The Equal Vote Coalition's 0-5 Star Proportional Research Committee

The Equal Vote Coalition's
0-5 Star Proportional Research Committee


Proportional Representation is the cutting edge of voting science and we are excited to be on the forefront.

After careful review of the leading options, our conclusion at the Equal Vote Coalition was that not only were none of the proposals ideal, but the field itself lacked sufficient objective metrics for comparing and evaluating proposals.

In 2018, The Equal Vote Coalition convened a team of local and international election scientists and voting method researchers to evaluate the proposals on the table, to develop better methods for comparing and testing proportional voting methods, and to consider and study new proposals and innovations in the field. 

The goal is to definitively determine the proportional method for tabulating 5 star ballots that is the most equitable, accurate, fair, simple, and resistant to strategic voting. This committee has nearly completed Phase 2 of the project.


Committee Project Outline:

1st. Leading voting methods worth considering were identified, and variations of each were studied closely to specify a version of each to test and compare. A set of project parameters was determined to define the scope of the project.

2nd. These systems were all simulated using computer modeling. To continue this phase the simulation results are being assessed to identify expected and unexpected outcomes, and to identify if negative outcomes can be improved with minor variations to those proposals. Once the methods have been further refined simulation can happen again, using even more sophisticated models. The simulations can measure election accuracy, ie. utility, and resilience to strategic voting.

Next. Voting methods will be compared across other metrics, such as simplicity to explain and understand, logistical viability, auditability, implicit bias, precinct summability, impacts on polarization and accountability, methods for rounding and dealing with surplus support for winners, and others. These metrics all fall under our pillars for good 5 Star proportional methods: Equity/Proportionality, Equality, Accuracy/Utility, Simplicity to Explain, Resistance to Strategic Voting, Ease of Auditing, and Tabulation Complexity.

3rd. The final phase of the project will include drafting and publishing a research paper outlining the study, presenting the data in both lay person friendly and high level formats, and explaining the findings, considerations, and conclusions.

Last. The committee will present their findings to the Equal Vote Coalition team of proportional representation and election science enthusiasts with the hope that Equal Vote can make an official recommendation or set of recommended options on this matter.


Project Parameters:

  • Voting methods must use a 0-5 star ballot. The goal of this committee is to find the best proportional method(s) for tabulating Proportional STAR Voting.
  • Whether voting methods fall under the Monroe, Thiele, or Phragman school of proportionality, all must pass basic proportionality requirements such as enabling a hare quota of voters to elect their preferred candidate and enabling any party supported by a group of voters voting on party lines using maximum and minimum scores to at-least win a share of seats proportional to that group. 
  • Voting methods must be non-partisan, ie. able to be used in non-partisan elections. We are not looking at Party List type systems.
  • Number of winners: We are looking at 3-7 winner elections. 5 winners is our baseline for consideration. More than 7 winners in one election results in very low thresholds (quotas) required to win. Very low thresholds can allow extremist factions to rise to power. Low thresholds and excessive numbers of winners can also result in decreased proportional geographic representation. Ideological and geographical representation are both important, and one need not come at the expense of the other. Exceptions can always be made if desired but for simplicity's sake 7 winners is plenty for most elections and for this project.
  • Number of candidates: For the sake of simplicity, as well as to keep it realistic, we are capping the number of candidates at 50.
  • Method must not be prohibitively complex. Methods which require over a page of code to tabulate were excluded.


Committee Participants and Contributors:

Dr. Keith Edmonds PhD, Co-Chair
Sara Wolk, Executive Director Equal Vote Coalition, Co-Chair
Dr. Jameson Quinn PhD, Co-Founder Center for Election Science
Clay Shentrup, Co-Founder Center for Election Science
Parker Friedland
Dr. Warren Smith PhD
David Hinds
Toby Pereira
Matija Skala
Neal McBurnett   
Matt Otis
Mark Frohnmayer, Founder Equal Vote Coalition


A general description of how proportional star voting works:

(This description is true for any of the variations which can be used.)

  1. Elect a Score or STAR Voting winner to the first seat.*
  2. Lower the ballot weight of those who voted for that winner.
  3. Return to step 1 and repeat until all seats are filled.

There are three main options for how to "lower the ballot weight" of voters who have already gotten someone elected: Unitary, Jefferson and Allocation. By extension there are three leading types of proportional star ballot systems which we are currently studying. Sequentially Spent Score, Allocated Score, and Reweighted Range Voting can be looked at as classical examples of each.

*Runoffs between the top two candidates for each seat can be added to each round, just to the final round, or not at all.


Here are a few of the options for tabulating proportional STAR:


Sequentially Spent Score:

1. Each voter votes using a 5 star ballot, and tabulation begins with each voter having a vote weight of 5 to "spend" on their candidates.
2. Elect the highest scoring candidate.
3. Voters who supported an elected candidate spend the number of points they gave them, which sets a cap on the score each voter has remaining to spend on future candidates. (Total score 5 - score given to winner = remaining score available to spend.)
4. Repeat these steps with ballots weights adjusted when applicable until all the necessary seats are filled.

Surplus Handling
For the second step, if the previous winner had received more than the threshold needed to win a seat (Threshold = quota of points required to earn a seat multiplied by the maximum score, 5), then the amount of weight to take away from all ballots supporting that round's winner is to be reduced proportionally to ensure that only the equivalent in ballot weight of that threshold of points is removed. This is known as Factional Surplus Handling and can be though about as "making change" for voters who collectively overpaid.

Variation: Sequentially Spent STAR includes a runoff between the two highest scoring candidates on the final seat up for election. This is intended to better incentivize honest and expressive voting and encourage voters to show their preference order.


Sequential Monroe

A variation on Allocated Score which may provide a more equality weighted vote.

  1. For candidate X, sort the ballots in order of highest score given to candidate X to lowest score given to candidate X.
  2. Calculate the sum of score given to X on the first hare quota of those ballots. Record this score as that candidate's hare quota score
  3. Elect the candidate with the highest hare quota score
  4. Set the ballot weight to zero for the voters that contribute to that candidate's hare quota score.
    • If there are several voters who have given the same score at the cusp of the Hare Quota then Fractional Surplus Handling is applied to those voters
  5. Repeat this process until all the seats are filled.
Note: Allocation is the reweighting mechanism which is used in the Single Transferable Vote (Multi-winner Ranked Choice) algorithm.

Reweighted STAR

A 5 STAR variation to Reweighted Range Voting in which a final runoff is performed for the last seat available has been proposed in order to incentivize voters to more honestly express their preference order and degree of support.

Each voter submits a ballot in which candidates are scored from 0 (worst) to 5 (best.) Each ballot is given an initial "weight" of 1.
1. The highest scoring candidate wins the first seat.
2. When a candidate wins, all ballots supporting that candidate are then reweighted, resulting in reduced vote weight going forward for voters who have successfully helped to elect a candidate. This reweighting happens in proportion to the amount of support given in order to ensure that all voters have an equitable amount of influence on the election
Reweighted ballot = 1/(1+2*SUM/5), where SUM is the sum of the scores that ballot gives to the winners-so-far
3. The remaining candidate with the highest total reweighted score wins each seat available- up until the final seat up for election.
4. For the final seat available, the two highest scoring candidates remaining runoff, with the candidate preferred (scored higher) by more reweighted ballots winning the final seat.