[EM] MDD,ER-Bucklin(whole) fails Mono-add-Plump

[C.Benham]

Mike Ossipoff wrote (6 Nov 2011):

> FBC is essential for public elections.
>  
> My current favorite is MDD, ER-Bucklin (whole)   (where 
> ER-Bucklin(whole) is defined
> as in the electowicki).
>  
> It's the Cadillac of FBC methods.
>  

Some years ago I also liked this.

> Is there an FBC-complying method meets UP and SDSC and that does 
> better by other criteria? 


Yes. IBIFA does.

http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2010-June/026572.html

25: A>B
26: B>C
23: C>A
03: C
(77 ballots)   B>C  51-26,   C>A 52-25,   A>B 48-26

All candidates have a majority-strength pairwise defeat, so MDD 
disqualifies no-one. No candidate
is top-rated  on more than half the ballots, so MDD,ER-Bucklin(whole) 
elects the most approved
candidate C.

Now say we add 23 ballots on which C is top-rated and all the other 
candidates are ignored.

25: A>B
26: B>C
23: C>A
26: C
(100 ballots)   B>C  51-49,   C>A 75-25,   A>B 48-26

Now B alone is without a majority-strength pairwise defeat, so  MDD 
disqualifies A and C (and B wins).

This is a failure of  the Mono-add-Plump criterion, which is met by 
IBIFA and SMD,TR and plain
ER-Bucklin(whole) and MCA and any method that I find acceptable.

> Is there an FBC-complying method that doesn't fail in the Approval 
> bad-example? 

Maybe  MDD,TR fills that bill, but it like MDDA  also fails mono-add-plump.

Chris Benham