A novel system for proportional representation with ranked ballots

Restless about the gawdawful American electoral system, thinking about an old proposal for reforming the Senate led me to this idea. It seems so simple and elegant to me that I cannot understand why I cannot find anyone else proposing anything like it … or debunking its flaws.

Knowing the tragic reality that Arrow’s Theorem makes a perfect electoral system impossible, I worry about what gotchas I might have missed. Many smart people have called for proportional representation in the US, but the kinds of mechanisms I have been able to find differ structurally from this proposal.

My amateur perusal of the standard ways of analyzing voting methods has not helped — they don’t address the way I handle proportionality, and I cannot work out the math alone. I write this partly in hope that a real expert can set me straight.

The essence

Most systems of proportional representation assume that each seat in the legislature exercises equal strength, so they may give a party a proportion of seats in the legislature corresponding as well as possible to the proportion of voters who cast a ballot for that party, giving a seat to the party’s most popular candidate, second most popular, and so on.

My weighted seats proposal invests different legislative representatives with different strength, proportionate to voters’ support for that rep. Big voter support might give a rep a seat with a strength of 1000, which would outweigh the combined efforts of a pair of less popular reps holding seats with a strength of only 400 each.

To elect a legislature with N seats:

1. Citizens cast ballots listing candidates in rank order of the voter’s preference. A ballot may list as few or as many candidates as the voter wishes.
2. An initial seating tally of the ballots identifies the top N candidates. They get seated as representatives.
3. A second strength tally of the ballots determines the power of each rep’s seat. Each citizen’s ballot delivers the strength of its vote to the seated rep ranked highest on that ballot. Reps’ power in the legislature equals the the votes the rep received in the strength tally.

Example

There are 7 candidates for 5 city council seats:

• Armstrong
• Bartlett
• Cole
• Davenport
• Eagle
• Furlong
• Gordon

Jane, a voter who liked upstart candidate Furlong, cast this ballot:

1. Furlong
2. Cole
3. Armstrong

Though Jane’s ballot supported Furlong, not enough other voters agreed. Furlong failed the seating tally, which produced a city council comprised of:

• Armstrong
• Bartlett
• Cole
• Davenport
• Eagle

In the strength tally, Jane’s ballot contributes its vote to the strength of her second choice, Cole. Tallying all 200k ballots produces these seat strengths:

• Armstrong — 65k
• Bartlett — 50k
• Cole — 45k (including 1 from Jane!)
• Davenport — 30k
• Eagle — 10k

This creates a few cases where a minority of strong reps can out-vote a majority of reps who are weak. Armstrong & Cole (65k + 45k = 110k) voting together out-vote Bartlett, Davenport, and Eagle combined (50k + 30k + 10k = 90k).

This should appeal to voters

Intuitive, honest voting

This system produces little need & advantage for voters to vote strategically. They just name the candidates they like, and rank their preferences honestly.

Wide candidate choice

Even when incumbency confers strong advantages, voters may choose from at least as many options as there are seats to fill, so they probably need to make compromises on less positions to pick a candidate to support.

A transparent proportionality mechanism

Unlike in complex proportional systems which cascade ballots’ votes to lower-ranked candidates, voters always have their vote strengthen the successful candidate they liked best.

Practically nobody feels they had a “wasted” vote

If a voter’s ideal candidate wins a seat by a big margin, it was still worth them taking time to vote, because their ballot makes that rep a little bit stronger.

If their ideal candidate does not win a seat, their vote still counts, lending strength to the seated rep whom they ranked highest.

Determining the seating tally

The overview above hand-waves identifying how we determine the candidates seated in Step 2. How should we define the “top” N candidates?

I’m not sure about the ideal method. I suspect that a range of methods would deliver fair and sensible results — and would feel both clear and fair to citizens. And this is the space with an opportunity to “tune” the system to prevent perverse outcomes and get characteristics we prefer — stronger or weaker tendency to support moderation, incumbency, et cetera.

Broad approval?

A simple method would be to tally every candidate appearance on every ballot as a vote for that candidate, much like approval voting. The candidates with the highest N tallies would get seated.

This can theoretically produce odd results. Imagine an election for a 5-seat legislature in which nobody ranked Candidate X in their top 5 … but everyone listed them on their ballot somewhere, so they get a seat. It is wildly improbable, but possible, that this could produce a rep with a seat with zero strength, because every ballot ranked another seated candidate higher.

It does seem likely that this system will produce occasional reps who have a very weak vote because many voters accept them but few prefer them. But a few reps with an equal voice but a weak vote may not be such a bad thing.

Top rank?

Another simple method would be to tally each ballot as a vote just for its top-ranked candidate. The N candidates ranked ^#1 most often would get seated.

This could get weird in a highly fragmented race. A candidate ranked ^#2 on every ballot would not get a seat, and it is reasonable to think that they should. Imagine an election for a 5-seat legislature in which 20 candidates are all ranked ^#1 on 4% of ballots … with 5 candidates ranked ^#1 on 5% of ballots. Those last 5 candidates would get seated despite not being categorically more popular. But again, these kinds of perverse results seem improbable with real ballots.

A blend?

We could tally a vote for only the three highest ranked candidates on each ballot. Or the four highest, or whatever. A mass of low-ranked support for a candidate could not win them a seat.

We could tallying a vote for every listed candidate, then tally an extra vote for each ballot’s ^#1 pick, so that between …

• Armstrong — 100 ballots as ^#1, 100 ballots ranked lower
• Bartlett — no ballots as ^#1, 250 ballots ranked lower

… Armstrong would get a seat with 2x100 + 100 = 300 votes over Bartlett’s 2x0 + 250 = 250 votes.

Something more sophisticated?

A lot of work has been done on various sophisticated positional voting rules which should inform yet more options. Condorcet methods have a lot of advantages, but they present implementation challenges and are complex enough that ordinary voters will find them opaque, so I hesitate to embrace them in this context, since it is not enough for the system to be fair, it also needs to support democratic consent by feeling fair.

Intended advantages

Undercuts gerrymandering & other districting challenges

So long as a district sends multiple reps, voters in the district can expect reasonably fair representation whatever the size & shape of their district, since each voter has their vote contribute equally to the strength of their preferred rep no matter what district they inhabit. Smaller districts produce weaker reps; bigger districts produce stronger reps, but a voter’s ballot delivers the same one-vote power of representation in either case.

Better matching of reps to voter preferences

Rather than having to choose from a few (or in the US, just two) political parties whose platforms may not map well to their preferences, a voter may pick a specific candidate whose program & priorities matches theirs well and expect that candidate to have a shot at a seat in the legislature. In many ways this should work as if there are as many different parties as there are reps in the legislature, which further suggests …

Complex issue-oriented coalitions

Reps would have more opportunities to assemble ad-hoc coalitions around specific issues. A “libertarian” rep might vote together with a “progressive” rep to decriminalize soft recreational drugs, then vote together with a “pro-business” rep to de-regulate an industry.

Less incumbency bias?

This system should do even better than many other ranked-ballot systems like IRV in allowing voters to support challenger candidates without worrying about spoiler effects. Incumbents will still tend to do will if they maintain popular support, and …

Democratic accountability reflected in reps’ shifting strength

Each election will redistribute power. Reps with growing popular support get stronger; reps with waning popular support get weaker. More frequent elections make reps more responsive to popular will; less frequent elections protect reps from popular whims.

Enabling complex unicameralism

This system enables a unicameral legislature with different classes of representatives voting together. I imagine a combination of a few very strong nationally-elected representatives together with a large number of individually weak locally-elected representatives as part of a a vision for a radically new US Constitution ….