[EM] Preferential voting system where a candidate may win multiple seats

Vidar Wahlberg canidae at exent.net
Thu Jun 27 09:56:30 PDT 2013

On Thu, Jun 27, 2013 at 08:31:23AM -0700, Chris Benham wrote:
> I'm a bit confused about the details of the method you say is used in Norway. You write that voters "may rank parties in a preferred order instead of only being able to vote for a single party". but further down you refer to the "one person, one vote" system.

My apologies, I did not explain that well.
Voters do not rank parties in a preferred list, they may only vote for a
single party today. My desire is that somewhere in the distant future,
voters do rank parties in a preferred list. I hope this clears up some
of the confusion.

> Since you are not attempting to do anything with surpluses, I don't see any point in using a quota at all.
> I suggest instead simply:
> *Use the best formula for apportioning seats in List PR 
> (based on first preference votes).
> If every list/party has at least one seat, finish.
> Otherwise, eliminate the party voted top on the fewest ballots and promote the next most preferred uneliminated candidate on those ballots to top. (In other words transfer the vote, Alternative Vote/IRV style).

This is basically what I'm doing, except using a quota to determine when
a party got enough votes to earn a new seat. I started off modifying
STV, but since there's no redistribution of surplus votes it's likely
more correct to call it IRV than STV now. I'm afraid "the best formula
for apportioning seats" is not that clear to me, though. Nor is it clear
when parties are to be eliminated in your example.
If I'm not to use a quota, but rather something like Sainte-Laguë as
it's done today, how would I know when to start excluding the smaller
May also mention that each county in norway (19 in total) got a
predetermined amount of seats based on size of population and area. A
good example is the 2009 election in Oslo county, who had 17 seats to
fill (16 filled using Sainte-Laguë, final seat using a more complex
system called "leveling seat", I believe this is primarily a
Scandinavian concept). This election also shows the weakness behind our
current system (luckily not as bad as the voting system in USA), where a
very left-wing oriented party managed to sum up 12917 votes and got
fairly close to win a seat (needed another 800 votes), but instead the
final seat went to a very right-wing oriented party. It's very likely
that those who voted for the left-wing party would instead vote for
another larger and slightly less left-wing oriented party if they had
this knowledge, which also would result in that party getting the final
seat. Just for the record, I'm not affiliated with either of these
parties, I just advocate for a better voting system.

As for eliminating the party voted top on fewest ballots, that does seem
to have a weakness I'm trying to mend. For example, take the following
7 A,B,E,C,D
9 C,B,D,E,A
6 B,D,E,A,C

Here B would be eliminated first, even though B is popular among all
these voters, where as A and C are popular among fewer voters. I believe
Ranked Pairs & Beatpath would rank B above A & C in this scenario.
This is why I'm contemplating on rather eliminating the candidates that
are least represented on the ballots regardless of rank, and rather fall
back to eliminate the candidate with least first preference votes if
there are multiple candidates least represented on ballots. I'm not
entirely certain of the implications of such a change, though. And for
it to have any effect, you would have to limit the amount of preferences
instead of listing all candidates as I did in the example above.

> I think some free-riding incentive in PR is unavoidable.
> Not using a quota and distributing surpluses might reduce proportionality a bit among sincere coalitions, but doing so allows parties (whose voters only care about their favourites and are happy to take "how-to-vote" advice from them) doing cynical preference-swap deals, motivated by nothing but increasing the chance that they will get an extra seat (by having the biggest surplus fraction of a quota).

True, avoiding free-riding does not seem to be a simple task, but as for
Hylland free-riding and parties which can win multiple seats, it seems
like a very risky gamble to not vote for your preferred party when the
step from x seats to x+1 seats is small enough. This form of free-riding
appears to be much more effective when a candidate can only win 1 seat
and you're certain that candidate is going to win.

Vidar Wahlberg

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