[EM] Jeff Fisher's concern about DMC

Simmons, Forest simmonfo at up.edu
Wed Sep 7 10:15:49 PDT 2005

Here is an "ABC" example that illustrates Jeff Fisher's concern as I understand it (see below):
Sincere zero info ballots:
45 A>>C>B
20 C>>B>A
35 B>>A>C
Pairwise cycle is A>C>B>A.
Approval order is A>B>C.
So the sincere DMC winner is B.
But in the near perfect information case the A faction might decide to strategically approve C, resulting in
45 A>C>>B
20 C>>B>A
35 B>>A>C
and an approval order of C>A>B,
which would make A the DMC winner.
If all three factions resort to this gratuitous approval strategy, then the approval order becomes A>C>B, which still gives the win to A.
As Jeff notes, the advantage of DMC over ordinary Condorcet without approval cutoffs seems to be lost, since without the approval cutoffs River, MinMax, Beatpath, and Ranked Pairs (whether margins or wv) all agree on A as winner.
Here are some of my feelings about this:
1.  If DMC does better than the other methods in the zero-info case, and does just as well in the informed cases, then DMC is still an improvement over the other methods.  (And DMC has all of the other 14 advantages as well.)
2.  The largest faction has a definite advantage in these strategical games.  If the other factions are unwilling to cooperate against the largest faction, then the largest faction has a strong claim on being the rightful winner.
This second point is also my answer to those critics of Top Two Approval Runoff that complain that the strongest faction could get a strawman into the runoff with the highest approval candidate.  I say that if they are that strong, and their opponents that fragmented, then they deserve to decide the winner.
My objection to Top Two Approval Runoff is that it is a very minor improvement on Approval at a large cost ... the need for pairwise information.  In a small group setting it would be very reasonable.
3. Most people (including Markus recently) complain that approval cutoffs are apt to be too stingy.  But here's a pressure in the generous approval direction.
4.  DFC doesn't suffer from this strategy problem, since giving C more approval than A gives C (whom the A supporters do not really approve of) a significant probability of winning, too.
On Thu 9/1/2005 10:50 AM, Jeff Fisher wrote ...

I have a problem that I posted in an Electo-wiki discussion last week; it
has no replies yet:


If a faction sees a Condorcet paradox looming, can it gain an advantage by
insincerely approving of the contender that it expects to defeat pair-wise?

Your polling data: Approval runs narrowly A>B>C, but pairings run A>C>B>A,
so 'B' stands to win under DMC. You're the tactician for faction 'A'. Can
your supporters insincerely increase approval of 'C' in order to eliminate 'B'?

If so, then it doesn't even matter if you over-do it and push your spoiler
ahead of yourself in approval: As long as you expect to win head to head,
you may hand out approval points with impunity and perhaps steal a victory.

Of course, once your faction's plan leaks out, 'C' will boost 'B', and 'B'
will boost you... and the faction controlling the most first place votes
will bury its nemesis and prevail.

So, in practice, will DMC degenerate into basic Condorcet with whatever
limitations that has?

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