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

[Jameson Quinn]

2010/5/20 Raph Frank <raphfrk at gmail.com>

> 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.
>
> I was talking about SPA, not SAV. SPA (summable proportional approval) is a
summable method which, with very high probability, corresponds to Sequential
Proportional Approval, first proposed by Thiele (c.1890). This in turn
corresponds, with high probability, to the following simple procedure, which
I think is easy enough for anybody to understand:

1. Collect approval ballots
2. Count the ballots and elect the approval winner
3. Select a droop quota of ballots which approve the approval winner and
discard them. First discard ballots which only approve already-elected
candidates; then randomly select the rest. If there are not enough ballots,
discard all available.
4. If the council is not full, repeat from step 2.

If you want to arbitrarily decrease the already-very-low probability that
this procedure doesn't correspond to Sequential Proportional Approval, then
simply repeat it an odd number of times and choose whichever candidate wins
the most.

Both SPA's meet the criterion above, though they are not exactly equivalent
(only probabilistically so).

JQ
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