# [EM] "unavoidable change" not enough?

Markus Schulze markus.schulze at alumni.tu-berlin.de
Tue Jan 1 06:13:07 PST 2002

```Dear Bart,

you wrote (30 Dec 2001):
> 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* ?

I guess that you are thinking of a criterion like this:

Suppose that the candidates are divided into two sets: X and Y.
Suppose that some voters vote some candidates of set X higher
without changing the relative order in which they vote the
candidates of set X and without changing the relative order in
which they vote the candidates of set Y. Then the winner must
not be changed from a candidate of set X to a candidate of set Y.

Especially for multi-winner elections this criterion seems desirable:
When some voters vote some Democrats higher without changing the
relative order in which they vote the Democrats and without changing
the relative order in which they vote the Republicans, then the
Democrats should not lose a seat to the Republicans.

However, this criterion is very expensive already for single-winner
elections. As far as I remember correctly, the MinMax method is the
unique single-winner Condorcet method that meets this criterion.

Markus Schulze

```