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

Kathy Dopp kathy.dopp at gmail.com
Sat Oct 4 16:12:41 PDT 2014

```On Sat, Oct 4, 2014 at 6:17 PM, Toby Pereira <tdp201b at yahoo.co.uk> wrote:
>
>  What I'm saying is
> that in your system, adding C changes which out of A or B is more deserving
> of the final seat, which seems wrong to me.

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?

v_i/v * s

That would be magic -- ignoring counting and calculating the
proportion of total voters each group comprises.

> When [AFTER] the first three seats are
> allocated, with C as part of the election, according to your system, the
> order of how deserving each group is to the next seat is C>B>A. B is more
> deserving than A.

Yes.

> However, if C is not there, you get A=B.

No. I think what you mean to say is that after allocating 2 winning
seats to group A and 1 to group B, group A and group B both are owed
1/2 a seat each to be proportionately fair, so that   2 candidates
each for group A and group B would be equally proportionately fair as
3 candidates for group A and 1 for group B.

> But why should
> the presence/absence of C make a difference to whether 3 seats to faction A
> and 1 to faction B or two seats each to A and B is the more proportional
> result?

C's presence makes a difference because group C wins one of the 4
seats, so that only 3 seats are divied up between group A and B.  C's
leaving does not change (by one iota) the division of the first 3
winning seats. Group C's absence merely makes a 4th seat available to
divy up between two groups rather than between three groups!

> It shouldn't. In that sense, C is irrelevant. Specifically, C is
> irrelevant to which out of A and B is furthest from their proportional
> allocation.

AGAIN, you are using a perverted definition of "irrelevant" that I
know of no one else who agrees with you. Group C is awarded 1 WINNING
CANDIDATE, so if group C is absent, there is one (1) more candidate to
award to the remaining groups.

>
>
>>5: A1, A2, A3, A4
>>3: B1, B2, B3, B4
>>1: C1, C2, C3, C4
>>How are you redefining the word "irrelevant" to label voting group C
>>as "irrelevant"?
>
> It's irrelevant to whether A or B is more deserving of the final seat
> (regardless of whether C is more deserving than both).

Obviously not.  If group C does not exist, there are only 8 voters in
your example, not 9 voters. Therefore, the relative proportions MUST
change between the two remaining groups unless you think magically
reducing the denominator in the proportion of voters calculation
should not alter the proportion of voters that each group comprises.

Again, you seem to have difficulty with the way the arithmetic of
fractions work, as I believe I observed in the first of your emails I

I think we're just going around in circles, so I'm ignoring the rest

You cannot remove or add voter groups who are voting for unique
combinations of candidates without altering the relative proportions
of voters out of the total population of voters because the total
number of voters is the denominator in every calculation of the
proportion of voters a voting group is.

--

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
```