Kevin Venzke stepjak-at-yahoo.fr |EMlist| wrote:
However, Majority Defeat Disqualification Approval ("MDDA," a good name even
without the punctuation) satisfies SFC, which at first glance seems to
require a beatpath notion: In practice, it seems to say that if there is a
(majority) defeat A>B but no defeat anyone>A, then B can't win, while if I
add a win C>A then B is no longer barred from winning. But MDDA "goes beyond
the call of duty" by making all of the defeats damning, and if all candidates
are damned, then adding C>A can only make A lose, no one else. So MDDA
satisfies FBC and SFC without the use of beatpaths, although it does use
a pairwise component.
Kevin,
You know how I feel about the concept of "majority defeat" for a
pairwise race. I believe that *any* pairwise defeat is by definition a
"majority" defeat because it requires a majority to vote for the defeat,
where "majority" is defined in terms of the number of voters who chose
to participate in that particular pairwise race.
We don't seem to be converging on this, but let me propose a criterion
to support my view. I'll call it the "Blank Ballot Criterion," or BBC
(if that acronym is not already taken). The criterion is that a blank
ballot should count as a vote but should not affect the final result. A
voter may turn in a blank ballot as a form of protest, indicating that
he disapproves of *all* the candidates. His ballot should count as a
valid vote, but it should not affect the final result.
No method that depends on "majority defeats" can pass this criterion if
it defines a majority it terms of the total number of voters.
Consider the case in which a voter votes on some offices in an election
but "abstains" from voting on others. How should his vote be interpreted
for the offices he does not vote on? Should he be considered a non-voter
for that office, or should his vote be interpreted as disapproval and
equal-last ranking of all the candidates? If the method passes BBC, the
interpretation doesn't matter. If it does not pass, then you need to go
into the mind-reading business and declare the voter's intention. That's
a bad business to be in when it comes to elections.
--Russ
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