mutual Quarter Burial Resistance property."

I don't  remember reading or hearing about anything like that with "Quarter" in the title
anywhere except in your EM  posts. 

A few years ago  James Green-Armytage coined the "Mutual Dominant Third" criterion
but never promoted it.  I took it up, but sometimes mistakenly reversed the order of the first 
two words. I now think the original order is better, because MDT is analogous with the 
better-known older Mutual Majority criterion.

I do remember suggesting  what is in effect "MDT Burial Resistance", because there is an
ok method that meets it while failing Burial Invulnerability: namely Smith,IRV.

I don't know of any method that meets  the MDQBR you refer to that isn't completely in
invulnerable to Burial (do you?), so I don't see how that criterion is presently useful.

In response to my question "is Unmanipulative Majority desirable?"  you wrote:

"In isolation (not affecting anything else), sure. It's desirable because  it limits the burying 
tricks that can be done."

I'm glad you think so.

"The mention of pushover strategy there would mean that the method would 
have to have some degree of monotonicity, I assume."

Yes.

"If A>X voters can cause A to win by rearranging  their ballots, then that would be a 
form of constructive burial. If, for instance, some subset of the voters who place X 
fifth can keep X from winning by rearranging their first-to-fourth preferences, then that 
would be destructive burial."

If those voters are sincere in ranking X fifth, i.e they sincerely prefer all the candidates
they rank above X to X; then I can't see that that qualifies as "Burial" strategy at all.

Normally the strategy you refer to would qualify as some form of  Compromise strategy.
(Do you have an example that doesn't?)

Chris Benham





Kristofer Munsterhjelm wrote (Fri.Nov.28) wrote:

Chris Benham wrote:
>  
> Kristofer,
> Thanks for at least responding.
>  
> "...I won't say anything about the desirability because I  don't know 
> what it implies;.."
> 
> Only judging criteria by how they fit in with other criteria is 
> obviously circular.

That's true. If we're going to judge criteria by how they fit in with 
other criteria, we should have an idea of how relatively desirable they are.

It may also be the case that it the tradeoff would be too great, by 
reasoning similar to what I gave in the reply to Juho about your 
Dominant Mutual Quarter Burial Resistance property. But if we consider 
this in more detail, we don't really know whether such tradeoffs are too 
great for, for instance, cloneproof criteria (though I think they are not).

> Do you (or anyone) think that judged in isolation this strategy 
> criterion is desirable?
> It is true that some desirable/interesting criteria are so "restrictive" 
> (as you put it) that
> IMO  compliance with them can only be a redeeming feature of  a method 
> that isn't
> one of the best.  (I  put Participation in that category.)

In isolation (not affecting anything else), sure. It's desirable because 
it limits the burying tricks that can be done.

If you're asking whether I think it's more important than being, say, 
cloneproof, I don't think I can answer at the moment. I haven't thought 
about the relative desirability of criteria, though I prefer Condorcet 
methods to be both Smith and cloneproof.

> Maybe some people would like me to paraphrase this suggested criterion 
> in language
> that is more EM-typical:
> 
> 'If candidate A majority-strength pairwise beats candidate B, then it 
> must not be possible for B's
> supporters (pairwise versus A) to use Burial or Pushover strategy to 
> change the winner from A
> to B.'

The mention of pushover strategy there would mean that the method would 
have to have some degree of monotonicity, I assume.

> "Destructive burial would be trying to make X not win,..."
>  
> Your "destructive burial"  looks  almost synonymous with *monotonicity*.

Hm, not necessarily. Without qualifications on the criterion, 
destructive burial would be constructive burial for *any* candidate, but 
also more than that. If A>X voters can cause A to win by rearranging 
their ballots, then that would be a form of constructive burial. If, for 
instance, some subset of the voters who place X fifth can keep X from 
winning by rearranging their first-to-fourth preferences, then that 
would be destructive burial.



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