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

[Kristofer Munsterhjelm]

On 10/05/2014 08:02 AM, Toby Pereira wrote:
> From: Kathy Dopp <kathy.dopp at gmail.com <mailto:kathy.dopp at gmail.com>>
>
>  >>  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?
>
> Well, it changes the overall proportion they should have, but it does
> not change the 5:3 correct ratio of A to B seats. 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.

That sounds like house monotonicity. I don't know if my example is 
translatable to Approval voting, but this left-right-center example 
seems to show that it's not always desirable for ranked voting. E.g. 
something like:

43: L>C>R
34: R>C>L
12: C>R>L

If you have one seat, then C is a compromise candidate, doesn't give too 
much bias to either the left or right wing, and thus provides 
proportionality. But in the two-seat case, balance comes from electing L 
and R; LC would bias to the left and RC would bias to the right.

For this case, let L "really" be L1, L2, L3, ..., Ln; and the same with 
C and R. That means the ballots are really L1 > L2 > L3 > ... > Ln > C1 
 > C2 > ..., etc.

So in the one-seat case:

L: 0 seats
C: 1 seat
R: 0 seats

(w = 0, x = 1) is preferable to

L: 1 seat       w + 1
C: 0 seats      x - 1
R: 0 seats

but in the 2-seat case:

L: 0 seats      w = 0
C: 1 seat       x = 1
R: 1 seat

is not preferable to

L: 1 seat       w + 1
C: 0 seats      x - 1
R: 1 seat.

You could argue that these are "entangled" factions (each group of 
voters ranks all the candidates, not just those he supports). But then 
you might have to clarify it to say that it doesn't hold in the case of 
entangled factions.