[EM] "unavoidable change" not enough?

[MIKE OSSIPOFF]

It's just occurred to me that if I move Smith from 5th place to 1st place, 
and move my
2nd through 4th place candidates down one rank position, it could be said 
that that
isn't an unavoidable change in how I mark the other candidates, since it 
could be
argued that that particular change could be avoided by making it into a 
different change,
by reversing some other candidate pair. I probably made the unspoken 
assumption that
all the other candidates are kept in the same order, for the unavoidable 
change in the
other candidates' marks on that ballot.

So here's perhaps a better wording of Monotonicity:

If, by a particular set of ballots, Smith wins, then modifying some of the 
ballots so as
to vote Smith higher, if possible without changing the order in which those 
ballots vote
the other candidates, if possible without changing how the other candidates 
are marked
on those ballots, then, after that change, Smith shouldn't lose.

[end of definition]

A similar change can be made in my definition of a fixed way for John to 
mark the
other candidates:

A way for John to mark the other candidates that, if possible, doesn't 
change the
order in which John's ballot votes those other candidates when John changes 
how
he marks Smith, and which, if possible, doesn't change how it marks those 
other
candidates when John changes how he marks Smith.

[end of definition]

These definitions are contrived to give the expected results with the 4 
kinds of balloting
that we encounter the most: Approval, CR, rankings, & Plurality. It isn't 
based on a
general study that would guarantee that it would give expected results with 
all
methods, or even with all proposable methods, and so it probably isn't the 
satisfactory
Monotonicity definition that Forest & Richard were looking for. It's 
intended more as
a stopgap.

My previous definition sounded more general, but I don't know if it could be 
made
airtight without making reference to keeping the other candidates in the 
same order.

My definitions before today, for Monotonicity & a fixed way of marking the 
other
candidates, I call that my "unavoidable change" definitions. Today's 
definition I call
my "if possible" definitions.

Maybe the unavoidable-change definitions can be fixed. I'd previously felt 
that
when we vote Smith higher in a ranking, the change in the other candidates' 
marks that
keeps them in the same order is unavoidable, but any change from that is 
avoidable.
Now that doesn't seem so justified to say, which is why I'm posting today's 
definitions.

What is the date or the message number for Forest's & Richard's latest 
definition
of Monotonicity?

Mike Ossipoff


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