[EM] Martin's Sixty-Forty Split Districts:

[LAYTON Craig]

Martin wrote (in part):

>Thus in both cases the sum is more proportional than the sum of its parts.
In
>particular, the five seat districts create a more proportional council,
despite
>being individually much less proportional than the four seat districts.

Great example.

>I've tried to make this example a little less extreme than the previous one
- at the
>expense, sadly, of simplicity.

The simplest way to think about it is in terms of 1 person electorates or 2
person electorates.  2 person electorates will elect the same number of
people (1 from each party) whether the support is 30%-70% or 50-50.  With a
significant number of 1 person electorates, the number of reps will tend to
be closer to the proportion of support.  It's a law of averages thingy.

>Whether, in general, it is better to have odd or even numbers of seats in
each
>district is beyond my ability to determine - but Layton appears to be able
to do so,
>and claims that odd numbers of seats will give a more proportional council
in
>general. Perhaps you should check out what he has to say?

I should point out that odd numbers will only be more proportional if you
have a two party system and a small number of members per district.  But STV
districts are rather mercurial; throw in a few strong minor parties and
independants and all your calculations fall to bits.  For instance, with a
single strong minor party (three party support ratio 40:45:15) you would
probably get a more representative legislature from six member districts
than with five or seven.

I say odd numbers because it appears that on average, they wind up being
more proportional.