[EM] "Unmanipulable Majority" strategy criterion (newly amended version)

[Kristofer Munsterhjelm]

Chris Benham wrote:
> Regarding my proposed Unmanipulable Majority criterion:
>  
> *If (assuming there are more than two candidates) the ballot
> rules don't constrain voters to expressing fewer than three
> preference-levels, and A wins being voted above B on more
> than half the ballots, then it must not be possible to make B
> the winner by altering any of the ballots on which B is voted
> above A without raising their ranking or rating of B.*
>  
> To have any point a criterion must be met by some method.
>  
> It is met by my recently proposed SMD,TR method, which I introduced
> as "3-slot SMD,FPP(w)":
> 
> *Voters fill out 3-slot ratings ballots, default rating is bottom-most
> (indicating least preferred and not approved).
> 
> Interpreting top and middle rating as approval, disqualify all candidates
> with an approval score lower than their maximum approval-opposition
> (MAO) score.
> (X's  MAO score is the approval score of the most approved candidate on
> ballots that don't approve X).
> 
> Elect the undisqualified candidate with the highest top-ratings score.*
>  
[snip examples of methods failing the criterion]

You have some examples showing that RP/Schulze/"etc" fail the criterion. 
Do they show that Condorcet and UM is incompatible? Or have they just 
been constructed on basis of some Condorcet methods, with differing 
methods for each?

I think I remember that you said Condorcet implies some vulnerability to 
burial. Is that sufficient to make it fail UM? I wouldn't be surprised 
if it is, seeing that you have examples for a very broad range of 
election methods.

> 93: A
> 09: B>A
> 78: B
> 14: C>B
> 02: C>A
> 04: C
> 200 ballots
> 
> B>A  101-95,  B>C 87-20,  A>C 102-20.
> All Condorcet methods, plus MDD,X  and  MAMPO and  ICA elect B.
> 
> B has a majority-strength pairwise win against A, but say 82 of the 93A 
> change to
> A>C  thus:
> 
> 82: A>C
> 11: A
> 09: B>A
> 78: B
> 14: C>B
> 02: C>A
> 04: C
>  
> B>A  101-95,  C>B 102-87,  A>C 102-20
> Approvals: A104, B101, C102
> TR scores: A93,   B87,   C 20
>  
> Now MDD,A and MDD,TR and MAMPO and ICA and  Schulze/RP/MinMax etc. using
> WV or Margins elect A.  So all those methods fail the UM criterion.

I did a bit of calculation and it seems my FPC (first preference 
Copeland) variant elects B here, as should plain FPC. Since it's 
nonmonotonic, it's vulnerable to Pushover, though, and I'm not sure 
whether that can be fixed at all.