# STV without Elimination

Norman Petry npetry at sk.sympatico.ca
Wed Sep 2 17:07:43 PDT 1998

```On August 24, 1998, David Catchpole wrote ("Re: Normative principles..."):

>Interesting note- if you take the principle into proportional multi-member
>elections you can get some form of Condorcet rule with PR. Expect an e-mail
>from me soon about "quota-Condorcet proportional election" (Geez, I know
>you can't wait...)

Actually, I am very interested in this proposal.  I've often wondered if
it's possible to design a multi-winner election method which solves the
problems caused in STV by the elimination of candidates.  Previous attempts
I've seen which try to use a pairwise method for this purpose fail to
satisfy the most important characteristic of STV (in my opinion), which is
that it provides proportional representation of factions/parties.
"Condorcet series"-type methods (which find a pairwise winner, elect
filled) are totally unsuitable as PR multi-winner methods, as the following
simple example demonstrates:

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}

Obviously, any method which gives 20% of the electorate 100% of the
representation is not proportional!  The problem is caused by the fact that
_all_ the voters get to decide on each candidate; L & R counterbalance one
another in the above example, with the result that their votes only serve to
elect compromise candidates from C.  This is fine when there's a single
winner -- a candidate from C should be chosen in that case (this would be
the Condorcet result, but usually _not_ the result produced by
IRO/MPV/AV/...), but it's an unacceptable multi-winner outcome.

To me, a voting system which can provide proportional representation without
the need for formally organised factions (parties) is very desirable, and I
wouldn't sacrifice this characteristic to achieve greater compliance with
IIA, guarantee monotonicity, or whatever.  These are relatively minor
problems -- it's desirable to solve them, if possible, but not by
sacrificing PR.

***

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?)

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?

***

The idea of using a pairwise method with STV has apparently been proposed
before.  On March 23, 1996, Mike Ossipoff wrote ("Re: [EM] multi-seat
pairwise?"):

>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.
>
>Also, I can tell where I got my paper (Xerox) copy:
>
>The Journal of Economic Perspectives, 1995, Winter Quarter. [...]

Mike:  I've tried to get a copy of this article through my local library,
but with no success.  Do you think you could post Tideman's Pairwise STV
method (if it's not too long, and you still have a copy).  It might be
interesting to compare it with David's proposal.

***

On August 25, 1998, David Catchpole wrote ("Patching Up Condorcet In
Multi-Winner Elections"):

>[...] 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!

Reverse-Ranked STV:

Given an election with V voters, C candidates and S seats to be filled,
conduct a series of STV elections for C-1, C-2,... S seats.  At the
beginning of each STV election, immediately eliminate all previously
defeated candidates, and transfer their votes to subsequent choices before
transferring surpluses.  The quota using this method will be as small as
possible initially, and will rise through each stage.

For example, suppose we're electing 5 candidates from a field of 9.  Begin
by conducting an STV election for 8 candidates.  The one candidate who is
defeated remains defeated for subsequent STV rounds, so his supporter's
votes immediately transfer to other candidates at the beginning of the 7
candidate election, etc.  Continue until the 5-seat election is reached.  By
this point, there will already be 3 candidates who are automatically
defeated (from previous stages), so it's only necessary to determine which 5
out of the 6 candidates remaining are the final winners.

Of course, this method will not always guarantee that a Condorcet Winner
will be elected.  If the Condorcet winner is everyone's second choice, but
the first choice of very few, the elimination in this method will _still_
cause the defeat of that candidate in the first round.  However, unlike
conventional STV, since the quota in the first round is [V/C]+1, rather than
[V/(S+1)]+1 (Droop quota, with [] indicating truncation), the quota is much
lower, so the negative effects of elimination should be substantially
reduced.  Also, I believe this method should be both house-monotonic (or at
least, "reverse-house-monotonic", if I can use that term) and proportional.

David:  Is this the method you were suggesting?

Anyone:  Any ideas on what useful properties this method might have?
References, if it's been suggested before?  Opinions on whether it's worth
the added complexity over conventional STV?

Norm Petry

```