[EM] Multiple Winners Revisted

[David Catchpole]

Well, I like pottering about with multiple winners, though I don't like
expressing preferences. On a practical level I favour STV methods, but if
you want more sophisticated and slightly more fair methods then I think
hybrid Condorcet methods appeal the most. What do I mean? Well, say
there's 5 candidates A-E with 2 to be elected. One conducts a preference
election and using some choice of a counting method one conducts
"sub-elections" amongst-

ABC; and
ABD; and
ABE; and
ACD; and
ACE; and
ADE; and
BCD; and
BCE; and
BDE; and
CDE.

Say the set BC wins all the sub-elections that include it (ABC,BCD,BCE).
Then BC is a hybrid Condorcet winning set. Problems that can arise- as in
single-winner Condorcet, there might not be a hybrid Condorcet winning
set; and there can be multiple hybrid Condorcet winning sets (say, BC and
DE). Resolving those problems to determine a final winning set in all
cases is a bit of a doozy. One way to resolve multiple winning sets, for
instance, might be to compare the possible winning sets in additional
sub-elections, say, if BC and DE are possible winning sets, BCDE. If there
were 6 candidates, A-F, and AB, CD and EF were all possible winning sets,
then the additional sub-elections would be ABCD, ABEF and CDEF.

OK- so that's the pie-in-the sky stuff. If you're unsure about
implementing STV completely, with redistributions, exclusions (not
necessarily random!), etc. you could try a quota preferential election
with candidates allocating their surplus. Exclusions would still be
necessary, but ties are rare and can usually easily be resolved (and not
always randomly!). If you're still worried about something even that
non-complex, I'd recommend a reverse d'Hondt style method. Start with the
nc candidates in the election and apply a quota of 1/(nc-1) the votes.
Redistribute surpluses either by votes or using candidate's instructions.
Exclude the candidate who doesn't make a quota, even after redistribution.
Then do the same with a quota of 1/(nc-2) of the votes and continue until
the quota's 1/(ne+1) the votes where ne is the number to be elected.

I don't think STV is difficult at all. I come from a country and am a
member of an organisation where STV is used frequently and counted
quickly. The most inefficient election I've ever witnessed was an 8-winner
FPTP election with about 30,000 votes that took 4 hours to count in a
small booth (~1500 votes) and took more than a week to be finalised.

On Thu, 15 Mar 2001, Moe St. Evergreen wrote:

> This list is called, "election-methods", but perhaps it should
> be called, single-winner-methods, as that seems to be the focus
> of this list.
>
> The only response I received to asking about multiple winner
> elections, was one specifying STV/Hare, and which was posted by what
> appeared to be an IRV advocate, who referred me to a rather loudly
> biased IRV advocating website, the so-called Center for Voting and
> Democracy (should be called the Center for IRV/STV, or else remove
> their personal bias from their Center's media outreach).
>
> Are there other good multiple winner methods that allow preference
> choice?
>
> Our organization is governed by a large committee, but members can
> create smaller regional committees, or philosophical/diversity based
> committees. In order to achieve proportional representation, we have
> a set maximum number of delegates on the large committee, and
> allocate, out of that number, a number of representatives from a
> smaller committee, proportional to the number of members in that
> smaller committee. Only members of a committee can vote for the
> delegates representing that committee.
>
> We currently use cumulative voting to determine the delegates of the
> smaller committees to the larger committee. The CV procedure was very
> easy to describe in our bylaws and to our members. CV also allows a
> person to allocate the same ranking (the same votes) to more than one
> candidate. CV also only needs to worry about ties for the last seats,
> and thus does not need any randomness in the middle of the process.
> It does have problems with undervotes and overvotes.
>
> STV/hare seems rather complex, and there seems to be some confusion
> on what the fairest implementation of STV is, and on the simplest
> procedural language. It also appears to be more arbitrary on ties,
> where an random/arbitrary tie break could, if I read it right,
> completely eliminate a candidate, that might otherwise have large
> majority approval.
>
> It seems to me that the Condorcet winner should always be among the
> winners in a multiple winner system.
>
> I think we would prefer rankings to CV, but I am not sure exactly
> what to advocate, and I am not sure I can trust the so-called Center
> for Voting and Democracy when it fails to balance its out biases.
>
> Any suggestions would be welcome,
> especially if they include pointers to well described procedures
> that can be easily tested and advocated.
>
> Thanks,
> - Moe.
>
>

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