[EM] FW: Google Alert - "proportional representation"

[Kristofer Munsterhjelm]

On 02/06/2014 12:23 PM, James Gilmour wrote:
> This paper MAY be of interest.
>
> The full text can be downloaded via the “Download” link on the top right
> of the screen.

This makes sense. They're trying to "leximaxize" Monroe's method in a 
similar way to how Tideman is a leximax version of Kemeny. As we know, 
Tideman/Ranked Pairs runs in polytime while Kemeny does not.

It doesn't seem that they had as much luck in the proportional methods 
case, though, since both methods stay NP-hard unless the voters are 
single-peaked. Still, I suspect (as I do with Kemeny) that for practical 
numbers of voters and candidates, it'll be practical. At least that's 
what I remember when doing some Kemeny and Monroe tests of my own.

On a side note, perhaps Courant's method could be used for party list, 
since it produces groups of different sizes. Just make the number of 
representatives from each party proportional to the size of the cluster 
that picked the party in question as representing them. This can easily 
be done by, say, Sainte-Lague once the weights are known. However, I 
don't know what method it would reduce to when voters plump for a single 
party. Hm. Could be interesting to find out.

(Now that I think about it, it might just reduce to the method used for 
the proportional division. Possibly, the cluster for party X would 
contain everybody who plumped for party X, so you'd get an ordinary 
Plurality count for the weights, which when passed through 
Sainte-Lague/D'Hondt/some other rounding method reduces simply to that 
method used as party list alone. But it still remains to see whether it 
would be a fair allocation when the voters *don't* plump.)