[EM] James, 4 March, '05, 0435 GMT (meaninfgulness and sameness)
James Green-Armytage
jarmyta at antioch-college.edu
Tue May 3 23:38:00 PDT 2005
Mike,
You are ignoring the obvious.
1. Here is a standard MMC definition, as it applies to ranked ballots:
"If more than half of the voters rank all candidates in set S above all
other candidates, then the winner should be a member of set S."
2. Like many ranked ballot criteria, MMC cannot be meaningfully applied to
non-ranked-ballot methods without being adapted in some way. You adapt it
as follows:
"If a set of voters consisting of more than half of the voters prefer all
the candidates in set S to all the other candidates, and vote sincerely,
the winner should be from set S."
3. I think that this is a meaningful adaptation, which retains the intent
of the original criterion. I assume that you will agree, since you wrote
it.
4. Here is a standard MC definition, as it applies to ranked ballots:
"If more than half of the voters rank candidate X above all other
candidates, then the winner should be candidate X."
5. Notice that MC is nothing more than a special case of MMC, where set S
contains only one member. Hence, the only difference between the
definitions of MMC and MC is that one replaces "candidates in a set S"
with a single candidate, e.g. "candidate X".
6. Thus, if we accept that the MMC definition given in (2) is a meaningful
MMC definition for non-ranked-ballot methods, then it follows (by 5) that
this is a meaningful MC definition for non-ranked-ballot methods:
"If a set of voters consisting of more than half of the voters prefer
candidate X to all the other candidates, and vote sincerely, the winner
should be candidate X."
My question to you is simple: Why are your MMC and MC definitions for
non-ranked-ballot methods so different from each other, when MC is just a
special case of MMC where the majority set has one member? If you use the
MMC definition in (2) to evaluate non-ranked-ballot methods for MMC
compliance, why not use the corresponding MC definition in (6) to evaluate
non-ranked-ballot methods for MC compliance?
Sincerely,
James
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