A Proportional Representation Method with STAR Voting (PR-STAR)


Over the past month or so I’ve been working on an adaptation of STAR voting for use with multi-member elections. This method takes party membership into account and first allocates seats to each party according to voter’s party preferences, as determined by the parties of the candidates they score; then within each party selects the winning candidates as a group all in one shot. Full details are provided in the document I posted here:

The chief advantages I believe this method has over other systems I’ve seen are that:

  • It’s easy for voters to understand and use (simple score voting)
  • Votes can be counted at the precinct level, and aggregated upwards
  • Ensures that the proportion of seats given to each party is as close as possible to the party preferences of the voters

I would appreciate any assistance in evaluating the effectiveness of this method under difference scenarios, determining whether it fails to meet any of its stated objectives, and comparing it to other proportional voting methods. Also, let me know if there is a better name for it, as PR-STAR might get confused with STAR-PR, even though these methods are different.
I have also posted example Perl code for ballot counting here:
along with an example list of candidates (6 parties with 3 candidates each):
and a small set of randomly generated ballots:
You can follow this pattern to simulate probably any other election scenario.


Wow, this is an impressive proposal. Thanks for digging in!

I’m personally hesitant to consider options that are based on party affiliation, though it sounds like if you skip step 1 this can work for non-partisan races as well. My reasoning is that our 2 party system is broken, and that any PR system that is built from that will fall into the same divisive partisanship traps, even if there are more parties at the table. I’d much rather see candidates judged as individuals.

I think, after reading the abstract here, that I get the general mechanics of it, but I wonder if you could make an attempt to distill this down to a simple layman friendly description of the mechanics for a non-partisan race?


Advantages: it’s proportional

Disadvantages: it’s not party agnostic

If you want simplicity, why don’t you just use RRV for electing the first n - 1 winners and then among the remaining weighted ballots, just use STAR voting instead of score voting to elect the last winner? Thus because you are only using STAR in the last round, STAR’s runoff doesn’t interfere with the reweighing process because there are no more reweighs after the last winner is chosen.


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RRV is not really simple and is not precinctable like single winner Score Voting is. In fact, it loses a lot of the advantages that Score has over IRV.


My thinking is that this method shouldn’t be party-agnostic in order to prevent a majority from obtaining more seats for their party than their actual proportion among all voters. However it needs testing against other multi-member voting methods in order to ascertain whether this is indeed the case, especially for cases in which voters score candidates across multiple parties. I‘d like to model my example candidates across three dimensions of a hypothetical political spectrum, then scatter voters across the same spectrum in different concentrations to see how closely the winners of the election match the spread of constituents. This would be similar to models that determine whether the winner of a single-seat election is the closest to the average position of all the voters, except that it can have multiple clusters.


For a non-partisan, multi-seat race (which this considers equivalent to a single party,) the method works much like STAR voting except that it considers all combinations of M out of N candidates, finds the two groups having the highest combined score, then finds which of those groups have the most votes. An example of this is shown on page 4.


I agree with the other comments that systems with explicit partisan voting should be avoided. I much prefer method like RRV. I invented a system (Local Hare Score) which improves on RRV in at least 3 ways. First the reweighing is done in a way which optimizes Bayesian regret and leads to the most people being the most satisfied. Second it is procedural rather than a mathematical optimization. This helps with understandably and speed. Third, it keeps single member constituencies but passes votes between them like Byron Becker’s Local PR.

A summary of the system is as follows:

  1. The existing equipopulous constituencies are grouped into clusters
  2. Voters provide a score from 0 to 9 to each candidate running within her cluster
    - Blanks are treated as 0
  3. All ballots initially have weight=9 representing the total amount of score which can influence the election
  4. The first winning candidate in each cluster is the one with the greatest sum of scores.
  5. As soon as a candidate is elected,
    - All the other candidates from their constituency are eliminated.
    - Ballots that scored the winner have their weight reduced
  6. A candidate won with surplus if sum(score/9)> (# voters in Cluster)/(# Constituencies in Cluster)
    -For a non-surplus win, voters have their weight reduced by subtracting the score, S, they gave that winner
    - For a surplus win, voters have their weight reduced by S/W
    Where W= sum(score/9)x (# Constituencies in Cluster)/(# Voters in Cluster)
  7. All scores on all ballots are adjusted to the minimum of the current score and the current weight to represent some of that weight having been spent
  8. The next winning candidate in each cluster is the one (who has not yet been eliminated or elected) with the greatest sum of scores after adjustment
  9. Loop back to step 5 until each cluster has elected a representative. Then stop.

This could easily have STAR added at step 4 if one desired. It would make it more complicated and I think it is complicated enough.

In this is proposed in a longer document which has a list of criteria to be satisfied. I would be happy to share if you are interested. I just can’t upload a pdf here and there there is not a final draft yet so it is not posted online.


Off the cuff, the down sides I see to that system are that it requires the ballots to be collected and counted centrally (within each cluster,) it doesn’t allow the possibility of multiple winners from the same existing voting district, and it seems keeping the voting districts would leave it susceptible to gerrymandering — maybe not gerrymandering the voters, but gerrymandering the candidates.


Thanks for the reply. Maybe I should have pointed out that clusters should be small, like 4 or 5. They are equivalent to the multi-member districts in STV just that each elected representative is to represent on of the districts. This was a choice to get rid of multiple winners and keep proportionality. This can be dropped if you do not like it and just run it like STV in a multi member district. I personally like the idea of having a specific one to one regional representative for each citizen because it means there are specific people who are held accountable. This should cover all your issues except for the gerrymandering which I do not think would be worse in this system than others. Also, keeping existing districts would reduce the chance for doing this.


Actually as it turns out such a STAR version of my system does already exist. https://www.starvoting.us/pr

I am just starting to dig in so it is not clear to me that the ballot spending/reweighing or the surplus handling is the same.