endolith / elsim

Election Simulator 3000: Monte Carlo simulations of voting methods and metrics under different voter models

Election Simulator 3000

This is a library of functions for simulating thousands of elections held using different voting methods (Borda count, Approval voting, etc.) under different voter models (impartial culture, spatial model, etc.) and estimating various metrics from them (Social Utility Efficiency = Voter Satisfaction Efficiency = VSE, Condorcet Efficiency, likelihood of Condorcet cycles, etc.)

For example, it can be used to reproduce Figure 1 from Merrill 1984:

Or the table of Effectiveness from Weber 1977:

	Standard	Vote-for-half	Borda
2	81.37	81.71	81.41
3	75.10	75.00	86.53
4	69.90	79.92	89.47
5	65.02	79.09	91.34
6	61.08	81.20	92.61
10	50.78	82.94	95.35
255	12.78	86.37	99.80

See /examples folder for more on what it can do, such as reproductions of previous research.

Goals

• Fast (~25,000 elections per second on Core i7-9750H)
• Flexible
• Well-documented, easily-used and improved upon by other people
• Well-tested and bug-free
• Able to reproduce peer-reviewed research

Requirements

See requirements.txt. As of this README, it includes numpy and scipy for the simulations, tabulate for printing example tables, joblib for parallelizing extreme examples, and pytest, hypothesis, and pytest-cov for running the tests. All should be installable through conda.

Optionally, elsim can use numba for speed. If not available, the code will still run, just more slowly.

Installation

One possibility is to install with pip:

pip install git+https://github.com/endolith/elsim.git

Documentation

Currently just the docstrings of the submodules and functions themselves, in numpydoc format. Now being rendered at https://endolith.github.io/elsim/

Usage

Specify an election with three candidates (0, 1, 2), where two voters rank candidates 0 > 2 > 1, two voters rank candidates 1 > 2 > 0, and one ranks candidates 2 > 0 > 1:

>>> election = [[0, 2, 1],
...             [0, 2, 1],
...             [1, 2, 0],
...             [1, 2, 0],
...             [2, 0, 1]]

Calculate the winner using Black's method:

>>> from elsim.methods import black
>>> black(election)
2

Candidate 2 is the Condorcet winner, and wins under Black's method.

Submodules and chained functions

Originally, the functions in submodules were meant to be chained together in a simple flow:

1. A function from elsim.elections takes parameters as input (number of candidates, number of voters, dispersion in spatial model, etc.) and produces an array of utilities (each voter's appraisal of each candidate).
2. Then a function from elsim.strategies converts each voter's utilities into a ballot.
3. Then a function from elsim.methods counts the collection of ballots and chooses a winner.

flowchart LR
    Parameters -- Election --> Utilities
    Utilities -- Strategy --> Ballots
    Ballots -- Method --> Winner

Loading

However, while implementing many different types of simulations, it has become more complicated. Some functions produce intermediate results, while others skip over multiple steps. I'm no longer sure the best way to organize these functions into submodules. Here is a diagram showing the flow of every function currently in the submodules:

%%{ init: { 'flowchart': { 'curve': 'monotoneX' } } }%%
flowchart LR
    %% elections.py
    Parameters -- <code>normal_electorate</code> --> Positions[Spatial positions]
    Positions -- <code>normed_dist_utilities</code> --> Utilities
    Parameters -- <code>random_utilities</code> --> Utilities
    Parameters -- <code>impartial_culture</code> --> ranked_ballots

    %% strategies.py
    Utilities -- <code>approval_optimal</code> --> approval_ballots
    Utilities -- <code>vote_for_k</code> --> approval_ballots
    Utilities -- <code>honest_normed_scores</code> --> score_ballots
    Utilities -- <code>honest_rankings</code> --> ranked_ballots

    subgraph Ballots
        approval_ballots[Approval ballots]
        score_ballots[Score ballots]
        ranked_ballots[Ranked ballots]
    end

    %% approval.py
    approval_ballots -- <code>approval</code> --> Winner
    score_ballots -- <code>combined_approval</code> --> Winner

    %% condorcet.py (moved out of order so it renders with fewer line collisions)
    ranked_ballots -- <code>ranked_election_to_matrix</code> --> Matrix
    Matrix -- <code>condorcet_from_matrix</code> --> Winner
    ranked_ballots -- <code>condorcet</code> --> Winner

    %% black.py
    ranked_ballots -- <code>black</code> --> Winner

    %% borda.py
    ranked_ballots -- <code>borda</code> --> Winner

    %% coombs.py
    ranked_ballots -- <code>coombs</code> --> Winner

    %% fptp.py
    ranked_ballots -- <code>fptp</code> --> Winner
    ranked_ballots -- <code>sntv</code> --> Winner

    %% irv.py
    ranked_ballots -- <code>irv</code> --> Winner

    %% runoff.py
    ranked_ballots -- <code>runoff</code> --> Winner

    %% score.py
    score_ballots -- <code>score</code> --> Winner

    %% star.py
    score_ballots -- <code>star</code> --> Winner
    score_ballots -- <code>matrix_from_scores</code> --> Matrix

    %% utility_winner.py
    Utilities -- <code>utility_winner</code> --> Winner

Loading

Tests

Tests can be run by installing the testing dependencies and then running pytest in the project folder.

Bugs / Requests

File issues on the GitHub issue tracker.

Similar projects

Election simulators

• 1D:
  • Election Methods in Pictures ("Voteline") by Ka-Ping Yee - 5 candidates, normal/uniform/bimodal distribution
  • Comparing Voting Systems for a Normal Distribution of Voters - Wolfram demonstration clone
• 2D:
  • Voting Simulation Visualizations by Ka-Ping Yee - "Yee diagrams"
  • Elections On The Plane - Yee diagrams by Brian Olson
  • Yee Pictures illustrating voting method behavior by Warren D. Smith
• ND:
  • Voter Satisfaction Efficiency by Jameson Quinn

Voting system implementations

• See the list on Electowiki