[EM] automatically-changed marks. Monotonicity.

[MIKE OSSIPOFF]

>>But I think it's reasonable to assume that
>>when we refer to changing X's rating, that doesn't include changing 
>>someone
> >else's rating too..."
>
>Mike is right: it IS reasonable to assume that when we refer to changing 
>X's
>rating, that doesn't include changing someone else's rating too.
>

I realize that in Plurality or in rank-balloting, changing how we mark one 
candidate
can automatically change how we mark another candidate. So I should have 
said
that changing how we mark one candidate should, reasonably, not include 
_avoidably_
changing how we mark another candidate.

By how we mark a candidate, I mean how we vote him, determined without
regard to or comparison to how we vote other candidates on the ballot. 
Examples are
what rank position we give to him, what points rating we give to him, 
whether or not
we vote for him. Sure, the rank position that we give to him invites 
comparisons to
other candidates, but it's a number that we give to him that can be looked 
at without
considering other candidates.

Here's a possible way to define voting a candidate higher:

A voter, John, changes his ballot to vote Smith higher if he changes how he 
marks
Smith on his ballot in such a way that it's possible to contrive other 
voters' ballots* so
that, when we then make that change, Smith, on John's ballot, is then voted 
over a
candidate over whom he wasn't voted before the change.

*unchanging ballots

[end of definition]

As Richard said, of course unforseen problems can lurk in a definition. When 
they do,
we work them out when we find them.

Of course in rank-balloting or Plurality, when you vote Smith higher that 
might mean
that you automatically thereby vote Jones lower, as Joe pointed out.

Here's an attempt to define Monotonicity:

If, by a certain set of ballots, candidate Smith wins, then if we modify 
some of the
ballots by changing how they mark Smith, in such a way as to vote him higher
without voting anyone else lower or higher except where that's an unavoidabe 
result
of voting Smith higher, then, after we've made that change, Smith shouldn't 
lose.

[end of definition]

One could add a similar paragraph about when Smith loses and someone votes 
him
lower, but it wouldn't be necessary.

Maybe that definition could be made more brief, or replaced by something 
more brief.
Possibly it has a flaw that I haven't noticed, of course.

Mike Ossipoff


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