STV is not house-monotonous!
Markus Schulze
schulze at sol.physik.tu-berlin.de
Mon Jul 27 08:02:56 PDT 1998
Dear Herman,
even if you use the Hare Quota, STV violates
house-monotonicity.
Example:
28 voters vote A > C > B > D.
40 voters vote B > A > C > D.
32 voters vote C > A > B > D.
80 voters vote D > A > C > B.
****
Hare Quota and two seats => Quota=90.
First round:
A=28
B=40
C=32
D=80
Candidate A is eliminated. The eliminated
candidate's votes are transfered to their
second choice: C.
Second round:
A=0
B=40
C=60
D=80
Candidate B is eliminated. The eliminated
candidate's votes are transfered to their
next choice: C.
Second round:
A=0
B=0
C=100
D=80
Thus: The candidates C and D are elected.
****
Hare Quota and three seats => Quota=60.
First round:
A=28
B=40
C=32
D=80
The surplus (20 votes) of candidate D is
transfered to the voters' next choice: A.
Second round:
A=48
B=40
C=32
D=60
Candidate C is eliminated. The eliminated
candidate's votes are transfered to their
next choice: A.
Second round:
A=80
B=40
C=0
D=60
Thus: The candidates A, B, and D are elected.
Summary: STV violates house-monotonicity
independently on whether you use the Hare Quota
or the Droop Quota.
Markus Schulze
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