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

I Like Irving donald at mich.com
Tue Apr 3 02:58:46 PDT 2001

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Martin,

You are in error when you claim that the individual districts of your
example are proportional.  This is not correct.  Each of your districts are
off by forty percent of a seat.  This is what makes your legislature not
proportional.  Your example is extreme, for in real life we could expect
some differences of proportionality to be offset by other districts.  But
as you concocted your example, you gave every district the same error of
proportionality, each received a forty percent loss for the same party, no
wonder the final results were off.

My original claim still stands, that was that if each district is
proportional then the total will be proportional.  This has nothing to do
with politics, it is pure mathematics.

The problem with small districts is that we can expect them not to be
proportional.

Five seats would be best for your sixty forty split districts.  If the
historical proportionality of the city has been sixty forty then I would
propose the following election system:
1) Two five seat districts.
2) Same quota for both districts, total votes of both districts
divided by twelve.
Both districts will elect six members if the voter turnout is about
the same for each district. If there is a difference of more than one
quota, then one district will elect seven and the other only five.
I like this sort of contest to get out the vote between the two districts.

But, I feel that a sixty forty split will be the exception, once the public
gets used to voting for more than one member per district.  The usual split
will become a near fifty for one faction and fifty for the other factions
together.  Under these conditions, an even number of seats for each
district will be best.

Besides, my original letter to Traxel also raised the question of gender
proportionality.  I repeat that concern.  If there are more than enough
qualified candidates of both genders, then the election method should allow
each gender to elect an equal number of members, if the voters wish to do
so.  An odd number of seats will not allow this to happen, an even number
of members in a district will allow this to happen.  This works both ways,
either male or female can be short one member in an odd member district.
It's not a shoo-in for the males to gain the extra seat.  Freedom of gender
proportionality is a valid concern.

Donald,

----------- Original Letter -----------
Date: Fri, 30 Mar 2001 19:47:33 +0100
From: Martin Harper <mcnh2 at cam.ac.uk>
To: election-methods-list at eskimo.com

I Like Irving wrote:

> LAYTON wrote:
> It's true that each electorate will be more
> proportional, but the body or legislature that is elected will be less
> proportional.
>
> Don: What you are saying does not compute.

Actually, you'll be interested to learn that it does compute.

> You agree with me that each
> electorate will be more proportional, but how can you say the legislature
> is going to be less proportional than the sum of its parts, that is, if all
> the electorates are proportional then the legislature must also be
> proportional.

Here's an example, for illustrative purposes. This is of course, just an
example: there are many many situations which could result in similar, or indeed
much worse, results. Also, while I will use Rep and Dem, the same could happen
with Male and Female, or Black and White, or indeed any other division you feel
is important.

Suppose that every district in Kansas has 60% Republican voters, and 40%
Democrat voters. There are three districts, and we're choosing 4 council members
from each district, for a total of 12. We also elect a mayor, who is the
thirteenth member.

Now, 60% of 13 is 7.8, so we should elect 8 Republicans, and 5 Democrats, if we
are to be proportional.

Now let's see what actually happens. The Republicans get their mayor elected,
with 60% of the votes. In each district, we give 2 seats to the Republicans, and
2 seats to the Democrats: this is a  proportional allocation, since 60% of 4 is
2.4. So, in total, the Republicans get 7 seats, and the Democrats get 5.

Now note that the individual districts are proportional, while the legislature
as a whole is not propotional. Now, you may claim that this nonproportionality
is unimportant, or won't happen in practice - but don't claim that it can't
exist...

Hope this helps,
Martin

Regards, Donald Davison - Host of New Democracy,  www.mich.com/~donald

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