[EM] MCA on Electowiki (re reference to Condorcet criterion)

C.Benham cbenhamau at yahoo.com.au
Wed Oct 27 08:43:43 PDT 2010


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
>

Again quoting from the linked-to page:

> The Condorcet criterion </wiki/Condorcet_criterion> is satisfied by 
> MCA-IR if the pairwise champion </wiki/Pairwise_champion> (aka CW) is 
> visible on the ballots
> and would beat at least one other candidate by an absolute majority. 
> It is satisfied by MCA-AR if at least half
>  the voters at least approve the PC in the first round of voting.


Both these claims are wrong, as we can see from this old Woodall example:

4: A>B
6: A>C
6: B>A
2: B>C
3: C>B

No candidate reaches the majority threshold of 11 in the first round, 
and A alone reaches it in the second so
all the suggested versions of MCA elect A (there being no need for any 
"resolution method").

But the Condorcet winner is B, who pairwise beats both other candidates 
with an absolute majority.

B>A 11-10,   B>C 12-9.

The page contains some other blunders and inanities that I might address 
later..

Chris Benham

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