Warren Smith wrote:
>Arguably STV multiwinner elections are still of interest for single-winner
>purposes since the FIRST winner is a single-winner IRV winner.
>
>
This seems to imply that multi-winner STV meets "House-Monotonicity":
"No candidate should be harmed by an increase in the number of seats to
be filled, with no change in the profile".
It doesn't and shouldn't. Multi-winner STV is not "re-weighted IRV".
In this Dec.1914 article, Woodall discusses this.
http://www.mcdougall.org.uk/VM/ISSUE3/P5.HTM
http://groups.yahoo.com/group/election-methods-list/files/wood1994.pdf
He mentions this example:
2 seats.
36: A>D
34: B>D
30: C>D
Condorcet supporters would all agree that the best candidate to fill a
single seat is D, but to fill two seats the
"Droop proportionality criterion" (DPC) says that we must elect A and B.
Quoting from that article:
The most important single property of STV is what I call the Droop
proportionality criterion or DPC. Recall that if v votes are
cast in an election to fill s seats, then the quantity v/(s
+ 1) is called the Droop quota.
- DPC. If, for some whole numbers k and m satisfying 0
< k <= m, more than k Droop quotas of voters put the
same m candidates (not necessarily in the same order) as the top m
candidates in their preference listings, then at least k of those
m candidates should be elected. (In the event of a tie, this should be
interpreted as saying that every outcome that is chosen with non-zero
probability should include at least k of these m candidates.)
In statements of properties, the word "should" indicates that the property
says that something should happen, not necessarily that I personally agree.
However, in this case I certainly do: DPC seems to me to be a sine qua
non for a fair election rule. I suggest that any system that satisfies DPC
deserves to be called a quota-preferential system and to be regarded as a
system of proportional representation (within each constituency)-an
STV-lookalike. Conversely, I assume that no member of the Electoral Reform
Society will be satisfied with anything that does not satisfy DPC.
The property to which DPC reduces in a single-seat election should hold (as a
consequence of DPC) even in a multi-seat election, and it deserves a special
name.
- Majority. If more than half the voters put the same set of candidates
(not necessarily in the same order) at the top of their preference listings,
then at least one of those candidates should be elected.
It is possible for multi-winner STV to fail to elect the IRV winner.
Adapting an old example from Adam Tarr:
3 seats, 100 ballots..
08: FR>R>LR>MR>ML
02: R>FR>LR>MR>ML
04: R>LR>FR>MR>ML
07: LR>MR>R>ML
15: MR>LR>ML>R
16: ML>MR>LR>L
15: ML>L>MR>FL>LR
13: L>ML>FL
11: L>FL>ML
09: FL>L>ML>MR
The IRV winner is "Lucky Right"(LR), but 3- winner STV elects first
ML, then Left, then MR.
The Droop quota is 25. Moderate Left(ML) is the only candidate that
starts with a quota so is first elected.
Then 15/31 of Moderate Left's surplus 6 votes go to Left, which raises
Left from 24 to 26.903 so now Left
has a quota and so is second elected.
The other 16/31 of ML's surplus 6 votes go to MR, raising MR from 15
to 18.09677votes.
Then MR also gets all of L's surplus of 1.903 votes (all originally
from ML) to raise L's score to 20 votes.
The tallies for the remaining unelected candidates are FR8, R6,
LR7, MR20, FL9.
None have a quota so we eliminate R, which gives FR10, LR11, MR20, FL9.
None have a quota so we eliminate FL, which gives FR10, LR11, MR29.
MR now has a quota so is the last candidate elected.
In the IRV election the elimination order is R, FL, FR, MR, ML, L.
Chris Benham