A novel system for proportional representation with ranked ballots

Restless about the gawdawful American electoral system, I have come up with a crackpot proposal for a system for electing a legislature or other body of respresentatives. 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. 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 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, listing as few or as many candidates as they wish.
2. An initial seating tally of the ballots identifies the top N candidates who 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 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 for Furlong become a rep in 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, since her first choice did not survive the seating tally. Tallying all 200k ballots produces these seat strengths:

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

So Armstrong can win a vote on a measure if they have just Cole with them: (65k + 45k = 110k) outweighs (50k + 30k + 10k = 90k) for Bartlett, Davenport, and Eagle combined.

This should appeal to voters

Intuitive, honest voting

This system produces little need & advantage for voters to vote strategically. They 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, they still get their ballot making 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 do 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 potentially 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. This could even produce a rep with a seat with zero strength if every ballot ranked another seated candidate higher! These weird results are improbable, but not impossible.

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 ballots would not get a seat! 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 would be improbable with real ballots.

Refinements?

We can imagine a range of systems for the seating tally. I am inclined to stick to something simple which all citizens could feel confident in understanding.

We could blend the methods by tallying 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 blend the methods by 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.

A lot of work has been done on various sophisticated positional voting rules which should inform yet more options … though I would hesitate to use a system complex enough that voters have a hard time understanding it.

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.

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. 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.

Complex unicamiralism

I originally started thinking about this system as a refinement to an old proposal for a nationally-elected Senate in the US. Having opened that door, I realized that this system enables multiple different types of representatives all voting together in a single legislature. For example:

A unicameral US Congress

Choose senators nationally

Why have two geographically-determined sets of national representatives? Choose senators in a national election using this method. Everyone in the country votes, and the top candidates become the Senate.

Having made that change, how about just ten senators? That’s about the maximum number of people who can have an unstructured discussion.

This helps significant but thinly-distributed minorities. If 10% of the American population shares interests but don’t hold a majority in any particular state or district, they could still elect a senator.

Replace the House Of Representatives with county “councilors”

To address regional interests, instead of tangling with creating fair congressional districts, leverage the somewhat-organic boundaries of counties. Have each county elect five councilors using this method. It would be OK that different counties have different populations, because different councilors would have different strength, reflecting how many people voted for them.

There are 3000+ counties in the US, giving us over 15,000 councilors! Best to have them cast votes electronically from their home county rather than send them to DC, which would make them more available to constituents.

These different reps vote together

Rather than having the weird two-stage process of current American bicameralism, in this system the two types of reps would vote together, at the same time. The senators would not just get drowned out by the councilors because each senator (representing millions) exercises so much more strength than any councilor (representing thousands). A measure supported by a strong majority of senators could pass if it was a bit short of a majority of councilors, or vice versa.

Enabling other novel structures of governance

Americans tend to assume that congressional reps have power in their home districts. In this system councilors could both govern their county and vote in congress. We could add more classes of representatives to congress and still have a unicameral single vote. I’d like to add 50 panelists chosen by sortition (like a jury) each with the strength of ⅟₅₀^th of the voting population. One can imagine other kinds of representatives.

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I intend to exercise this voting system in a broader hypothetical new US Constitution, but that’s a post for another day ….