starvote

A simple STAR Voting tabulator

Copyright 2023 by Larry Hastings

STAR voting is a relatively-new electoral system. It's simple to vote and simple to tabulate. While a completely fair and perfect electoral system is impossible, STAR Voting's approach makes reasonable tradeoffs and avoids the worst pitfalls. It's really great!

This module, starvote, implements a simple STAR Voting tabulator. It requires Python 3.7 or newer, but also supports CPython 3.6. (starvote relies on dictionaries preserving insertion order, which is guaranteed as of Python 3.7, but happened to work in CPython 3.6.)

Features:

• Supports four electoral systems:

  • STAR Voting, the snazzy new single-winner voting system.
  • Bloc STAR Voting, a multi-winner variant of STAR voting that fills multiple seats with the most popular candidates.
  • Allocated Score Voting, a proportional representation electoral system, and so far the only such system officially authorized to be a "Proportional STAR Voting" method.
  • Reweighted Range Voting (aka "RRV"), an alternative proportional representation electoral system. RRV isn't a STAR variant, but like STAR it's a form of score voting. So the ballot and instructions to the voter are identical to a STAR-PR election. The RRV algorithm is much simpler than Proportional STAR Voting, and its "never discard a voter" approach is appealing.

• Implements the Official Tiebreaker Protocol for STAR Voting and Bloc STAR Voting elections.

• Provides a user-configurable final tiebreaker mechanism if the election (or one round in the election) ends in a tie.

  • The default tiebreaker mechanism randomly shuffles all the candidates in advance of running the election, then breaks the tie in favor of the candidate(s) that appear earliest in the list.
  • Alternatively, you may choose to randomly pick a candidate (or candidates) from the tied candidates, on demand.
  • You can also implement your own custom tiebreaker.
  • If you specify that there should be no tiebreaker, in the event of an unbreakable tie the election will raise an UnbreakableTieError exception.

• All election tabulation calculations are performed using only integers and fractions. This guarantees the calculations are 100% consistent and accurate across all platforms. Floating-point rounding errors are impossible--because floats are never used!

• Supports running elections specified in CSV files using https://star.vote/ format.

• Also supports running elections specified in a convenient custom file format called starvote format.

• starvote 2.0 passes its test suite with 100% coverage on all supported versions.

• starvote has no external dependencies.

A quick STAR Voting primer

When you vote using STAR Voting, your ballot looks something like this:

Amy    0 1 2 3 4 5
Brad   0 1 2 3 4 5
Chuck  0 1 2 3 4 5
Darcy  0 1 2 3 4 5

To vote, give every candidate a score from 0 to 5. 5 means you like them the most, 0 means you like them the least. (If you don't pick one of the scores, that's the same as a 0.) If you give two candidates the same score, that means you like them equally--you don't have a preference between them.

To figure out who won, you apply the STAR method: Score, Then Automatic Runoff.

In the first round, the score round, you add up the scores of all the candidates. The top two scoring candidates automatically advance to the second round.

In the second round, you examine every ballot to see which of the two remaining candidates they preferred. If one has a higher score, that ballot prefers that candidate. If the ballot scored both candidates the same, they have no preference. The candidate that was preferred by more ballots wins the election. It's that simple!

What's so good about STAR Voting?

Electoral systems are a surprisingly deep topic. They've been studied for hundreds of years, and there are many many different approaches. There are a number of desirable properties and undesirable properties that electoral systems can have. And, bad news: it's impossible for there to be one best-possible voting system. There are mutually exclusive desirable properties. You can't make a one-size-fits-all system that avoids every problem.

STAR Voting avoid the worst problems of electoral systems. The remaining undesirable properties were chosen as the least-bad option.

Here are some desirable properites STAR Voting displays:

• It's monotonic. Giving a candidate a higher score can never hurt them, and giving a candidate a lower score can never help them. (And yes, this is not always true of voting systems. The increasingly popular Instant Runoff Voting fails this; paradoxically, it's possible to hurt a candidate you prefer by giving them a higher score.)
• It's resolvable. Ties are unlikely.
• It complies with the majority loser criterion. If a majority of candidates like one candidate the least, that candidate will never win a STAR Voting election.

Here are some desirable properties STAR Voting doesn't have:

• It's not a Condorcet method, which is a very particular property of an electoral system. Let's say you have an election with three candidates, A, B, and C. You ask each voter to vote in three head-to-head races: "which do you like better, A or B?", "which do you like better, B or C?", and "which do you like better, A or C?" If there's one candidate that wins in every such head-to-head vote in the election, they would be the "Condorcet winner", and an electoral system that guarantees the "Condorcet winner" will win the election is called a "Condorcet method". STAR isn't a Condorcet method, because Condorcet doesn't take into consideration the strength of preference. So STAR can arguably give a better result. (On the other hand, STAR does guarantee the opposite: a Condorcet loser will never win a STAR election. And, as a practical matter, it's frequently true that the winner of a STAR election just happens to be the Concorcet winner.)
• It doesn't satisfy the majority criterion. The majority criterion requires: "if one candidate is ranked first by a majority of voters, that candidate must win".
• It doesn't satisfy the later-no-harm criterion. Later-no-harm requires that if you've already expressed a preference for a candidate on your ballot, you shouldn't be able to harm that candidate by expressing another preference for another candidate later on the ballot. STAR fails this; giving a higher vote to a less-preferred candidate might mean that your more-preferred candidate doesn't get elected. The STAR Voting team wrote an essay on why they gave up on this criterion. The short version is: electoral systems that satisfy later-no-harm generally also exhibit the spoiler effect, which is a worse property. But achieving later-no-harm and avoiding the spoiler effect makes your electoral system even worse!

API

election

To use starvote, import starvote, then call the election method:

def election(method, ballots, *,
    maximum_score=5,
    print=None,
    seats=1,
    verbosity=0,
    ):

election tabulates an election based on your parameter and returns a list containing the winners. (Even for single-winner STAR Voting--in that case, the list will only contain one element.)

method specifies which election system you want to use, via predefined Method objects. The allowed values are:

• starvote.STAR_Voting,
• starvote.Bloc_STAR_Voting,
• starvote.Allocated_Score_Voting, and
• starvote.Reweighted_Range_Voting.

Since those are a lot to type, starvote also provides nicknames, respectively:

• starvote.star,
• starvote.bloc,
• starvote.allocated, and
• starvote.rrv.

ballots should be an iterable containing individual ballots. Ballots are dict objects, mapping the candidate to that ballot's score for that candidate. The candidate can be any Python value; the score must be an int.

maximum_score specifies the maximum score allowed for any vote on any ballot.

seats specifies how many seats the election should fill. STAR Voting is a single-winner method, so this should be 1 when using STAR Voting; for all the other methods, seats must be greater than or equal to 2.

verbosity specifies how much output you want. The current supported values are 0 (no output) and 1 (output); values higher than 1 are currently equivalent to 1.

print lets you specify your own printing function. By default election will use builtins.print; your replacement print function should have the same signature.

Functions for specific electoral systems

starvote also exports functions implementing each of the supported electoral systems:

• star_voting implements single-winner STAR Voting.
• bloc_star_voting implements multi-winner Bloc STAR Voting.
• allocated_score_voting implements Allocated Score Voting.
• reweighted_range_voting implements Reweighted Range Voting.

These functions take much the same signature as election, with the following changes:

• They don't take the method positional parameter; the method is implicit in the function. All four only take one positional parameter, ballots, which is required.
• star doesn't take a seats parameter. The other three have a seats keyword-only parameter, and this parameter is required--it doesn't have a default. (A required keyword-only parameter is pretty rare in Python!)
• Note that these functions also always return a list, even star_voting.

Reference implementation of Allocated Score Voting

starvote ships a copy of the reference implementation of Allocated Score Voting. Since this requires both NumPy and Pandas, it's not imported by default. (I didn't want starvote to have any external dependencies. The unit test suite runs correctly whether or not these external dependencies are installed.)

You can import it with import starvote.reference; the directly-callable function is starvote.reference.allocated_score_voting_reference. You can also use the Method object

If you want to integrate it into the starvote module, callstarvote.reference.monkey_patch(). This does three things:

• Adds the function to the starvote module directly, as starvote.allocated_score_voting_reference.
• Adds it to starvote.__all__ so that symbol gets brought in by from starvote import *.
• Adds the appropriate Method object to starvote.methods, using the name 'Allocated Score Voting (reference)' and the nickname allocated_r.

Note: the reference implementation doesn't support tiebreakers. allocated_score_voting_reference does accept a tiebreaker argument, but currently it must be None.

Ties

The good news is, STAR Voting elections rarely result in a tie in the real world. But ties can still happen. The good news is, STAR Voting has a sensible, thorough protocol on how to break a tie. The bad news is, not all ties are breakable--some ties genuinely represent the ambivalent will of the voters.

starvote gives you control over how to break ties in elections, through the tiebreaker parameter to election and the election-specific functions. starvote also has two predefined tiebreaker functions, but you can substitute your own--or none at all.

The default tiebreaker in starvote is predefined_permutation_tiebreaker, passing in candidates=None.

predefined_permutation_tiebreaker

The main tiebreaker for starvote is predefined_permutation_tiebreaker. This is a class; you should instantiate it and pass in the instance as the tiebreaker argument when you run the election.

predefined_permutation_tiebreaker resolves the tie in favor of an ordered list of candidates.

Given these three variables, defined at the time it breaks the tie:

• candidates, an ordered list of all candidates participating in the election,
• tie, an iterable of the tied candidates, and
• desired, the number of winners we wanted.

predefined_permutation_tiebreaker computes the winners of the tie as follows:

winners = [c for c in candidates if c in tie][:desired]

In other words, it returns a desired-length subset of tie, preferring candidates that appear earlier in candidates over those that appear later.

predefined_permutation_tiebreaker accepts a candidates argument, which should be an ordered pre-chosen list of all candidates. The default value is None, which instructs predefined_permutation_tiebreaker to scan the ballots at the start of the election, produce its own list of all the candidates, randomly shuffle that list, and use that list as the candidates list.

If you pass in your own candidates list, you may also pass in a string for the description keyword-only parameter, which should be text describing the source of this ordered list of candidates.

on_demand_random_tiebreaker

If you prefer more unpredictability in your life, you can choose on_demand_random_tiebreaker to break ties. on_demand_random_tiebreaker will simply pick a random candidate (or candidates) on demand, using Python's random.sample function. on_demand_random_tiebreaker is a function; you should simply pass it in as the tiebreaker parameter.

UnbreakableTieError

If you explicitly set tiebreaker to None, and an election results in a tie, starvote will raise an UnbreakableTieError exception. You can get a text description of the tie by calling str on the exception; you can also get a list of the tied candidates in its candidates attribute.

Writing your own tiebreaker

You can write your own tiebreaker and pass it in in the tiebreaker parameter to your chosen election function. Custom tiebreakers can be either a function or a class.

A custom tiebreaker function should have this signature:

def custom_tiebreaker(options, tie, desired, exception):

Here's what these four parameters will contain:

• options is a starvote Options object. options has attributes mapping to the arguments you passed in to election. You should obey options.verbosity when deciding whether or not to print, and you should print using options.print. options also has the following convenience methods:

  • options.heading is a context manager that prints a heading to the output if options.verbosity is 1 or greater. You pass in the heading as a string. You can nest headings.
  • options.print_candidates will print an iterable of candidates. You pass in the iterable as the first (and only) positional argument. Also accepts a numbered parameter; if numbered is true, it prints the candidates in order, prepended by their ordinal number (starting with 1). If numbered is false, print_candidates attempts to sort the candidates before printing them.

• tie is a list of the tied candidates.

• desired is the desired number of winners.

• exception is the UnbreakableTieError for this tie. If you can't break the tie, you should raise this object.

Note that starvote will also parse the tiebreaker function's docstring. The first line of the docstring will be used as a "heading" printed during election initialization, with the rest of the docstring will be printed as the body of that heading if options.verbosity is 1 or greater.

You can also write a custom tiebreaker class. The only requirement is that the class inherits from starvote.Tiebreaker, and it supports a __call__ method with the same signature as a custom tiebreaker function. (However, here the docstring is ignored; it's up to you to call options.heading and options.print.)

Tiebreaker classes can also optionally have an initialize method:

def initialize(self, options, ballots):

This will be called during initialization of the election, before any processing of the votes. Here's an explanation of the two parameters:

• options is the same object as the options passed in to a custom tiebreaker function.

• ballots is the iterable of ballots passed in to the election function.

Whichever kind of tiebreaker you write, you should add it to starvote.tiebreakers. That's a dict mapping names to tiebreakers. Tiebreakers you add to that dict will be available to starvote format elections parsed by parse_starvote.

Code example

Here's an example of computing a poll between Amy, Brian, and Chuck:

import starvote

ballots = [
    {'Amy': 1, 'Brian': 3, 'Chuck': 5},
    {'Amy': 5, 'Brian': 2, 'Chuck': 3},
    {'Amy': 4, 'Brian': 4, 'Chuck': 5},
]

winners = starvote.election(starvote.STAR, ballots, verbosity=1)

(This example is included as example.py in the starvote Git repo.)

After this example code finishes, the winners variable will contain the list ['Chuck']. The example also produces this output:

[STAR Voting]
  Tabulating 3 ballots.
  Maximum score is 5.
[STAR Voting: Initializing ordered permutation tiebreaker]
  Computing a random permutation of all the candidates.
  Permuted list of candidates:
    1. Brian
    2. Chuck
    3. Amy
  Tiebreaker candidates will be selected from this list, preferring candidates with lower numbers.
[STAR Voting: Scoring Round]
  The two highest-scoring candidates advance to the next round.
    Chuck -- 13 (average 4+1/3) -- First place
    Amy   -- 10 (average 3+1/3) -- Second place
    Brian --  9 (average 3)
  Chuck and Amy advance.
[STAR Voting: Automatic Runoff Round]
  The candidate preferred in the most head-to-head matchups wins.
    Chuck         -- 2 -- First place
    Amy           -- 1
    No Preference -- 0
  Chuck wins.
[STAR Voting: Winner]
  Chuck

starvote format

starvote also defines a custom text format for specifying elections called starvote format. It's heavily used for testing starvote itself, though it could be used to run real elections.

starvote format looks kind of like INI format, but it isn't exactly the same.

Why'd I write this? I got tired of CSV files. It's very handy to add metadata about how to run the election to the election file itself. And starvote format is so much easier to read and edit than the equivalent https://star.vote/-format CSV file.

Definition

A string that contains an election in starvote format is called a starvote format election.

starvote format is a line-oriented format. Leading and trailing whitespace per-line is ignored (and stripped). Lines that start with # are comments. Empty lines and comments are (mostly) ignored.

Non-empty lines that aren't comments are either an assignment line, a pragma line, or a section line.

A pragma line ends with a colon (:). Pragma lines are free-form; currently there's only one defined pragma. (When parsing a line, pragma take precedence over assignment.)

An assignment line must contain an equals sign (=); the text before the equals sign is the "name", and the text after the equals sign is the "value". What effect this has depends on what section we're in.

A line that starts with [ and ends with ] defines a section. You specify the name of the section between the square brackets. You can only specify a section once. Only two sections are supported: options and ballots.

The options section specifies how to run the election. Assignment lines in the options section specify options; each name maps to a parameter to the election function. Here are all the supported names:

    maximum score = <integer>
    method = <string>
    seats = <integer>
    tiebreaker = <string | list>
    verbosity = <integer>

A starvote format election can specify each of these a maximum of once.

An assignment line in the options section can also use list mode. list mode allows you to set an option to a list of values, rather than a single value. To use, set a name to the value [. The "name" is set to an empty string, and the starvote format parser activates list mode. While in list mode, non-empty lines are appended to the list currently being defined. To deactivate list mode and finish defining the list, specify ] on a line by itself. Notes:

• If you set a value to [], it's set to an empty list, and the parser doesn't enable list mode.
• You can't use pragmas or change sections while in list mode.
• You can't nest lists.

The only option that supports lists is tiebreaker. If tiebreaker is set to a string, this specifies the name of the tiebreaker in the starvote.tiebreakers dict to use for this election. If tiebreaker is set to a string, parse_starvote looks up that string in the options.tiebreakers dict and uses the tiebreaker found there. If tiebreaker is set to a list, this defines a pre-permuted list of candidates which is passed in to predefined_permutation_tiebreaker. (This lets you predefine a permuted list of candidates. You shouldn't use this in a real election, but it's useful in test elections as it makes the election deterministic.)

The ballots section defines ballots. In this section, names are candidate names, and values are the score for that candidate. Individual ballots are separated by blank lines and/or comment lines--to start a new ballot, just add a blank line, or a comment line.

The ballots section supports one pragma: ballots. This lets you repeat a ballot multiple times. To use, add a line to the ballots section as follows:

    n ballots:

where n is the number of times you want to repeat a ballot. This will repeat the subsequent ballot n times. For example, to repeat a ballot 5 times, add this line just above the ballot:

    5 ballots:

(You're explicitly permitted to have blank lines between the ballots pragma and the ballot it's repeating.)

Example

Here's a sample starvote format election:

[options]

seats=3
method=Bloc
tiebreaker = [
  Chuck
  Brian
  Amy
  ]
verbosity = 1

[ballots]

Amy = 1
Brian = 2
Chuck = 5

Amy = 1
Brian = 5
Chuck = 3

Amy = 1
Brian = 3
Chuck = 3

3 ballots:
Amy = 1
Brian = 3
Chuck = 3

APIs

The starvote module provides two functions that handle starvote format.

The first is parse_starvote:

starvote.parse_starvote(starvote, *, path="<string>")

parse_starvote takes one positional parameter: election, which must be a string in starvote format. It parses the string and returns a kwargs dict. You can run that election by calling election and passing in this dict, using ** to turn the contents of the dict into keyword arguments:

starvote.election(**kwargs)

You may also pass in a keyword-only parameter path, which should represent the filename if the starvote format election was loaded from a file; if specified, it'll be included in exceptions, for context.

The second is load_starvote_file:

starvote.load_starvote_file(path, *, encoding='utf-8')

load_starvote_file takes one positional parameter: path, which must be a str, bytes, or pathlib.Path object. It opens that file, reads the contents, passes those contents in to parse_starvote, and returns the result. You may specify the text encoding using the encoding keyword-only parameter; the default encoding is 'utf-8'.

Command-line module

The starvote module supports being run as a script (python -m starvote). Run it without arguments to see usage.

To use, specify the path to a single file on the command-line. starvote will read in the file, run the election, and print the result.

The path may be a CSV file. CSV files should end with the file extension .csv, and be in https://star.vote/ format. By default elections in CSV files are run using STAR Voting.

Alternatively, the path may be a starvote format file. starvote format files should end with the file extension .starvote and contain a starvote format election in UTF-8 format.

For example, you can run this from the root of the source-code repository:

% python3 -m starvote test_elections/test_election_breakable_tie_in_automatic_runoff_round_using_max_score_count_round.starvote

to see how starvote handles ties during the automatic runoff round.

Multiple-winner elections

starvote also implements several multi-winner electoral systems:

Simply instantiate your Poll object passing in the enum constant starvote.Bloc_STAR, starvote.Proportional_STAR, or starvote.Reweighted_Range for the electoral_system parameter, and the number of seats in the seats keyword-only parameter:

poll = starvote.Poll(electoral_system=starvote.Bloc_STAR, seats=2)

You can experiment with these with the command-line version of the module, too. You can specify the electoral system with -e, the number of seats with -s, and the maximum score with -m:

% python3 -m starvote test_elections/test_election_reweighted_range_sample_election.starvote

Warning

I haven't found a single test corpus for Bloc STAR Voting. I'm following the rules as best I can, and the results I'm getting make sense. But so far I can't confirm my implementation is correct--there's a very real possibility I got something wrong.

I do have one sample poll for Reweighted Range Voting, so I have some confidence that my implementation is okay. And I do test against the reference implementation of Allocated Score Voting a little.

Thanks

Huge thanks to Tim Peters for his continuous input during the development of this library. Although Tim didn't have any input on the library itself--if you don't like the library it's 100% my fault!--he tirelessly answered all my questions about voting during its development, and convinced me to change my approach several times.

License

starvote is licensed using the MIT license. See the LICENSE file.

It seems particularly relevant to repeat here: there is no warranty for this software. I've done the best job I can implementing this election system tabulator. But this software could have bugs, or my understanding of the rules could be wrong, and either of these could affect the results of elections you run with this software. Use at your own risk.

The source code repository includes sample ballots downloaded from https://star.vote/. The licensing of these sample ballots is unclear, but they're assumed to be public-domain or otherwise freely redistributable.

Changelog

2.0.3 - 2023/05/27

• Normalized nomenclature for Method objects. Now, every method has an official correctly-spelled correctly-capitalized name, and exactly one "nickname". The nickname is always lowercase, and would return True for isidentifier. These are used in the starvote.method map; a variant of these names is also bound as module attributes (changed so they're valid identifiers).
• Improved starvote.reference.monkey_patch. It's now data-driven and thus more reliable.
• Added starvote.reference.__all__, in case you want to from starvote.reference import *.
• Doc fixes.

2.0.2 - 2023/05/27

• Renamed the tiebreaker parameter candidates to tie.
• Evicted some testing-only tiebreakers from the starvote module. They're now in their own script, which only gets loaded when working with the test suite.

2.0.1 - 2023/05/27

• Changed the nickname of the reference version of Allocated Score Voting to "Allocated-R".

2.0 - 2023/05/27

A complete rewrite! The 1.x code base was pretty smelly. This codebase is much, much cleaner--and I think I squashed one or two bugs too.

starvote has an entirely new, functional API. election runs the election for you, and takes two required positional parameters: method, which specifies which electoral system you want, and ballots, an iterable of ballot dicts.

You can also now pass in a handler for unbreakable ties. By default, unbreakable ties are now broken using a pre-chosen randomize list of candidates. (election can still raise UnbreakableTieError exceptions if you prefer.)

You can also call the voting method functions directly: star, bloc_star, proportional_star, and reweighted_range are all functions, too. These omit the method parameter but still require the ballots parameter.

There's also a new text format for storing an election, starvote format, with the .starvote file extension. starvote format is a nice alternative to .csv files.

• Added the election, star_voting, bloc_star_voting, allocated_score_voting, and reweighted_range_voting functions.

  • Removed the Poll class.

• Now consistently use the official names for all methods:

  • STAR Voting
  • Bloc STAR Voting
  • Allocated Score Voting
  • Reweighted Range Voting

  ("Proportional STAR Voting" is a category of electoral systems. It's not itself a voting system, and it's definitely not restricted to "Allocated Score Voting". "STAR-PR" is another name that category.)

• Replaced the ElectoralSystem enum with the Method class. Instances (e.g. starvote.STAR_Voting) contain all the metadata needed by election to run the election.

  • methods is a module-level dict mapping strings to Method objects.

• Implemented the STAR Voting Official Tiebreaker Protocol for STAR Voting and Bloc STAR Voting.

• All vote tabulation uses strictly int and fractions.Fraction objects. Vote tabulation is now 100% consistent and accurate, from run to run, across all platforms.

• Added the parse_starvote function, which parses a starvote format string, runs the election, and returns the result.

• Added the load_starvote_file function, which loads a starvote format file from disk and parses it with parse_starvote.

• Added the Tiebreaker class, and the on_demand_random_tiebreaker and predefined_permutation_tiebreaker tiebreakers.

  • tiebreakers is a module-level dict mapping strings to tiebreakers.

• Added the reference implementation of Allocated Score Voting. This requires both NumPy and Pandas, so it's not imported by default. You can import it with import starvote.reference, and you can integrate it into the starvote module by calling starvote.reference.monkey_patch(). The reference implementation doesn't support tiebreakers.

• When running the module from the command-line using python -m starvote:

  • You may now specify a .starvote file. Its should be in UTF-8, and the contents should be a starvote format election.

  • When specifying a .csv file, starvote uses several default values: method is STAR Voting, seats is 1, verbosity is 1.

1.5.1 - 2023/05/24

• Renamed a bunch of names in the API.
  • Renamed PollVariant enum to ElectoralSystem.
  • Renamed variant parameter to electoral_system.
  • Renamed max_score parameter to maximum_score.
• Changed command-line module options to match.
  • Changed -v|--variant to -e|--electoral-system.
  • Changed -m|--max_score to -m|--maximum_score.

1.5 - 2023/05/22

• Added support for Reweighted Range Voting, an attractive alternative to Proportional STAR. Like STAR-PR, RRV is a proportional representation electoral system. But RRV is simpler to understand, simpler to implement, and it never throws away votes. Thanks to Tim Peters for suggesting it!
• Added the max_score parameter to the Poll constructor. Now you can use whatever range you like. (The minimum score is still always 0.)
• Changed the spelling of "Bloc STAR". I thought the "Bloc" was always properly capitalized (as "BLOC STAR"), but nope, it's not.

1.4 - 2023/05/21

• Automated the test suite.
• Add logging prints for tie-breaker preference round for Proportional STAR.
• Fixed presentation in __main__ for multiple winner elections that end in a tie.

1.3 - 2023/05/21

• Added support for Proportional STAR polls. The only visible external change is the new Proportional_STAR enum value.
• Renamed the winners parameter on the Poll constructor to seats. Sorry to break your code, all zero people planetwide who already started using the parameter! But this new name is a big improvement.

1.2 - 2023/05/20

• Add support for Bloc STAR polls:

  • Added PollVariant enum containing STAR and BLOC_STAR values.
  • Added variant and winners parameters to Poll.

• Add the list of tied candidates to the UnbreakableTieError exception as the new candidates attribute.

1.1 - 2023/05/20

• Bugfix: raise UnbreakableTieError if there's a three-way tie for second place. Previously starvote only noticed if there was a three-way tie for first place.
• Added sample output for every sample poll in sample_polls/. These outputs have been confirmed correct by inspection, and could in the future be used as part of an automated test suite.

1.0 - 2023/05/20

• Initial release.