[EM] Hybrid/generalized ranked/approval ballots

[Kristofer Munsterhjelm]

Peter Zbornik wrote:
> Kristoffer,
>  
> just a small P.S. to my email below.
>  
> Maybe the problems with the incomplete ballots and dynamic quotas below 
> have something to do with electing a fixed number of seats.
> That's just a hunch.
>  
> I think you mentioned that a variable number of seats might give better 
> proportional representation than a fixed number.
>  
> However electing a variable number of seats will probably have little 
> political support in my party, so this question is more a question out 
> of curiousity.
>  
> Peter

It's relatively easy to see that variable number of seats can give 
better PR than a fixed number. Consider a party list situation like this:

50: Party A
50: Party B

If the number of seats is fixed to an odd number, then either A or B 
will be given undeserving majority. If the number of seats is variable, 
then that shouldn't happen - the method, if sensible, would determine 
that an even number of seats would be more accurate and so use it.

The same sort of reasoning can be done with any fraction. If each party 
is supported by an exact fraction of small (but different) denominator, 
then it might be possible to represent every group "perfectly" by a 
council of size equal to the least common multiple, or some factor thereof.