Proportional Representation Without All the Hassle

Photo by Tom Radetzki on Unsplash

In 1949, Germany adopted a voting method called mixed member proportional voting, or MMP.

After the use of the absolute-majority Two Round System (TRS), see Two-Round System, in the German Empire, and the use of a pure proportional representation system in the Weimar Republic, see Mixed Member Proportional, a new electoral system was established by the Parliamentary Council in 1949.

With MMP, you vote for both a candidate, to represent your local district, as well as a party. Whoever gets the most votes represents your district. Parties are also awarded a share of the total seats relative to the percentage of the party votes that were cast.

So let’s say we’re dividing the country up into 10 districts, with 30 total seats, and the Green Party gets approximately 20% of the votes. That means they earn 6 seats (20% of 30). But now let’s say Greens won 2 of the district seats. We then subtract away those 2 from their total of 6, leaving them with 4 more seats to fill from their party list. That is, they would have submitted a list of their candidates ahead of time, and we’d go down that list and elect the first 4 people on it. There are some oddities that can happen, like what the Greens are entitled to 0 seats due to their national performance, but still win a seat in a local district? But those nuances aren’t too important to the general idea. The general idea is, we get proportional representation but still have local geographic representation.

Modernizing and Simplifying

While MMP has worked out quite well, even being adopted in New Zealand and several other countries, a lot has been learned about the science of voting in the years since it was invented in 1949. Hence we now propose a similar voting method I shall simply call American MMP, or AMMP for short. There are two main differences from traditional MMP:

  1. We use approval voting instead of plurality voting for selecting the local representatives.
  2. We use asset voting (aka “candidate transferable voting”) instead of party lists.

Approval voting simply means that voters can vote for (“approve”) as many candidates as they like. Thus a cast ballot for AMMP looks like the image below-right (“current ballot”).

The idea with asset voting is that we can achieve proportional representation without having the system itself be aware of party affiliation. Voters vote for candidates rather than parties, so there are no party lists, and no inherent disadvantage for independent candidates. In the simplest form of asset voting, you simply choose one candidate and then the candidates have some window of time during which they can redistribute their votes. So suppose the Green gets 5%, the Democrat gets 47%, and the Republican gets 48%. The Green could simply give her votes to the Democrat to prevent the Republican from winning. Hence the notion of candidate transferable voting.

The trick with asset voting is that it automatically becomes proportional when used for multi-winner elections. Suppose we’re electing 3 winners, hence a candidate needs to have over 25% of the vote to be assured of a seat. But two Green Party candidates each have 13%. They can thus negotiate to decide which of them gives her votes to the other, and be assured of at least that one seat for their party. Even if two candidates are independent, they can still use such a technique if they are merely somewhat ideologically aligned, to prevent a worst case scenario.

There are some interesting debates to be had about asset voting, and it certainly has political precedent, but it has the advantage of being extremely simple and not requiring party lists, which disadvantage independent candidates and put a huge amount of power into party machines which control their party lists.

Bringing it Together

So AMMP is forged of two rather unrelated ideas: approval voting and asset voting. But how would they work together? Approval voting allows voters to vote for any number of candidates, but with asset voting, we want all voters to have equal power, so we don’t want some voters to have more votes than others. There are two basic solutions to this.

First, you can simply divide each ballot equally between all approved candidates, so that a candidate who is one of three approved on a given ballot receives “1/3 of a ballot” for the asset voting phase. This is simple for voters, because they simply fill in an approval voting ballot and are done. But it’s more work for election officials, and probably requires voting machine upgrades, because it requires division (or a clever counting trick that I won’t go into here).

Another approach is that, like with MMP, we simply vote for two things. Imagine instructions which specify:

  1. Select All Candidates You Approve of to be Your District Representative
  2. Select Your One Favorite to be Your National Representative

There are pros and cons here and it’s probably mostly about political viability, simplicity, etc. more so than optimal outcomes.

Your local district representative is the candidate who gets the most approvals. We then award the candidates their share of the favorites for the asset voting phase which achieves proportional representation. Imagine the MMP scenario above, where we’ve elected the 10 local representatives and now have to choose the remaining 20 to create proportionality. We simply give the candidates a time window, say one hour, during which they can transfer any surplus votes, and the “richest” 20 are then elected at the end of that time. If we want to make things more straightforward, we just automatically eliminate the poorest non-winning candidates, one at a time, and force them to either redistribute their votes at that time, or lose them. There are a few different ways to handle this detail, and it doesn’t seem too important a detail.

Remember how we said that if the Green Party won 6 seats nationally, but had already taken 2 of the district seats, they’d have them subtracted from the 6 to make 4? The same thing has to happen for AMMP. Suppose a candidate gets 1.7 seats worth of “favorites” but has already won a local seat. Then we have to subtract 1 seat, to leave him with 0.7 seats worth of favorites, which can then be transferred to his philosophical allies.

Remember the problem with MMP where the Greens might be entitled to zero seats nationally, even though they won a district election? One solution to that is to create “overhang” seats which are awarded to the other parties to compensate them for this and make things more even. The AMMP version of this problem is that a candidate wins a seat despite having fewer than a seat worth of favorites. Suppose you won a district election but only had 0.4 seats worth of favorites for instance. The overhang analog then would be to create 0.4 seats worth of favorites and award them evenly to all other candidates. Whether this would even be worth the effort is an open question. If there is a relatively small number of national seats relative to district seats, it becomes a fairly rare occurrence in the first place.

Simple Example

In its simplest incarnation, a voter would see something like this:

We would instantly elect the 10 (or whatever number) local district winners via approval voting, then award the “favorites”. Then we’d subtract favorites for seat-winners, so if Adam Robertson won a seat and had 2.4 seats worth of favorites, he’d wind up with 1.4 seats worth of favorites. (Optionally, we would then add the overhang votes if any district winners had less than a seat worth of favorites.)

We would then eliminate the candidate with the fewest favorites, giving her the option to tell us whom to transfer her favorites to. This would repeat until the remaining candidates matched the number to be elected. Presumably each of these elimination rounds would start by giving the guaranteed winners with surplus votes a chance to transfer those surplus votes, but there are several ways to handle this and it’s fairly arbitrary.


While AMMP is somewhat novel, and its ultimate rationale a little esoteric, it is largely based on two very well vetted ideas: MMP and approval voting. And it has some major advantages in terms of simplicity, like not requiring any voting machine upgrades. And by being party-agnostic, it’s fair to independents, unlike party list systems.

Thanks to Warren Smith for inventing the idea that was the genesis for this refinement.

Advocate of Score Voting and Approval Voting. Software engineer. Father. Husband. American.