[EM] question/comments re DMC

[Warren Smith]

OK, Now that I finally understand the DMC voting system (which is quite interesting), 
I have a few comments and questions...

>(15+3 reasons to love DMC from J.Heitzig & F.Simmons)
> 1. Allows to distinguish important from minor preferences. 

--range does too, only better.

> 2. Immunity from second place complaints. Unlike in MinMax and 
> Beatpath, the DMC winner always defeats the candidate which would win
>  if the winner were not present. 

--nice. Also true of range.

> 3. Smith-efficiency. The DMC winner
> always has a beatpath to each other candidate...

> 15. [related to 3] Defeats other methods. In every situation, the DMC 
> winner is either identical to or defeats the winner of each of the 
> following methods: Approval Voting, Condorcet//Approval, 
> Smith//Approval, DFC, TAWS.

--I consider this criterion 15 to be artificial.  No matter what ranked ballot method you
have (X) I con construct a new one Y so the Ywinner always is same as or beats the Xwinner
pairwise.  In particular I can make X=DMC to get Y=a method that pairwise beats DMC...
This fact suggests to me that this criterion is meaningless...

> 4. Good defendability of the winner against contenders. In addition 
> to Immunity from second place complaints and Smith-efficiency, the 
> DMC winner also always defeats her most approved contender (unlike 
> Condorcet//Approval, Smith//Approval, Beatpath). More generally, the
>  DMC winner always defeats or is more approved than any other 
> candidate (unlike in Beatpath).

> 5. Strange winners are seldom. Unlike in Beatpath, the least approved
>  candidate cannot win in DMC unless she defeats all other candidates.

> 6. Robustness against "noise" candidates.. cloneproof...

--also true of range.

> 7. Easy and transparent algorithm. 

--way truer of range...

> 8. Robustness against counting errors. Since DMC uses only the 
> ordering by approval score and not the precise approval scores, and 
> uses only the direction of the pairwise defeats...

--sounds kind of silly claim to me, and anyhow is truer of range since range has
fewer tie-possibilities that can matter.

> 9. Avoids margins/winning votes debate.

--truer of range...

> 10. Avoids a discussion of "cycles"...

--also true of range...  and probably truer...

> 11. Allows to construct a complete ordering. If necessary, one can 
> also assign final ranks to all candidates such that the k-th ranked 
> candidate is the DMC winner when all k-1 candidates above her are 
> removed from the race. This ordering arises naturally from the 
>  is a pair of 
> neighboured candidates in the list such that the lower candidate 
> defeats the upper candidate, swap the topmost such pair. When no such
>  swappings are indicated further, each candidate defeats the next 
> one, the DMC winner is listed on top, and the candidate listed at 
> k-th position would become the DMC winner when all k-1 candidates 
> above her were removed.

--truer of range more simply...

> 12. Combines instead of separates the available types of information.
>  DMC combines the approval and ranking information...

--so does range (albeit different interpretation of words, you need to be a bit generous)

> 13. Monotonicity. Unlike IRV, DMC is monotonic, that is, reinforcing
>  the DMC winner on some ballots cannot turn her into a loser.

--I would like to know more about this.  In private email I was complaining to Heitzig
that I did not see an evident "meaning" of the "last-approved level" datum (call it L) 
supplied by the voter in addition to the rank-ordering.  
It does not seem to me really to have anything to do with
voter satisfaction with candidates, except in Heitzig's mind - I argued
to him that L was merely a move in a game with no evident connection to voter
satisfaction with anybody.  I said to him I wanted to know about DMC voting strategy so
that I could feel such a connection existed...  Anyhow, after a bit more thought...
I think one could go a long way toward alleviating my complaint by proving (if true)
the following TWO MONONITICITY PROPERTIES:
  M1:  interchange order of two neighboring candidates in your rank-order vote ==>
     (A>B becomes B>A) cannot decrease B's chance of winning, cannot increase A's.
  M2:  minimally change your vote so now approve of A ==> cannot decrease A's chance of winning.
Which of these are true? Both?

> 14. Clone-proofness.

--Also true of range.  (I keep harping on this since I'm nasty, but also in some sense it
seems to me that DMC is striving to try to turn condorcet methods into something more
like range voting, but it would be simpler just to use range voting.  :)

> 16.  Like any method that makes germane use of both ordinal and
> approval information it is well adapted to three-slot ballots, i.e.
> voters that don't want to submit complete rankings can opt to have
> their approval order extended by the order of their favorite.

--(also true of range)
I'm a bit worried here.  Heitzig was telling me DMC could be done with equality rankings
like A>B=C>D=>F too.  However...  in the plain Condorcet world, permitting equalities
*and* using winning votes makes a big difference and you need to do *Both*
to reap the benefits.  So I would like to know how DMC handles that, in view
of the previous remark 9 that DMC eliminated  the margins/winnign votes debate.

Heitzig was also telling me he supported DMC using partial-ordering votes not
merely full orderings.  But then again issues arise... there is no such thing
as "last approved level"...  I think more thought is desirable...

> 17.  It is resistant to the burying strategy that plagues some
> Condorcet methods.  This is related to reason number 9.

--could you be more precise?

> 18. "DMC" is a better name.  It doesn't matter if the D stands for
> Definitive, Definite, or Democratic, "D Majority Choice" is a good
> sell.

--:)

wds