[EM] "Unmanipulable Majority" strategy criterion

[Kristofer Munsterhjelm]

Chris Benham wrote:
> 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.

That's odd, because the example I gave in a reply to Juho was yours.
http://listas.apesol.org/pipermail/election-methods-electorama.com/2006-December/019097.html

Note that the method of that post (which I've been referring to as 
"first preference Copeland") is neither monotonic nor cloneproof, 
although it was claimed to be both. Perhaps it'd be possible to make a 
variant of it in some way, though, so that it's both, but it seems that 
Burial resistant Condorcet methods tend to be nonmonotonic (unless you 
consider Black to resist burial).

This leads me to wonder what monotonic preference ordering methods exist 
(that is, methods where A>B differs from A, unlike FPTP), and whether 
any of those, modified with one of the minimal "Condorcet-ifying" tweaks 
(Condorcet, else; limit to Smith; Smith,,) would also resist burial.

> "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?)

I see; yes, it would be a compromise strategy. Perhaps a better kind 
would be a setwise constructive burial. Set-limited constructive burial 
would take your unmanipulable majority criterion to a set, but the 
question is whether, for

"If A is ranked above one or more{1} in S by a majority of the ballots, 
then there should be no way for those who rank any{2} in S above A to 
rearrange their ballots so that someone in S wins",

if {1} should be "one or more" or "all", and if {2} should be "any" or 
"all".

In any event, we could then proceed to create another form of 
destructive burial where S is simply the set of all candidates minus the 
winner. For that criterion to have any power, {1} should probably be 
"one or more" and {2} "any", but then it would seem to be overly 
restrictive. So I tried to add the restriction that the strategists 
can't add candidates to "push" A lower, but that, as you point out, 
turns it into a compromising strategy.

The general idea of destructive burial as a strategy would be "anybody 
but Bush" camps cooperating to push off Bush, not minding who they get 
instead. You can see the compromising even there; the kind of reasoning 
that would lead to such strategy would be "this evil is really evil, I 
don't care who I get as long as I don't get this guy", which is a 
lesser-evil compromise. You can probably also see that the scenario 
would be pretty unrealistic for most real elections, since there'll 
always be very minor candidates that nobody wants to have elected, 
therefore such a campaign would never be purely destructive burial.