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A reference implementation for counting votes with ranked choice voting (RCV).

Table of Contents


This is a reference implementation in Python of the core vote counting algorithms for ranked choice voting (RCV) as specified by California Senate Bill 1288 (2016).

SB 1288 was passed by the California Legislature but was vetoed by Governor Jerry Brown. Though it did not become law, it still serves as a useful reference as an RCV specification.

The legal language describing the RCV vote counting algorithms was developed with an emphasis on being clear, consistent, and complete, with the goal that any two conforming implementations would produce the same results for a given set of equivalent inputs and tabulation parameters. The legal language describing the vote counting was proposed in a new Division 22 of the California Elections Code, Chapters 1 and 2.

This reference implementation is intended to supplement that legal language as an additional means to document the intended intepretation, clarify any ambiguities, and avoid misunderstandings.

As a reference implementation, the programs and test cases can be used as a starting point for conformance testing of other implementations.

Repository Structure

The sb1288 directory contains a Python package with the reference implementation programs. The tests directory contains test programs and data that document the intended behavior and which in some regards are as important as the Python programs in the sb1288 directory for documenting the intent of the legal language.

The vote counting algorithms in this reference implementation cover both single-winner RCV, also known as instant runoff voting (IRV), and multi-winner RCV, also known as single transferable vote (STV).

For multi-winner RCV, SB 1288 specifies a version of the weighted inclusive Gregory method, so that when a winner's surplus is distributed to other candidates, all ballots counting for that winner are transferred, but each ballot is transferred at a reduced transfer value representing that ballot's share of the winner's surplus as a portion of the winner's total vote count. The winner retains a vote total equal to the threshold. As a result, a ballot can subsequently count for a subsequent candidate as only a fraction of a whole vote.

Both single- and multi-winner algorithms can be invoked with the sb1288.tabulate() function, which takes as a first argument the number of seats to be elected. That function resides in the sb1288/ file. That file contains additional documentation about the tabulate() function.

Use Examples

Three ways to run an RCV tabulation are:

Caller gives data directly

After importing the sb1288 package with:

import sb1288

tabulation of RCV votes can be accomplished by calling the sb1288.tabulate() function, which is defined as:

def tabulate(nbr_seats_to_fill, candidates, ballots,
      max_ranking_levels, tie_breaker, options={}):

For example:

elected, status, tally = sb1288.tabulate(1, " A B C", [
      [4, ' A B C'],
      [3, ' B A C'],
      [2, ' C B A']
      3, ' C A B', {})

will tabulate a contest that:

  • produces one winner, i.e. uses the IRV algorithm
  • has three candidates (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
  • does not specify any special tabulation options

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 three-tuple consisting of:

  • elected, a set of winners
  • status, a dict 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 candidates largest vote total in any round
  • tally, a dict showing the essential round-by-round vote totals of the tabulation

In this particular case, the results would be as if the following assignments had occured:

elected = ('B',)
status = {
      'A': sb1288.Status('A', 'defeated', 2, 4),
      'B': sb1288.Status('B', 'elected',  2, 5),
      'C': sb1288.Status('C', 'defeated', 1, 2)
tally = {
      'A': (4, 4),
      'B': (3, 5),
      'C': (2,),
      ':Overvotes': (0, 0),
      ':Abstentions': (0, 0),
      ':Other exhausted': (0, 0)

Caller gives data in JSON files

An alternative way to run a tabulation is with the sb1288.tabulate_with_json() function which reads the tabulation input from a named JSON file and by default prints the results.

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

  "description": "An example RCV contest"
  ,"nbr_seats_to_fill": 1
  ,"candidates": " A B C"
  ,"ballots": [
    [4, " A B C"],
    [3, " B A C"],
    [2, " C B A"]
  ,"max_ranking_levels": 3
  ,"tie_breaker": " C A B"
  ,"options": {}

and then executing the Python statement:

elected, status, tally, tab_spec = sb1288.tabulate_with_json(
      '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],
    ["A", "defeated", 2, 4],
    ["C", "defeated", 1, 2]
  "tally": {
    "B": [3, 5],
    "A": [4, 4],
    "C": [2],
    ":Abstentions": [0, 0],
    ":Other exhausted": [0, 0],
    ":Overvotes": [0, 0]

If the second argument is omitted or set to the empty string, the JSON output is printed to stdout rather than being written to a file.

The first three return values are the same as are returned using the sb1288.tabulate() function. The fourth return value is a dict of tabulation specifications reflecting the net result of 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.

Command line using JSON files

A third way to run an RCV tabulation is from the command line. The previous example could be run as:

python -m sb1288.with_json example.json example-results.json

Depending on the configuration of your computer, other command names might be used, for example python3 instead of python when running a Python version 3.x.

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


Tests can be run using the Python unittest module. For example in a local copy of this repository, change the working directory to the tests directory and run one of the following commands:

python -m unittest discover

python3 -m unittest discover

That should run 182 tests, all without errors, typically in less than a second, though speeds vary depending on the type of computer being used.

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

  • traditional unittest tests specified in tests/unittest/test\*.py files and which are typically dependent on the internal design and implementation of this reference implementation

  • tests with inputs and expected results that are specified in JSON files and which are designed to be typically applicable to other conforming implementations of the California RCV vote counting algorithms

The JSON-based tests are typically run from a test*.py 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 Python dict and which includes a "description" name / key.

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

The programs have been written and tested for Python versions 2.7.x, beginning with 2.7, and versions 3.x, beginning with 3.2. The unit tests for the command line interface assume that the Python command name is python for versions 2.7.x and python3 for versions 3.x. Change the values for PYTHON_2_CMD and PYTHON_3_CMD in tests/unit/ if your computer uses different commands.


This reference implementation focuses on the core vote counting algorithms and does not offer all of the functionality that a voting system would need to provide to support a California RCV election. For example, it does not provide all of the information needed for reporting. Specifically, it does not support any information about precincts.

There are several areas where the legal language allows some leeway in the specifics of how RCV vote counting is performed. They include:

  • resolution of ties for which candidate should be eliminated in a round
  • decisions about whether an IRV tabulation should continue once a majority winner has been identified
  • the manner in which ballot rankings are expressed

This reference implementation provides some features to support that functionality, but other implementations that conform to the legal language can provide other modes of support.

California RCV vote counting algorithms may be modified by California Secretary of State regulations provided those modifications do not change who is elected. This reference implementation does not currently reflect any such proposed or adopted regulations.

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

For a reference implementation written in Python, optimizing the amount of memory, CPU time, or elapsed time to tabulate votes was generally not a priority. Instead, there has been some preference for writing the programs so that they more closely parallel the provisions of the legal language.

Running the automated tests in Python 3 requires at least version 3.2.

In order to focus on issues of core RCV functionality and to allow programs to run under different versions of Python, all test data has been limited to using ASCII characters. Non-ASCII characters are not supported.


This reference implementation includes an extension to the STV tabulation logic that provides for alternative conditions for defeating candidates: batch defeats of multiple candidates and deferred distribution of surplus. These features were part of preliminary versions of SB 1288, but were later removed and identified for specification as California Secretary of State regulations, as authorized by SB 1288.

For more information about these features, please read this additional description.


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 David Cary; licensed under Apache License, Version 2.0


A reference implementation of the core ranked choice voting (RCV) vote counting of California SB 1288 (2016).







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