# [EM] STV-PR is not reweighted IRV and not House-Monotonic (was " corrections to older posts re IRV public election data")

Chris Benham chrisbenham at bigpond.com
Sat Nov 12 09:14:42 PST 2005

```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.

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
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

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