[EM] Satisfaction Approval Voting - A Better Proportional Representation Electoral Method

[Raph Frank]

On Thu, May 20, 2010 at 4:54 PM, Jameson Quinn <jameson.quinn at gmail.com> wrote:
> The relevant criterion is "If more than k Droop quotas approve of p
> candidates ONLY, then at least min(k,p) of these candidates must be
> elected". Otherwise, if you have 2 droop quotas approving 4 candidates, then
> the method fails because you apply the criterion just to the 2 unelected
> candidates.
>
> And yes, SPA does pass the criterion as I stated it, and I can prove it.

I am not sure this is true.

If there is 2 seats and 6 candidates, and the votes are

60: A1, A2
40: B1, B2, B3, B4

Results:

{A1,A2} gives satification
60: 100%
40: 0
Total: 6000%

{A1,B1} gives satification

60: 50% (= 3000%)
40: 25% (= 1000%)
Total: 4000%

This means that the {A1, A2} option beats {A1,B1} and by symmetry that
means that the A faction get 2 seats.

This breaks Droop, as the B faction is entitled to 1 seat, as they
represent more than a Droop quota.