[EM] MCA on electowiki

[C.Benham]

Jameson Quinn wrote (18 Oct 2010):

>I edited Electowiki to essentially replace the Bucklin-ER article with a
>new, expanded MCA article. In this article, I define 6 MCA variants. I find
>that as a class, they do surprisingly well on criteria compliance. Please
>check my work:
>
>http://wiki.electorama.com/wiki/Majority_Choice_Approval#Criteria_compliance
>  
>

>     Criteria compliances
>
> All MCA variants satisfy the Plurality criterion 
> <http://wiki.electorama.com/wiki/Plurality_criterion>, the Majority 
> criterion for solid coalitions 
> <http://wiki.electorama.com/wiki/Majority_criterion_for_solid_coalitions>, 
> Monotonicity <http://wiki.electorama.com/wiki/Monotonicity_criterion> 
> (for MCA-AR, assuming first- and second- round votes are consistent), 
> and Minimal Defense 
> <http://wiki.electorama.com/wiki/Minimal_Defense_criterion> (which 
> implies satisfaction of the Strong Defensive Strategy criterion 
> <http://wiki.electorama.com/wiki/Strong_Defensive_Strategy_criterion>).
>

It is well known that in general run-off methods fail  mono-raise (aka 
Monotonicity), and these methods
are no exception.

22: A
23: A>C
24: B
27: C>B
02: D>C
06: E
(104 ballots)

TR scores:           A45,   B24,   C27,   D2,   E6.
Approval scores: A45,   B51,   C52,   D2,   E6.

I am assuming that 3-slot ballots are used, and since no candidate has 
either a Top Ratings or Approval
score that reaches the majority threshold the runoff will be between the 
TR winner A and the Approval
winner C. 

A wins that runoff 45-29, but if the 2 D>C ballots change to D>A the 
Approval winner changes to B and
now A loses that runoff 47-49.

22: A
23: A>C
24: B
27: C>B
02: D>A  (was D>C)
06: E
(104 ballots)

TR scores:           A45,   B24,   C27,   D2,   E6.
Approval scores: A47,   B51,   C50,   D2,   E6.

Also I would quibble that methods that use ballots that don't allow 
voters to express a full ranking of the
candidates really properly meet  Majority for Soild Coalitions, but 
instead just meet a restricted form of
it (which is nonetheless very valuable).

And I'm surprised that a MCA advocate doesn't mention the Favourite 
Betrayal criterion. Of course the
suggested runoff  "variants of MCA" also fail that.

Chris Benham

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