[EM] STV with party lists

[Bjarke Dahl Ebert]

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.

So what to do about this?
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.
Two advantages:
 - 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