[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 10:33:34 PST 2005
Sorry about the multiple posting.
In my explanation below of the STV procedure for my example, I wrote:
>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.
>
Of course it is MR whose score is raised to 20 votes. (corrected
version below).
Chris Benham
Chris Benham wrote:
>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 MR'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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>------------------------------------------------------------------------
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