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

[Jameson Quinn]

2010/5/20 Kristofer Munsterhjelm <km-elmet at broadpark.no>

> Jameson Quinn wrote:
>
>> If you're looking for simple proportional systems, you could look at
>> "total representation", where district-based representatives win with a
>> majority, but some extra seats are assigned to the highest-vote-getting
>> losers of underrepresented parties to help balance.
>>
>> I believe that SAV is not that great a system. It requires too much
>> strategy from the voters; you have to know how many voters like you there
>> are in order to know how much to split up your vote. A faction which spread
>> its vote to thin could end up entirely unrepresented - even if it were a
>> majority faction.
>>
>
> > I would propose SPA (Summable Proportional Approval) voting.
>
> [...]
>
>
>  The math is complicated. However, it's only to make the process summable,
>> and thus to make recounts verifiable. If you don't need summability, you
>> just reweight the individual ballots to deduct a Droop quota, which is
>> trivial mathematically.
>>
>
> Hm, that's an interesting approach. The problems of reweighting
> a weighted positional system doesn't appear in your method as there are
> just two levels - approved and not (somewhat like Plurality in that
> respect).
>
> Does SPA meet the following criterion?
>
> "If more than k Droop quotas approve of p candidates, then at least
> min(k,p) of these candidates must be elected".
>
> (I'm not sure if it can be met, but it seems like a reasonable Approval
> extension of the Droop proportionality criterion)
>
> 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.

You can make a stronger, harder criterion: "If more than k Droop quotas
approve of no candidates outside the list P of p candidates, with p>k, and
each voter from this group approves at least (k+p)/2 of them, then at least
k of these candidates must be elected". I believe that SPA passes this
criterion, but I haven't proven it yet.

JQ
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