[EM] Clarification of AERLO & Strong FBC
MIKE OSSIPOFF
nkklrp at hotmail.com
Tue Apr 6 17:03:11 PDT 2004
Sorry, I was in a hurry when I wrote my most recent reply about that.
Say the method is ERBucklin(whole), with AERLO, and you rank X in 1st place,
and Y in 2nd place. And say you make your automatic equal ranking line
somewhere below Y.
That ballot votes X over Y by the definitions of that term that have been
posted here. And that ballot votes X over Y in the meaningful sense of the
term: If it turns out to be between X & Y, and if it's close enough, then
your ballot (especially combined with another X>Y ballot) could change the
winner from Y to X.
If no one above your AERLO line wins, then Y and everyone else above that
line are automatically promoted to 1st place, with X. But that doesn't
change the fact that you're meaningfully voting X over Y.
So, the that ballot's voter isn't ranking voting anyone equal to hir
favorite. Strong FBC isn't violated by the fact that AERLO could promote Y
to 1st place if needed.
So the answers to question 2 are:
Butcklin needs equal ranking because it doesn't meet Strong FBC. But with
equal rankings, and with AERLO added, the resulting method meets Strong FBC
(unless I've overlooked something, of course).
The voter doesn't need to rank anyone equal to his favorite, in the sense
that, for any outcome (outcome 1) that s/he could get by doing that, there's
an outcome to which that voter doesn't prefer outcome 1. In other words, an
outcome just as good as outcome 1, as judged by that voter.
I use the word "prefer", because we've discussed its meaning here.
AERLO might rank someone equal the that voter's favorite, but the voter
needn't do so. If that sounds like a mere evasion, then I repeat that the
voter who voted the ballot described above has voted X over Y in the most
accepted, meaningful sense of the term.
Mike Ossipoff
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