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

[Kathy Dopp]

On Mon, Oct 6, 2014 at 12:39 PM, Toby Pereira <tdp201b at yahoo.co.uk> wrote:

>
> I'm not sure I follow. Are you saying I calculated the numbers incorrectly?

I believe your numbers were OK, just not the interpretation of the
minimum one being the more proportional.

> If not, then in the first example 2/0 gave a score of 100.505 (lower - more
> proportional)  and 1/1 gave a score of 101 (higher - less proportional), so
> 2 seats to the largest faction was the winning result.
>
> In the second example, 2/0 gave a score of 101.502 (higher - less
> proportional) and 1/1 gave a score of 100.002 (lower - more proportional),
> so one seat each was the winning result, so the result swapped depending on
> whether the smallest faction had 1 or 3 voters (and no seats allocated in
> either case).

Yes.  With fewer voters, the 300 voters are a relatively larger
proportionate share of the entire population and so merit both seats,
given true proportionality.

I agree with you that this result is truly on the cusp.

However, this again is *not* a case of an irrelevant faction or
candidate altering the results because if you remove that faction with
one voter entirely, you still get the same resulting proportionate
apportionment of two candidates to the group with 300 voters.

Thus it is true, that varying the amount of voters in any one faction,
while holding the number of voters in other factions constant, will,
at some point, alter the overall proportions of the voters in other
factions relative to the number of seats that are proportionate under
a truly proportionate system.

So, perhaps there is an improved alternative over a truly
proportionate allocation of seats to voters. Perhaps the voting groups
who cannot win seats should be taken out of the equation as, I
believe, some party list systems do when calculating winners.

In the example you just gave, increasing the number of seats to 3
would solve the problem of under-representation of the slightly less
than 1/3rd of voters  who don't get a seat.  Some theory says
candidates will move position to attract more voters away from the
larger group in this case.

Your example is something to consider, I agree.


-- 

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