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Instant-Runoff Voting

Instant-runoff voting---also called ranked-choice voting, or the alternative vote---is a system of voting where voters rank candidates in order of preference rather than simply marking their most preferred candidate. Vote counting happens in rounds. In each round, the candidate with the fewest, top choice votes is eliminated and votes for that candidate are distributed to the next ranked candidate on the ballot.

Post-Election Auditing

A post-election audit is a procedure where some subset of the cast ballots are selected at random and compared to the electronic record used to produce the election tallies. The goal of an audit is to convince the losers that they did not win the election. To accomplish this goal, the audit is designed in such a way as to provide a statistical bound on the chance that an incorrect election outcome is not detected and corrected.

In recent years, researchers have designed several methods of auditing plurality elections and very recently methods have been proposed for auditing IRV elections.

IRV Data

In order to design and compare post-election audits, researchers need access to real election data. Some of this data is available, but scattered on various county websites. As a result, researchers have to track down different data sets, frequently posted online in different formats. This makes comparisons difficult as there is no standard corpus of data to use to evaluate auditing algorithms.

The data directory contains ballot data for IRV elections in a simplified version of the .blt file format used by OpenSTV.

There does not seem to be any remaining documentation on the full file format; however, this Stack Overflow answer provides a good, if incomplete, overview. The version used by the files below uses only a subset of the features that OpenSTV supports. For example, consider the following.

# Created by Stephen Checkoway
5 1
1 1 2 3 0
1 1 4 - 0
1 4 2 1 0
1 5 - - 0
1 1=2=3 2 - 0
"Example election"

This example contains several parts:

  1. Lines at the beginning of the file starting with # are comments and are ignored.
  2. The first noncomment line consists of two numbers: the number of candidates and the number of seats. Since these are IRV elections, the latter number will always be 1, except for the 2009 Aspen City Council election which used a modified IRV algorithm to elect two council members.
  3. The next lines are the individual ballots. The 1 at the beginning is, apparently, the weight of the ballot. It will always be 1. The positive, space separated numbers are the candidates ranked in order of preference. A - indicates that no candidate was given for that rank where as a sequence of numbers separated by = indicate that each of those candidates was marked---i.e., an overvote. A value of -=- denotes an overvote for which the official election data does not indicate the candidates marked. The 0 denotes the end of the ballot.
  4. The line containing only 0 denotes the end of the ballots.
  5. If there are n candidates, then the next n lines will be the names of the candidates in double quotes.
  6. The final line is the description of the election in double quotes.

IRV Code

The code directory contains some Python code for manipulating this data as well as some extra scripts that were helpful for creating the data from the official formats. The obsolete directory has some obsolete code.

The data from the San Francisco Bay Area and Pierce County was produced from "ballot image files" and "master lookup files" provided by the corresponding jurisdictions. The Python script takes the two files as input and produces a .blt file as output.

The data from the two 2009 Aspen elections was produced from an unofficial CSV file containing the election results using the Python script. (I am attempting to get the official data.)

code/elections is a Python module that contains functions for reading and writing .blt files, running IRV elections, producing lower and upper bounds on the margin of an IRV election, and for treating the ranked ballot data as if it were for a Condorcet method and producing the Condorcet winner---if one exits---and a lower bound for the Condorcet margin. In addition, if CPLEX is installed, the exact margin of an IRV election can be computed. This module contains all of the code used to produce the results in this technical report.

The code, and in particular the api is somewhat documented and an example appears below.

An older version was called There is no real documentation for the older module, but a sample interactive session is in obsolete, as is the code.

For the Condorcet functions, the numpy Python module is required. To compute the exact margin of an IRV election, the CPLEX optimization library and the python wrapper need to be installed. Since CPLEX is not free, the functionality to solve integer-linear programs is abstracted slightly. It should be relatively simple to add a new optimization library, if desired.

There are many different forms of IRV that differ slightly in the details. The IRV functions in the elections module implement three different candidate elimination rules: the base IRV elimination rules, the San Francisco RCV rules, and the complete IRV rules.

Base IRV elimination rules : These rules eliminates the candidate with the fewest votes in each round until a single continuing candidate is the top-choice on a majority of the continuing ballots. Ties are broken arbitrarily, but deterministically---that is, they will always be broken in the same way.

San Francisco RCV elimination rules : These rules eliminates the largest set of candidates in each round for which the sum of the votes for those candidates is /less than/ the votes for all of the other candidates. Candidates with the same number of votes are treated equally, either both are eliminated or neither are. The one exception to this is when the largest elimination set consists of a single candidate who has the same number of votes as another candidate. As with the Base IRV elimination rule, in this case, the candidate selected for elimination is chosen arbitrarily, but deterministically. Furthermore, a warning about this case is printed to standard error.

Complete IRV elimination rules : These rules are identical to the base rules except that they continue until there are only two candidates who remain rather than stopping once a single candidate gets a majority of the votes.

The rules to use can be selected by using the rules keyword argument to the relevant functions with the values elections.irv.BASE_IRV_RULES, elections.irv.SF_RCV_RULES, or elections.irv.COMPLETE_IRV_RULES.

Other rules are possible, but not implemented. For example, the 2009 Aspen City Council election used very different rules for electing two city council members and the Burlington mayoral elections treat overvotes differently. The Aspen rules could be implemented without too much difficulty. The Burlington rules would require changing the "ballot cleaning" rules and modification to the basic tree data structure used to represent the set of ballots.

Elections Module Example

Below is a simple Python script that will read in a .blt file, compute various bound, and then print the results. Note that computing the Condorcet winner and lower bound requires the numpy package and computing the IRV margin exactly requires the CPLEX library and Python wrapper.

#!/usr/bin/env python

import sys

from elections import blt, irv, condorcet

if len(sys.argv) != 2:
    print 'Usage: %s election.blt' % sys.argv[0]

election = blt.read_blt(sys.argv[1])
winner, _, elim_order = irv.irv(election)
slb = irv.irv_simple_lb(election, rules=irv.COMPLETE_IRV_RULES)
lb = irv.irv_lb(election)
ub = irv.irv_ub(election, winner=winner, elim_order=elim_order)
margin = irv.irv_margin(election, winner=winner, elim_order=elim_order, ub=ub)
m = condorcet.build_condorcet(election)
cwinner = condorcet.condorcet_winner(m)
clb = condorcet.condorcet_lb(m, winner=cwinner)

print 'IRV: %d; %d <= %d <= %d <= %d' % (winner, slb, lb, margin, ub)
print 'Condorcet: %d; %d' % (cwinner, clb)


Python code to manipulate some election results.






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