# 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

```