Count votes for a Meek's method RCV / STV election contest using the reference rule, with optional extensions.

Usage no npm install needed!

<script type="module">
  import meeksPrfJs from '';



Count votes for a Meek's method RCV / STV election contest using Javascript software.

Table of Contents

Quick start

For use with Node, this package can be installed with npm, by creating a new directory / folder, for example meeks-prf, and then from the command line, changing to that directory and running the command:

npm install meeks-prf-js

You can then tabulate a contest with the command:

node . input.json results.json

where the file input.json has the contest input data and results.json is the output file to which results will be written. A sample input file is provided at ./uses/sample-01-in.json.

More generally, if the current directory is not the project directory, you can use the command:

node path-to/meeks-prf input.json results.json

Other ways of using the package are described below.


Use this Javascript package to count votes for a ranked choice voting (RCV) / single transferable vote (STV) election contest using the Proportional Representation Foundation's reference rule for Meek's method and various extension to that rule.

The Javascript programs in this package can be directly used in modern browsers. The package also includes versions of those programs that have been converted for use in Node. Use in other browsers requires additional support not included in this package.

Meek's method is a form of RCV / STV that supports proportional representation in multi-winner elections. It can provide a fairer and more comprehensive transfer of surplus than other forms of STV, including variations of the weighted inclusive Gregory method (WIGM) which also involves transfers of surplus as fractions of a vote. Any form of STV tends to provide fairer results than other traditional election methods and greatly reduces the practical opportunities for tactical voting. Meek's method tends to accomplish these goals better than other forms of STV. However the trade-off is that Meek's method is more computationally intensive, to the extent that it is typically not practical to count votes with Meek's method without the assistance of a computer for contests with more than a few winners.

The reference rule published by the Proportional Representation Foundation is particularly significant because it ensures that independent but conforming implementations will always produce the same result, provided that any ties are consistently resolved.


This is version 1.0.0 of the Meeks-PRF-js project. It has stable, well tested functionality. Unlike earlier versions, this version is intended for general use. With this version, discrepancies about the 'type_of_altdefs' option were resolved for its default value to be 'if_no_new_electeds'. This version includes functionality that is similar to v3.0.0 of a related Python project, with some additional improvements.

Repository structure

The src directory contains the Javascript vote counting programs that can be run directly in modern browsers and which are ES modules. The run directory has corresponding programs that can run in Node v10 and later. The tests directory contains test programs and data. The docs directory has public API documentation as HTML.

The vote counting tabulation algorithm can be invoked with the Meek.tabulate() function, where Meek is the imported / required name for the meek.js file from either the src or run directories. Those files contain additional documentation about the tabulate() function.

Use Examples

Three ways to run a Meek's method tabulation are:

Caller gives data directly

After importing / requiring meek.js, for example with:

import * as Meek from 'path-to/src/meek.js';

tabulation of RCV votes can be accomplished by calling the Meek.tabulate() function, which is defined with the signature:

function tabulate(nbrSeatsToFill, candidates, ballots,
      maxRankingLevels, tieBreaker, excluded, protectedzz,
      options={}, progressCallback=null):

For example:

const results = Meeks.tabulate(1, " A B C", [
      [4, ' A B C'],
      [3, ' B A C'],
      [2, ' C B A']
      3, ' C A B', '', '', {}, null);

will tabulate a contest that:

  • Produces one winner.
  • Has three candidates with identifiers A, B, and C.
  • Has nine ballots, two of which rank C first, B second, and A third.
  • Allows a voter to rank up to three candidates.
  • Uses a tie breaker ranking for resolving ties, picking for elimination the earliest ranked candidate of any tied candidates; so C is picked for elimination if tied with A or B (or both) and A is picked for elimination if tied only with B.
  • No candidates are excluded from the tabulation.
  • No candidates are protected from defeat and thus assured of being elected.
  • Does not specify any special tabulation options.
  • Does not use a progress callback function.

The above example uses a short cut for specifying a sequence of strings by writing them in a single, delimiter-separated string with the first character specifying what the delimiter is.

The result of the function is a data object that includes the following three properties:

  • 'elected', a set of winners.
  • 'statuses', a data object showing the status of each candidate.
    • Whether the candidate was elected or defeated.
    • The round in which the candidate was elected or defeated.
    • The candidate's vote total when elected or defeated.
    • The candidate's keep factor for the last tabulation iteration.
    • Whether the candidate was pre-designated as being excluded or protected.
  • 'tally', a data object showing the round-by-round vote totals and other statistics of the tabulation.

For the example mentioned above, the results would be as if the following assignments had occurred:

results.elected = new Set(['B'])
results.statuses = {
      'A': Status('A', 'defeated', 2, D(4.0), D(1.0)),
      'B': Status('B', 'elected',  2, D(5.0), D(1.0)),
      'C': Status('C', 'defeated', 1, D(2.0), D(0.0))
results.tally = {
      'A': [D(4.0), D(4.0)],
      'B': [D(3.0), D(5.0)],
      'C': [D(2.0),],
      ':Votes for candidates': [D(9.0), D(9.0)],
      ':Overvotes': [D(0.0), D(0.0)],
      ':Abstentions': [D(0.0), D(0.0)],
      ':Other exhausted': [D(0.0), D(0.0)],
      ':Total votes': [D(0.0), D(0.0)],
      ':Quota': [D(4.500000001), D(4.500000001)],
      ':Total surplus': [D(0.0), D(0.499999999)],
      ':Iterations': [1, 1]

where D is an alias for the Decimal9 class, which is used internally to represent numbers of votes.

Caller gives data in JSON files

An alternative way to run a tabulation is with the WithJson.tabulate() function, where WithJson is the name for the default export from the with_json.js file. That function reads the tabulation input from a named JSON file and writes the results in a JSON format to a file.

For example, the previous example can be tabulated using a file named example.json with the following content:

  "description": "An example RCV contest"
  ,"nbrSeatsToFill": 1
  ,"candidates": " A B C"
  ,"ballots": [
    [4, " A B C"],
    [3, " B A C"],
    [2, " C B A"]
  ,"maxRankingLevels": 3
  ,"tie_breaker": " C A B"
  ,"excluded": ""
  ,"protected": ""
  ,"options": {}

and then executing the Javascript statement:

async [const results, tab_spec] = WithJson.tabulate(
      'example.json', 'example-results.json')

which writes a file example-results.json with the following content:

  "description": "An example RCV contest"
  ,"elected": ["B"]
  ,"status": [
    ["B", "elected", 2, 5.0, 1.0],
    ["A", "defeated", 2, 4.0, 1.0],
    ["C", "defeated", 1, 2.0, 0.0]
  ,"tally": {
    "B": [3.0, 5.0],
    "A": [4.0, 4.0],
    "C": [2.0],
    ":Votes for candidates": [9.0, 9.0],
    ":Overvotes": [0.0, 0.0],
    ":Abstentions": [0.0, 0.0],
    ":Other exhausted": [0.0, 0.0],
    ":Total votes": [9.0, 9.0],
    ":Quota": [4.500000001, 4.500000001],
    ":Total surplus": [0.0, 0.499999999],
    ":Iterations": [1, 1]

If the second argument is omitted or set to the empty string, the JSON output is printed to stdout.

The results return value is the same as returned by the Meek.tabulate() function. The second return value is a data object that documents the merged tabulation input specifications. It reflects what was found in the input JSON file and any included files. The input JSON file can have an 'include' property with a value that is a list of JSON file names from which other property/values are included, but which can be overridden by corresponding property/values in the primary input JSON file.

In the above example, the lines indicating that there are no excluded candidates and no protected candidates could be omitted, since those are the default values for JSON files.

Command line using JSON files

A third way to run an RCV tabulation is from the command line using Node. This was mentioned in the quick start section. The previous example could be run as:

node path-to/run example.json example-results.json

If the example-results.json argument is omitted or given as an empty string, the JSON results are printed to stdout.

Note that the second command line value, the one following 'node', can name either the project directory or its run directory.


Tests can be run using Jest. When this package is installed using npm, Jest is also installed as one of its development dependencies.

To run tests, change the working directory to the tests directory and run the command:

npm run test

That should run 21 test suites with a total of 559 tests, all without errors, typically in less than 15 seconds, though speeds can vary depending on the type of computer being used.

There are two kinds of tests in the tests directory tree:

  • more traditional unit tests specified in tests/unit/*test.js files and which are typically dependent on the internal design and implementation details of programs in the src directory.

  • tests with inputs and expected results that are specified in JSON files and which are designed to be typically applicable to any conforming implementation of the reference rule, except for those tests that apply to extensions to the reference rule.

The JSON-based tests are typically run from a *test.js file in the same directory as the JSON files specifying the test. A group of related tests are specified in similarly named JSON files, sometimes sharing a base JSON file for common data. For example, files abc-007-1.json and abc-007-2.json might specify two related tests and reference (include and possibly override) a common abc-007-base.json file.

The JSON files specify a JSON object which is convertible to a Javascript data object and which includes a "description" property.

Global parameters for the JSON-based test cases may be set in the file tests/all-tests-spec.json.


This implementation focuses on the core vote counting algorithms and does not offer all of the functionality that might be expected to support tabulation of an election. For example, it does not directly supply support for end-user report formats.

Neither the programs nor the test cases enforce specific maximum limitations on the sizes of input to the STV tabulation. Sizes of contests that can be tabulated generally depend on the amount of resources, especially memory, available to the software.

This package can reliably handle large numeric values up to 9,000,100 to nine decimal places of accuracy. The program will not accept more than that many ballots as input, even if they have been pre-summarized into fewer ballot groups.

Numeric values much larger than that start to lose precision when converting to or from native Javascript number values and to or from JSON number values.

This implementation can use ballot trees to more efficiently process large numbers of ballots with larger numbers of rankings. However this version does not attempt to strictly minimize the resources that are used or to manage a time vs. space tradeoff.

As an example of what this program can accomplish, it has tabulated in a desktop browser non-trival contests with half a million individual ballots, none of them pre-summarized into multi-ballot ballot groups, each ballot ranking 100 candidates, and the contest electing 20 winners. Such tabulations complete within a few minutes. Due to special cases that result in persistently slow convergence rates, it is possible that smaller contests could take extraordinarily long to tabulate.

In order to focus on issues of core functionality, all test data has been limited to using ASCII characters.


This implementation includes several extensions to the reference rule. These include::

  • Handling anomalous ranking patterns.
  • Reporting some exhausted votes as abstentions.
  • An option to always count votes for at least one round.
  • An option for whether or in which rounds to check for perform alternative defeats (a.k.a. multiple defeats).
  • An option for when in a round to check for performing alternative defeats.
  • Support for vacancy re-tabulations, including the ability to designate some candidates as being excluded (a.k.a. withdrawn) and others as being protected from defeat and thus be assured of being elected.
  • An option for helping tabulations run faster by internally representing the rankings of ballots and ballot groups in a ballot tree.

The rest of this section briefly describes each of these extensions. The extensions are also described in the HTML-based documentation of the public API.

The anomalous ranking patterns that are allowed include::

  • duplicate rankings (ranking the same candidate more than once at different ranking levels)
  • overvoted rankings (ranking two or more different candidates at the same ranking level on a ballot)

The reference rule implicitly assumes that these anomalous ranking patterns do not occur in the ballots submitted for tabulation. See the documentation for the Meek.Tabulation class for the specifics of how these anomalous ranking patterns are handled.

There is an option, turned on by default, that counts votes for the first round even if doing so is not required to determine all winners because there is not an excess of hopeful candidates. The reference rule can be strictly followed in this regard by using the option {"always_count_votes": false} in Javascript or JSON. The value of this option has no effect if there is an excess of hopeful candidates and as a result, counting votes for one or more rounds is required to determine winners.

There are two options that control whether and how alternative defeats are performed. Alternative defeats can involve defeating one or more candidates at a point in the tabulation when no candidates or only one candidate would be defeated. Alternative defeats are also known as multiple defeats, batch defeats, and deferred surplus distribution. By default, alternative defeats are not performed.

Alternative defeats can be activated with the alternative_defeats option, setting it to a value of "Y" value or activating it only for certain rounds with a sequence of "Y"s and "N"s.

There is also an option, "type_of_altdefs", that controls the point in the tabulation algorithm at which the alternative defeats is checked. In order for this option to have an effect on a round, the "alternative_defeats" option must be a "Y" for the round. In addition to doing the check at the end of step B.2.e, as allowed by the reference rule, there are also options to check in the middle of step B.2.e, if no candidates were elected in the iteration, or to check at the beginning of step B.3, just before doing end-of-round single defeats.

There is support to exclude and protect candidates. An excluded candidate is not eligible to be elected or receive votes and is marked as defeated before the first round of tabulation. The reference rule uses the term "withdrawn" rather than "excluded". A protected candidate is assured of being elected.

The ability to exclude and protect candidates can be useful when using the ballots of a previous election to fill one or more vacancies. For a typical use case, exclude all previous candidates who are unwilling or otherwise not eligible to fill the vacancies, protect all candidates that will continue to serve, set the number of seats to fill to the sum of the number of protected candidates plus the number of vacancies to fill, and then retabulate the contest.

When there are protected candidates, there are separate quotas for protected candidates and unprotected candidates in order to ensure that an excess of unprotected candidates will not be elected.

In order to help tabulations run faster for larger constests, there are options to use a ballot tree to represent ballots internally. If used, the ballot tree can be either static or dynamic.

Other commands

Other development commands defined for this project include:

  • npm run build

    Will re-build the node-compatible versions of the programs in the run directory.

  • npm run build-one -- src/<file-name.js>

    Will re-build in the run directory a single node-compatible version of the file(s) listed at the end of the command.

  • npm run build-docs

    Will re-build the HTML-based documentation of the public API that is stored in the docs directory.

  • node path-to/<package-directory> --version


    `node path-to/run --version

    Will print the version number which consists of a major, minor, and patch version number using semantic versioning.


This project is licensed under the Apache License, Version 2.0 (the "License"); you may not use contents of this repository except in compliance with the License. A copy of the License is in the LICENSE file and may also be obtained at:

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

Copyright 2016-2019 David Cary; licensed under Apache License, Version 2.0