Jobst, I think you misunderstood some of my comments, so we should go
around privately at least once before troubling the rest of the group
(or dropping this thread)...
It's only when preferences are trumping each other that approval
might become significant.
They do not trump each other in the set of those candidates which
are left after we considered all double defeats.
That's already understood. However, to claim the DMC method as its own
justification is a tautology. It begs the question of why it was valid
to drop a doubly defeated candidate when the only pair-wise defeat is
against someone other than the winner.
Immunity from 2nd place complaints... Otherwise a majority could
boycott the winner...
How does one boycott an office holder? This sounds like a Euro thing
not applicable in the US.
Whenever there is a Condorcet paradox, any candidate we choose as the
winner is going to face a majority that preferred another.
one opens the door to "first place" complaints.
What is this?
Complaints from the candidate with the highest approval rating --
presumably the most popular candidate (but not really, once tactical
voting runs rampant under DMC).
However, DMC sometimes treats one candidate's
approval as the reason that someone *else* should win,
How's that? Please give an example!
I already have... adding approval to your least threatening rival
increases your chances of doubly defeating your most threatening
rival, and it doesn't even matter if you over shoot and boost your
rival's approval above your own, DMC still picks you as long as you
win head to head.
What this does is motivate factions to add massive approval for
strategically chosen rivals, destroying its meaning as "approval".
We're left with the candidate having the most *first place* votes
being able to control the outcome of a paradox.
In short, DMC is interesting on its surface, but no more
interesting than any other cycle breaker.
It's not a cycle breaker.
It is what it is, whether you express it that way or not.
It does avoid looking at cycles altogether.
It may avoid looking, listening and speaking of cycles, but it breaks
them anyway.
That's one of the main advantages.
That's a mirage, a matter of appearance only. Cycles (Condorcet
paradoxes) can exist, and DMC resolves them whether you want to admit
it or not. You may not deny their existance (and DMC's handling of
them) just because DMC does not identify them on the way to selecting
its winner.
By using approval data to pick anyone other than the most
approved, DMC gives voters an incongruous motivation
Could you give an example...
I already have. Take a case where the second most approved candidate
wins DMC. There's someone further down the list among the doubley
defeated candidates who beat that winner head to head. If the most
approved candidate sees this coming, then he can win by drumming up
approval for that loser, turning our would-be winner into a doubley
defeated one, leaving #1 as the winner.
If you are looking for ABC's... You, Kevin and perhaps Forest are best
at manipulating those. I am not a mathematician. If someone can
demonstrate that candidates can never have enough maneuvering room for
insincere approval in paradox cases, then we will all be grateful.
Otherwise, I'll assume that candidates in DMC will be telling their
supporters to falsely approve rivals they beat pair-wise.
-- JRF
