[EM] Comparing ranked versus unranked methods

[Forest Simmons]

On Tue, 19 Feb 2002, Adam Tarr wrote:

> The problem with Webster and PAV is not its fairness in allocation, which 
> is arguably impeccable in the ideal, but rather its manipulability as 
> compared to d'Hondt.  Since d'Hondt has a (very slight) bias toward larger 
> parties, it eliminates the incentive to split parties and encourages 
> coalition building, which is crucial for PAV to work.

Good explanation.  If f(n) is the representation to be alloted a party of
size n, then two parties of size n/2 "earn" total representation of
2*f(n/2).  So if 2*f(n/2) is greater than f(n) there is a pressure towards
fragmentation. 

More generally, if for each pair of n and m such that both f(n) and f(m)
are one or greater it is true that f(n+m) is greater than f(n)+f(m), then
there is a pressure towards fragmentation of parties down to the minimum
quota size min{n: f(n)>0}.

Forest