[EM] Question on RCV/IRV multi-seat method used in Minneapolis

[Raph Frank]

On Wed, Sep 24, 2008 at 8:05 PM, Abd ul-Rahman Lomax
<abd at lomaxdesign.com> wrote:
> If I'm correct, votes for the already-chosen candidate, found on
> these remaining ballots once elimination starts, will be disregarded and the
> next-lower choice awarded the votes, pending victory or elimination.

It depends on the count method, but it is true in most cases.

Meek's method is the only current system than I can think of where it
wouldn't be true as if you transfer to an already elected candidate,
your vote is reduced in weight by the keep value rather than passed
down at full strength.

> (In Asset Voting, I'd use *exact* quotas, probably the Hare quota, --
> votes/seats -- and exact fractional transfers, though they would presumably
> be rounded to some reasonable accuracy, sufficient to make a change of
> result from roundoff error very unlikely.)

Under Asset, quota selection gets interesting (though we did discuss
this on the Range/Score voting list).

Assume 100 votes and 4 seats:

quota: 25 (Hare for 4 seats)

Result that is only possible in theory
seats: 4
remainder: 0

Likely result (only needs 1 elector refuses to assign a vote for this to happen)
seats: 3
remainder: 25

quota: 21 (Droop for 4 seats)
Result would probably be
seats: 4
remainder: 16

quota: 23 (average of Droop and Hare)
Result would probably be
seats: 4
remainder: 8
or less likely
seats: 3
remainder: 33 (which is bad)

By reducing the quota, more people are represented.  In this context,
maybe a good quota for asset would be (votes cast)/(seats + 0.5).  In
effect, the quota is the average of the Droop and Hare quota.

The question is at what point the last seat ends up unfilled and that
depends on how many hold outs there are.  I can't see a real national
election having zero hold outs.

In a situation where the vote split is 51 for one party and 49 for the
other, maybe it is better to split the seats 2-1 and leave one
unfilled, than to give 2 seats each.

There are also issues with how to handle a district based system and
how to handle a single national constituency.  If it was a district,
then maybe 2-2 is better than 2-1, but if it was national, then maybe
50-49 is better than 50-50, if the votes are nearly equally balanced.

To a certain extent, the Hare quota is the same as the Droop quota for
one fewer seat.  In practice, I don't think the +1 part of Droop would
make much difference as there will always be at least 1 hold out who
won't assign in a real election.

A Hare election with 10 seats will end up being a Droop election with
9 seats, except for a 1 in a million chance that all the votes are
assigned under Hare and thus all 10 seats are filled.