[EM] STV anomaly - Part of my vote went to someone who was not on my list
Jim & Mary Ronback
Jim_Ronback at dccnet.com
Fri Apr 29 14:28:37 PDT 2005
I was trying an experiment to see how block voting, with a 51 to 49 %
split, would behave with the STV method for counting votes for 4 seats
from 10,000 ballots. Block A, B, C, D candidates have 5100 votes in
total but they are almost evenly distributed. A's 1st preferences > B >
C > D and Block E, F, G, H candidates have 4900 votes in total. with
each of A, B, C, D's preference counts are greater than any of E, F, G,
H preferences.
The "Meek" method in pSTV Windows version 0.7 from
http://stv.sourceforge.net/ , seems to give counter-intuitive results as
shown below.
My initial naive expectation was that the block voters for A, B, C, D
candidates should win all four seats since each of them has more first,
second, third and fourth preference counts than each of the candidates
in the block E, F, G, H at every level. Also I did not expect H to be
eliminated since it has more first place preferences than F!
I got trapped into thinking that first preferences should have much
more weight in determining the winners in STV. Thus the results looked
counter-intuitive. Part of the problem arises from how votes from
eliminated candidates get re-allocated and how surplus votes from
winning candidates get reallocated
Once a candidate is eliminated or elected, those ballots which had him
listed first, have the remaining preferences, after the next one, ignored.
Where I get hung up, is the fact that ALL of the votes of an eliminated
candidate gets re-allocated to the next preferred candidate on the list,
ignoring any of remaining preferences on that voter's ballot.
The voter who picked a losing candidate as a first preference, loses
considerable control of how he wanted to allocate portions of his vote
to his remaining preferences. Also, he has NO IDEA BEFOREHAND as to what
fractions of his vote will get reallocated to other candidates. As a
result, some fractions of his vote may eventually get re-allocated to
candidates that were NOT on his list. I think this is where I and the
the public gets VERY apprehensive about STV.
To minimize this problem, there should be some rule added to STV, so
that the votes of an eliminated candidate is allocated to each of the
remaining candidates on his list in a manner inversely proportional to
their ranking. So, in the example below, when E gets eliminated, his
1200 votes should be allocated in round two by (1/2)/(1/2+1/3+1/4) =
6/13 to F, 4/13 to G and 3/13 to H. Note: This is different from the
ranking of voters for F whose next ones on the list were G, H and E.
In round four when H gets eliminated, the 1250 votes should be
allocated to F and G in proportion to 4/7 and 3/7 respectively,
instead of all to F.
And so on...
A similar rule could also be made for re-allocating surpluses from
elected candidates according to the ALL the preferences remaining on the
lists of the ballots.
These similar anomalies also occur in BC-STV and it should be eliminated
or minimized in BC-STV.
The question is: Would this additional complexity in allocating votes of
eliminated candidates and surpluses of elected candidates more
equitably, make the voters and the candidates any happier that the
system becomes more(?) proportional by following the voters wishes more
closely and is thus more democratic?
Yours democratically,
Cheers from sunny Tsawwassen.
Jim Ronback
Tsawwassen, BC
Canada
PS. In spite of these shortcomings, I'll vote yes for BC-STV on May 17
and hope that Elections BC will make these improvements if and when it
gets implemented.
--------------------------------------------------------------------------------------------------------------
Ballot input:
1299: A B C D
1276: B C D A
1274: C D A B
1251: D A B C
1200: E F G H
1224: F G H E
1226: G H E F
1250: H E F G
Election: Ballot data from D:\Program Files\pSTV\Block.blt.
Method: Meek STV
Number of Ballots: 10000
Threshold Name: Droop Dynamic Fractional
8 candidates running for 4 seats.
R| A| B| C| D| E| F|
G| H|Exhaus|Surplu|Thresh
--+-------+------+------+------+-------+------+------+-------+-------+------+------
1|1299.0|1276.0|1274.0|1251.0|1200.0|1224.0|1226.0| 1250.0| 0.0|
0.0|2000.0
2|1299.0|1276.0|1274.0|1251.0| |2424.0|1226.0| 1250.0|
0.0| 424.0|2000.0
3|1299.0|1276.0|1274.0|1251.0| |2000.0|1650.0| 1250.0|
0. 0| 0.0|2000.0
4|1299.0|1276.0|1274.0|1251.0| |3031.4|1868.6| |
0.0|1031.4|2000.0
5|1299.0|1276.0|1274.0|1251.0| |2000.0|2900.0| |
0.0| 900.0|2000.0
6|1299.0|1276.0|1274.0|1251.0| |2207.1|2000.0| |
692.9| 484.3|1861.4
7|1299.0|1276.0|1274.0|1251.0| |1888.3|2062.5| |
949.2| 330.5|1810.2
8|1299.0|1276.0|1274.0|1251.0| |1852.5|1849.5|
|1198.0| 181.2|1760.4
9|1299.0|1276.0|1274.0|1251.0| |1774.3|1803.5|
|1322.2| 106.7|1735.6
10|1299.0|1276.0|1274.0|1251.0| |1745.7|1752.9|
|1401.4| 59.2|1719.7
11|1299.0|1276.0|1274.0|1251.0| |1724.5|1731.0|
|1444.4| 33.3|1711.1
12|1299.0|1276.0|1274.0|1251.0| |1714.0|1716.9|
|1469.1| 18.5|1706.2
13|2550.0|1276.0|1274.0| | |1707.7|1709.5|
|1482.8| 856.9|1703.4
14|1703.4|2122.6|1274.0| | |1704.3|1705.2|
|1490.5| 427.9|1701.9
Round 1: Count of first place rankings.
Round 2: Eliminating candidate E.
Candidate F is elected.
Round 3: Transferring surplus votes.
Round 4: Eliminating candidate H.
Round 5: Transferring surplus votes.
Candidate G is elected.
Round 6: Transferring surplus votes.
Round 7: Transferring surplus votes.
Round 8: Transferring surplus votes.
Round 9: Transferring surplus votes.
Round 10: Transferring surplus votes.
Round 11: Transferring surplus votes.
Round 12: Transferring surplus votes.
Round 13: Transferring surplus votes.
Eliminating candidate D.
Candidate A is elected.
Round 14: Transferring surplus votes.
Candidate B is elected.
Winners are A, B, F, G.
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