# [EM] General PR question (from Andy Jennings in 2011)

Kathy Dopp kathy.dopp at gmail.com
Sun Oct 5 09:34:53 PDT 2014

```On Sun, Oct 5, 2014 at 2:02 AM, Toby Pereira <tdp201b at yahoo.co.uk> wrote:
> From: Kathy Dopp <kathy.dopp at gmail.com>
>

>>First, adding more voters (group C) means that the denominator of the
>>ratio (proportion) for each (every) voting group changes.
>>How could I change the denominator of the quantity v_i/v (the
>>proportion of each voting group)  without changing the proportion of
>>seats that each group should have?
>
> Well, it changes the overall proportion they should have, but it does not
> change the 5:3 correct ratio of A to B seats.

Yes. However, it changes the NUMBER of seats allocated in the 5:3
ratio, allocating those seats in EXACTLY proportional fashion.  I.e.

For three seats:

5 voters 1.875 seats  gives 2 seats
3 voters 1.125 seats  gives 1 seat

For four seats:

5 voters 2.5 seats - a tie for the forth seat gives 2 or 3 seats
3 voters 1.5 seats  - a tie for the forth seat gives 2 or 1 seats

It's just SIMPLE arithmetic.

If you don't like it, then you are arguing AGAINST PROPORTIONAL

> I would argue that if
>
> Faction 1: w seats
> Faction 2: x seats
> Faction 3: y seats
>
> is more proportional than
>
> Faction 1: w+1 seats
> Faction 2: x-1 seats
> Faction 3: y seats
>
> then with the same voting patterns
>
> Faction 1: w seats
> Faction 2: x seats
> Faction 3: z seats
>
> is more proportional than
>
> Faction 1: w+1 seats
> Faction 2: x-1 seats
> Faction 3: z seats
>
> for any x, y, w, z. Sainte-Laguë, D'Hondt and my system fit this criterion.

Yes. I AGREE and so does my formula minimization algorithm.

However, you have just altered your example from our prior discussion
by including a third faction in each example; whereas, in all your
prior examples you were comparing the split of candidates with and
without a third faction (i.e. you were comparing having two factions
versus three factions) and you are insisting on using a system of
allocating candidates that was Not proportionate.

I obviously agree with your new altered example which has three
factions and the same number of candidates in both cases.

--

Kathy Dopp
Town of Colonie, NY 12304
"A little patience, and we shall see ... the people, recovering their
true sight, restore their government to its true principles." Thomas
Jefferson

Fundamentals of Verifiable Elections
http://kathydopp.com/wordpress/?p=174

View my working papers on my SSRN:
http://ssrn.com/author=1451051
```