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

Kevin Venzke stepjak at yahoo.fr
Thu Mar 8 09:00:48 PST 2007


--- Warren Smith <wds at math.temple.edu> a écrit :
> > 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?

C has the most approval and will win whenever C is approved/favorite on
both ballots. When C is uniformly approved then C will always win no
matter which two ballots are drawn.

The only reason I can see that the "favorite" distinction exists is for
the case that there are not two candidates approved in common between
the two drawn ballots.

Kevin Venzke


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