STV without Elimination

[David Catchpole]

> 5 Seats
> 3 Factions: {L,C,R} (left, centre, right)
> 15 Candidates {L1..L5, C1..C5, R1..R5} (5 from each faction, assume lower
> numbers are most popular)
> Faction support within electorate: L - 40%, C - 20%, R - 40%
> 
> STV Result: {L1, L2, C1, R1, R2}
> 
> Condorcet Series Result: {C1, C2, C3, C4, C5}

With 5 seats, percent votes, the revised Droop Quota is 100/(6-z)=16 2/3 + 
where z is an infinitesmal but non-zero value

With 5 seats, 15 candidates, the number of 6-candidate contests is
15!/(9!6!)=15*14*13*12*11*10/(6*5*4*3*2)=91*55=5005 which is too big,
but it doesn't necessarily mean anything because 5 candidates make quota
at-large, and we can show that this means that they would win the
6-candidate elections that they are all in, as

L1,L2,C1,R1,R2,L3 ->L1,L2,C1,R1,R2
L1,L2,C1,R1,R2,L4 ->L1,L2,C1,R1,R2
L1,L2,C1,R1,R2,L5 ->L1,L2,C1,R1,R2
L1,L2,C1,R1,R2,C2 ->L1,L2,C1,R1,R2
L1,L2,C1,R1,R2,C3 ->L1,L2,C1,R1,R2
L1,L2,C1,R1,R2,C4 ->L1,L2,C1,R1,R2
L1,L2,C1,R1,R2,C5 ->L1,L2,C1,R1,R2
L1,L2,C1,R1,R2,R3 ->L1,L2,C1,R1,R2
L1,L2,C1,R1,R2,R4 ->L1,L2,C1,R1,R2
L1,L2,C1,R1,R2,R5 ->L1,L2,C1,R1,R2

Isn't that the sheer beauty of n+1- size elections with Droop?- they never
require exclusion. I think it's pretty too that you can use it to such
effect to find "Condorcet slates"

> David:  Does the method you propose still guarantee proportional
> representation? (to be specific: if we assume voters are divided into
> factions of varying size, and each voter ranks candidates from their faction
> ahead of all other candidates, is the outcome proportional?)

Yes, yes and verily yes.

> 
> I've tried to follow your subsequent posts ("Patching Up Condorcet In
> Multi-Winner Elections", August 25th), but have had difficulty visualising
> how the method would work.  Would you be willing to provide an example,
> showing how the result satisfies IIA (in that particular case, of course),
> where conventional STV would not?

I'm working on it right now... Keep posted!

> >Niklaus Tideman has proposed a Pairwise STV that doesn't use any
> >elimination. It's extremely calculation-intensive, and may not
> >be computable for big public elections with ordinary-speed
> >computers. I have a copy of it somewhere. I can send it if you
> >like. Either I'll find the e-mail copy, or, if I don't still
> >have it, I'll copy the essentials into e-mail from my paper copy.

Tideman's system basically weights STV outcomes. I've read his articles,
and when I think of it, his system, while it may possibly avoid
monotonicity, does diverge significantly from what I suggested. By the
way: My mud-fling with Mike (no hard feelings!) convinced me that the
"patching up" should be done by a different method to that I suggested in 
my earlier posting- one which attempts to maintain a high degree of
resistance to splitting even when such resistance would not be absolute.

> >[...] One system of exclusion which I think holds promise
> >is effectively to hold an STV election of n-1 people (with Droop quota-
> >ha!) which leaves one person out. [...]
> 
> I'm not sure if this is what you had in mind, but this sentence suggested to
> me an STV variant that might be superior to conventional STV in terms of
> results, and is not very complex (here, it appears to only be a small part
> of your overall method).  The method is similar to the "Ranked STV" method
> Mike and I proposed earlier for preparing party lists, but reversed.  I'll
> call it "Reverse-Ranked STV", until someone comes up with a _good_ name for
> it!

I like the term "quota significance". This particular exclusion method I
think gains its strength from its proportionality and the likelihood of
mutual preferences in an election, which reduces the risk of
non-monotonicity with this method.