# [EM] Multiple Winners Revisted

David Catchpole s349436 at student.uq.edu.au
Thu Mar 15 23:14:31 PST 2001

```On second thoughts the "reverse d'Hondt" idea isn't so crash hot if you
want non-complexity. Maybe simple d'Hondt would be the way to go...

On Fri, 16 Mar 2001, David Catchpole wrote:

> 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
> 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.
> >
> > 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.
> >
> > 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.
> >
> >
>
> -------------------------------------------------------------------------------
> "You have the right to scream your head off. Should you give up the right
> provided for you."
> 	Grouch cop, "Elmo in Grouchland"
>
>

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"You have the right to scream your head off. Should you give up the right