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

Vidar Wahlberg canidae at exent.net
Wed Jun 26 18:12:38 PDT 2013


I'm new here, I'm not a mathematician and merely a layman on the subject
of voting methods so please grant me some leeway, but do feel free to
correct any misconceptions I may have.

Briefly about my goals:
I'm trying to find a better alternative to the voting system used in
Norway (party-list PR, counting votes using a modified Sainte-Laguë
method where first divisor is 1.4 instead of 1), where you still vote
for parties rather than persons and may rank parties in a preferred
order instead of only being able to vote for a single party. A party may
win multiple seats in each district.
The short answer to "why not vote directly for persons?" would be that
in Norway there's more focus on the goals of a party rather than the
goal of its politicians, and some may argue that the extra abstraction
layer is a good thing, as well as I'd like an alternative that won't be
completely alien to the common people. I'm hoping that any discussion
that may arise won't focus on this aspect, though.
As of why I'm interested in this then that's because I'm arguing for a
preferential election rather than the "one person one vote" system which
I believe is leading us towards a two/three party system, and I need to
know (better) what options are out there.

So far I've not been able to find much information on preferential
voting system where you vote for a party rather than a person. If anyone
have more insight and can guide me to more literature I would appreciate

And here's the part where I hope you'll be gentle:
I tinkered a bit on my own. Where as I am a fan of Ranked Pairs and
Beatpath, I find those difficult to explain to someone with no insight
in voting systems, and neither could I figure out how to apply RP in a
way where a candidate can win multiple seats.
The basics behind PR-STV on the other hand are fairly easy to explain,
and I did manage to implement a way of counting votes to candidates
which can win multiple seats based on the ideas behind STV, but I'm no
expert on voting methods and would like to hear your thoughts.

This is the general approach:
1. Calculate quota (Droop): votes / (seats + 1) + 1
2. Tally votes, assign seats to candidates with enough votes to exceed
   the quota [1]: candidate.seats = candidate.votes / quota
3. Calculate new vote weight:
   vote.weight = vote.weight - candidate.seats * quota / candidate.votes
4. Exclude candidate with least votes and redistribute those votes [2]
5. Repeat step 2-4 until all but one candidate has been excluded (which
   gets the final seat)

[1]: Since a candidate is not excluded from further seat allocations
upon reaching the quota the surplus votes are not redistributed. I do
not know which adverse effects this may have that are not present in STV
where candidates are excluded upon reaching the quota.
[2]: It troubles me to decide which candidate that should be considered
to have the fewer votes. If I choose the one with fewest first
preference votes, then I may exclude a candidate that is very popular as
a second choice, while a candidate that is popular by a few and despised
by many may stay longer in the election. Since votes to elected
candidates are not distributed to secondary preference then this issue
is likely elevated. I'm contemplating on rather excluding the candidate
that is least common on any ballot, regardless of rank, but I'm not
certain on the implications this would cause.

Since a candidate may win multiple seats, it should be more difficult to
use Hylland free riding for tactical voting.

Am I completely off with this, or could something like this be a viable
preferential voting system for proportional representation using STV
where a single candidate (party) may win multiple seats? Or maybe I'm
reinventing the wheel?

Vidar Wahlberg

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