[EM] D2MAC can be much more efficient than Range Voting (corrected)

[Warren Smith]

> Recall that in D2MAC you specify a favourite and as many "also approved"
> options as you want. Then two ballots are drawn and the winner is the
> most approved option amoung those that are approved on both ballots
> (if such an option exists), or else the favourite option of the first
> ballot.
> 
> If voters are sincere, the result will be this:
>   55%: favourite A, also approved C
>   45%: favourite B, also approved C
> Winner: C

> --WDS correction: actually, it appears to me that the winner is
> A with probability 30.25%
> B with probability 20.25%
> C with probability 49.50%
> with social average utility = 7.03

>Heitzig: 
That's definitely wrong: No matter what two ballots are drawn, both approve of C
and C is the most approved option. Hence C is elected with certainty.

--WDS: Huh?
So suppose both ballots are "favorite A, also approved C."

Are you claiming C wins with certainty???

>Heitzig: Yes, of course. Doesn't that follow from the definition of the method? 
The set of options approved on both ballots is {A,C} of which C is the 
most approved member.

>Heitzig: Ah, now I understand the problem. I thought it was obvious that the 
favourite option is approved. Therefore the others were called "also" 
approved. So, to be precise: "Approved" means "favourite" or "also 
approved"

--WDS:
ok, let us review.  
The two drawn ballots are both "favourite A, also approved C" and btoh A and C are
approved.  I do not understand why C wins with certainty here.
Refer to the defn of the method at top.   If not the favourite "more approved"
than mere approval?  And even if both are considered equally approved
by the two ballots, then why is C winning with certainty?

wds
http://rangevoting.org