Is STV house-monotonous?

Herman Beun chbeun at worldonline.nl
Mon Jul 27 07:16:18 PDT 1998

```Hi Markus,

Markus Schulze <schulze at sol.physik.tu-berlin.de> schreef:

> STV violates "housemonotonicity."

If that is the case, it looks like I will not be able to solve my
problem in the way I proposed. Unless of course, STV's (and my
method's) violation of house-monotonicity is limited in most cases.

> Example:
>
>   28 voters vote A > C > B.
>   40 voters vote B > A > C.
>   32 voters vote C > A > B.
>
> One seat: Candidate C is elected.
> Two seats: Candidates A and B are elected.

Ermmm, no, not in the way _I_ would do an STV vote. Look:

Quota (Hare) = 100 for 1 seat, 50 for 2 seats.

First round:
Count only 1st preferences:
A    B    C
28   40   32

Candidate A is eliminated (in both the 1 and the 2 seat case),
the eliminated candidate's votes are transferred to their
second choice: C

Second round:
Results now:
A    B    C
-   40   60

In the 2 seat case, C reaches the quota now. Since there
are no other candidates left than B, B gets the other seat.

In the 1 seat case, a third round is necessary. Candidate B
is eliminated and his/her votes transfered to their third
choice: C, since A has been eliminated already.

Third round:
Results now:
A    B    C
-    -   100

C reaches quota (and is the last candidate anyway) and
is elected.

This is the STV procedure I have been testing so far, and this one
seems house-monotonous (at least, I haven't seen any examples of the
contrary).

Something else is that STV for one seat does not find the Condorcet
winner, which would be A.

The above can be used to illustrate my own "elimination method": We
do a STV count for 1 (apparent) seat. The first candidate eliminated
is A, who comes last on the party list. The next candidate eliminated
is B, who comes second last. So the party list becomes:

1. C
2. B
3. A

As you see, if the party gets 1 seat in parliament, this will be
candidate C, who would also have been the outcome of a normal 1 seat
STV election. If the party gets 2 seats, this will be C and B, which
would also have been the outcome of a normal 2 seat STV election.

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Herman Beun                                                    Arnhem
http://home.worldonline.nl/~chbeun/                        Gelderland
CHBeun at worldonline.nl                                       Nederland
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