MIKE OSSIPOFF nkklrp at hotmail.com
Sun Dec 30 19:54:25 PST 2001

Bart wrote:

I think I have actually seen definitions of monotonicity which already
take this into account. You only need to specify that the remaining
candidates stay in the same relative order -- no need to mention
"avoidable/unavoidable changes" since such changes are always avoidable.

But you can't specify that the other candidates remain in the same relative
order,
since that would be violated in Plurality. Say your vote is on Jones, but
then you
vote Smith higher by moving your vote from Jones to Smith. Before you did
that,
you were voting Jones over the other candidates, and now you no longer are.
You've changed the relative order of how you're voting the other candidates.

Well I guess you could say that the meaning of a change in order doesn't
include
voting A equal to B when you'd previously voted A over B. But I don't know
how well
that would work when the criterion is applied. It seems better to allow for
Plurality's
change in order.

Bart continued:

So maybe something like [starting from Mike's proposal]:

[begin definition]
If, by a particular set of ballots, Smith wins, then modifying some of
the ballots so as to vote Smith higher *without changing the relative
order* in which those ballots vote the other candidates, then, after
that change, Smith shouldn't lose.
[end of definition]

Again, there's the problem that there's a good case for saying that, when
you
move your vote to Smith in Plurality, you're unavoidably changing the order
in which
you vote the other candidates, when you take that vote from Jones, whom
you'd
previously voted over everyone.

Also, why allow any avoidable fudging of how we vote the other candidates?
In Approval
and CR it's possible to vote Smith higher without in any way changing how we
mark
the other candidates, and when we apply Monotonicity to those methods, isn't
that
the kind of ballot-change that we're talking about? Maybe it isn't necessary
to say
that if possible we don't change the other candidates' marks, but even if we
can get
by with that, in the sense that the criterion works ok that way, when we
speak of voting
Smith higher in Approval or CR, we don't mean also changing other people's
ratings.

Bart continued:

I have never heard of a definition of monotonicity which attempted to
deal with situations where more than one candidate is modified in
relation to the remaining candidates. I think you would be opening a
can of worms by doing so, & don't know what the value would be.

Yes it's a can of worms, but it's already open, and the question is how to
put the worms
back in the can.

It's something that can't be ignored in Monotonicity, since with Plurality
you can't vote Smith higher without changing how some other candidate is
voted in
relation to other candidates. (The candidate from whom you took your vote
when you
moved it to Smith).

Mike

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