# [EM] STV with party lists

Bjarke Dahl Ebert bjarke2003 at trebe.dk
Wed Nov 12 15:35:03 PST 2003

```Dear Election-methods readers,

Here in Denmark we use the modified Sainte-Laguë method for party list
PR for parlament elections. It is based on districts, but a principle of
"extra candidates" ensures that there is proportionality in the country
as a whole.

For distribution of seats within each party, a simple
first-past-the-post method for "personal votes" is used within each
district (unless the party chooses to use party-ordered lists, in which
case they pretty much decides the seats).
Often, this rule leads to election of the "party's district seat" with
less than 20% of the party's personal votes in the district.

Of course I think that a kind of STV for selection of seats within the
party would be better :-).

But then I came to think about a strategy-problem specific to this kind
of voting (Party-list PR as the "outer method" with seat distribution
within each party as an "inner method"):

Assume that CPO-STV is used within each party.
Then, if some party is going to get either one or two candidates in a
district, and I really want the "traditional local condorcet winner" of
my party to win, then I don't want my party to get two seats in my
district, because then the condorcet winner will maybe loose! So I don't
vote for my party, in the hope that it will only get one seat in my
district.

Proposal: Define "Sequential CPO-STV" thus: To elect N candidates using
Sequential CPO-STV, first elect N-1 candidates using Sequential CPO-STV
(so this is an inductive definition). Then, in the Condorcet matrix,
consider only the combinations of N candidates that contain the already
elected N-1 candidates.
- Much cheaper calculation. We avoid the combinatorial explosion of
standard CPO-STV
- "Monotonicity": if B>A, then B elected candidates will include all of
A elected candidates.
The last property avoids the mentioned strategy problem.

What is the big disadvantage of this method? Maybe plain CPO-STV can
find a combination of seats which is just a little bit "better", but
isn't my method still a lot better than plain STV?

- Bjarke

```