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

Chris Benham cbenhamau at yahoo.com.au
Thu Jun 27 08:31:23 PDT 2013


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.

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).

Based on the updated tallies (that include votes transferred from eliminated parties) repeat until the final apportionment leaves no party without a seat.*

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).

I hope that helps.

Chris Benham

Vidar Wahlberg wrote (26 June 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
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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