[EM] Possibly making Sainte-Lague even more STV-like

[Vidar Wahlberg]

On Thu, Sep 05, 2013 at 11:42:44AM +0200, Kristofer Munsterhjelm wrote:
> So a Sainte-Laguë based on DAC or DSC is better than one based on
> Plurality - and we know how to do the generalization - but there
> isn't much else to be said about it. (It might also be weakly
> monotone, which would be nice since STV isn't.)

Will be a bit short as I've been busy lately.

I looked briefly into DAC/DSC, I couldn't visualize how to expand that
to a multi-seat system, though. May look more into it at a later time.

However, I want to elaborate a bit more on the SL/RP system I mentioned
earlier:
There were two issues you pointed out. First was that in an election
with 3 parties (L, C, R), strong support for L & R where all agreed on C
being the preferred winner in a 1-seat election, but in a 2-seat
election it would make more sense to let L & R to win.
This criticism I share.
On the other hand, when I implemented this idea I had a typical
Norwegian parliament election in mind (for 169 seats), so my question to
you would be; While this would not be a good system for few seats and
parties with distinguished differences, won't that problem quickly
diminish when you have significantly more seats and parties?

The second issue you raised was that an A>B>C>* preference, where A had
won some seats while B had not would not weight down the B>C preference
as it should. Again you're absolutely correct so I've changed the
implementation. Currently I've set it to be that with the same
preference, A having 2 seats and B having 3 seats and C having no seats
the weight for A>(B>C>*) would be 1/(2 * 2 + 1), the weight for B>(C>*)
would be 1/11 (2 * (2 + 3) + 1) and the weight for C>* would also be
1/11 (vote weight is the SL divisor for the accumulated amount of
seats). It's a small task to change the deweighting if it should be
more/less, or if the weight should be fixed (to 1/11 in this case) for
all preferences in the vote. I've not pondered much on either of these
aspects yet.
I've done some quick tests, and I do see some peculiar artifacts, like
not getting the exact same result when each vote only got one preference
as when using plain Sainte-Laguë. There are smaller changes, such as
some parties winning an extra seat while others losing one. I can only
imagine that this is because I'm currently using floating points rather
than rational number and thus get rounding errors, the algorithm is too
slow for rational numbers with the data sets I'm using. I will fix this
later.


-- 
Regards,
Vidar Wahlberg