[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
>

Now quoting from the referred-to Electowiki page:

> Majority Choice Approval (MCA) is a class of rated voting systems 
> which attempt to find majority support for some candidate. It is 
> closely related to Bucklin Voting, which refers to ranked systems 
> using similar rules. In fact, some people consider MCA a subclass of 
> Bucklin, calling it ER-Bucklin 
> <http://wiki.electorama.com/wiki/ER-Bucklin> (for 
> Equal-Ratings-[allowed] Bucklin). 


Who are these people?  As I understand it, ER-Bucklin is a method that 
uses ranked ballots that allow equal-ranking
whereas MCA is a method that uses 3-slot ratings ballots (but could be 
extended to more than 3 rating slots).


> Voters rate candidates into a fixed number of rating classes. There 
> are commonly 3, 4, 5, or even 100 possible rating levels. The 
> following discussion assumes 3 ratings, called "preferred", 
> "approved", and "unapproved".
>
> If one and only one candidate is preferred by an absolute majority 
> <http://wiki.electorama.com/wiki/Absolute_majority> of voters, that 
> candidate wins. If not, approvals are added to preferences, and again 
> if there is only one candidate with a majority they win.
>
> If the election is still unresolved, one of two things must be true. 
> Either multiple candidates attain a majority at the same rating level, 
> or there are no candidates with an absolute majority at any level. In 
> either case, there are different ways to resolve between the possible 
> winners - that is, in the former case, between those candidates with a 
> majority, or in the latter case, between all candidates.
>
> The possible resolution methods include:
>
>     * MCA-A: Most approved candidate (most votes above lowest possible
>       rating)
>
Until I read this, the only versions of MCA that I was aware of were 
this one and another that differs only by using a hybrid
FPP-Approval ballot that restricts voters to indicating one candidate as 
most preferred plus they can approve as many
candidates as they like.  (The latter version was an early suggestion 
that seem to quickly fall out of favour).

> MCA-P: Most preferred candidate (most votes at highest possible rating) 

I've heard of this, as a 3-slot method with a different name.  The 
strategic incentive for voters to not use any rating-slot
other than the top one is even higher than it is with "MCA-A".

>
>     A note on terminology
>
> "Majority Choice Approval" was first used to refer to a specific form, 
> which would be 3-level MCA-AR in the nomenclature above (specifically, 
> 3-MCA-AR-M). Later, a voting system naming poll 
> <http://betterpolls.com/v/1189> chose this term as a more-accessible 
> replacement for "ER-Bucklin" in general.
>

As I previously implied, this is news to me.  How exactly does this 
mysterious "3-MCA-AR-M" method work?


Chris Benham





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