[EM] PR and monotonicity

Kevin Venzke stepjak at yahoo.fr
Wed Jul 16 21:17:35 PDT 2003

 --- Clinton Mead <cryptor at zipworld.com.au> a écrit : 
> Is there a system that passes all three of the above criteria? I've been 
> thinking about this, and I can't seem to get monotonicity and 
> proportional representation to go together. Or is this the start of a 
> new arrows theorem, there is no "proportional representation system" 
> (even when we don't include Independence From Irrelevent Alternatives).
> Clinton Mead.

This probably isn't academic enough for you, but I think monotonicity and
proportionality intuitively can't co-exist.  Let me show why I think so
(sorry these are Approval ballots, but it may still demonstrate my thought):

33 A
31 BC
2 B
34 D

Say we're filling 3 seats.  "ABD" looks best, because they cover everyone.
But what if the 34 D voters voted BD instead?  Now it's not proportional to
elect B (too much power to the BD voters); C should take his place.  B loses by 
getting more votes.

In short, monotonicity means you can't punish someone for getting more votes.  
That can be completely at odds with proportionality.

(With Approval ballots, I suspect the only monotonic multiwinner method would
be to take the top N candidates.  Not proportional, of course.)

Kevin Venzke
stepjak at yahoo.fr

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