[EM] "unavoidable change" not enough?

[Bart Ingles]

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.

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]

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.  What
would you call it, *multiple monotonicity* ?

Bart


MIKE OSSIPOFF wrote:
> 
> 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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