gridvoting-jax 0.13.0

Spatial voting simulations on a grid with random challengers (with float32 JAX backend)

gridvoting-jax

A JAX-powered derivative of the original gridvoting project

This library provides GPU/TPU/CPU-accelerated spatial voting simulations using Google's JAX framework with float32 precision.

Origin and Development

This project is derived from the original gridvoting module, which was developed for the research publication:

Brewer, P., Juybari, J. & Moberly, R.
A comparison of zero- and minimal-intelligence agendas in majority-rule voting models.
J Econ Interact Coord (2023). https://doi.org/10.1007/s11403-023-00387-8

Migration to JAX: The computational backend was refactored from NumPy/CuPy to JAX using Google's Antigravity AI assistant. This migration provides:

• ✨ Unified CPU/GPU/TPU support through JAX
• 🚀 Improved performance through JIT compilation
• 💾 Float32 precision for efficiency
• 🔗 Better compatibility with modern ML/AI workflows

Original Project: https://github.com/drpaulbrewer/gridvoting

---

Quick Start

Spatial Voting Example

import gridvoting_jax as gv

# Use a pre-built example or create your own
# Triangle 1 from Brewer, Juybari & Moberly (2023)
# Voter ideal points: [[-15, -9], [0, 17], [15, -9]]
# https://doi.org/10.1007/s11403-023-00387-8
model = gv.bjm_spatial_triangle(g=20, zi=False)
model.analyze()

print(f"Device: {gv.device_type}")  # Shows 'gpu', 'tpu', or 'cpu'
print(f"Core exists: {model.core_exists}")
print(f"Stationary distribution: {model.stationary_distribution[:5]}...")

Budget Voting Example (New in v0.9.0)

import gridvoting_jax as gv

# Create budget voting model (divide $100 among 3 voters)
model = gv.BudgetVotingModel(budget=100, zi=False)
model.analyze()

print(f"Alternatives: {model.number_of_alternatives}")  # 5151
print(f"GiniSS inequality: {model.GiniSS[:5]}...")

# Get voter utility distributions
utility_values, probabilities = model.voter_utility_distribution(voter_index=0)

# Get GiniSS inequality distribution
gini_values, gini_probs = model.giniss_distribution(granularity=0.10)

---

Installation

Google Colab (Recommended)

All dependencies are pre-installed! Just run:

!pip install gridvoting-jax

Local Installation

pip install gridvoting-jax

GPU Support: JAX automatically detects and uses NVIDIA GPUs (CUDA) when available. An Nvidia A100 works well if you have one, but even an old 2017 gaming Nvidia 1080Ti will run some models.

TPU Support: JAX automatically detects TPUs on Google Cloud. TPUs we tried have been quirky with this code.

CPU Support: Should run with most CPUs. It will fall back to CPU mode if a GPU or TPU is not detected. RAM >=32GB is useful for some tasks.

CPU-Only Mode: If you have a GPU or TPU but want to force CPU-only execution, set environment variable GV_FORCE_CPU=1:

GV_FORCE_CPU=1 python your_script.py

Docker Usage

⚠️ EXPERIMENTAL - Docker Images Under Development
The new Docker infrastructure is still being tested and may not work correctly in all environments. Images should be finalized after a few patches (v0.10.1, v0.10.2, etc.). Please report any issues on GitHub.

The project uses a multi-tier Docker image system hosted on GitHub Container Registry (GHCR):

• Base Images: JAX + CUDA + OSF data (built once)
• Release Images: Versioned releases from PyPI (~30s builds)
• Dev Images: Local development with mounted source code

Quick Start - Local Development:

# CPU testing with your local source code
./test_docker.sh --dev --cpu tests/

# GPU testing (auto-detects CUDA 12 or 13)
./test_docker.sh --dev --gpu tests/

Testing Specific Versions:

# Test a specific release
./test_docker.sh --version=v0.9.1 --gpu

# Run OSF validation
./test_docker_osf.sh --dev --gpu --quick

Detailed Documentation:
See docs/docker.md for comprehensive Docker usage guide including:

• Image types and GHCR paths
• Development workflow
• CI/CD pipeline
• Troubleshooting

Building Images Locally:

# Build base images (one-time, slow)
docker build -f Dockerfiles/base/Dockerfile.jax-cpu -t base/cpu:local .

# Build dev images (fast)
docker build -f Dockerfiles/dev/Dockerfile.dev-cpu -t dev/cpu:local .

Float64 Precision: By default, JAX uses 32-bit floats for better GPU performance. To enable 64-bit precision for higher accuracy:

import gridvoting_jax as gv
gv.enable_float64()
# All subsequent JAX operations will use float64

---

Requirements

• Python 3.9+
• numpy >= 2.0.0
• matplotlib >= 3.8.0
• jax >= 0.4.20
• chex >= 0.1.0

Google Colab: All dependencies are pre-installed (numpy 2.0.2, matplotlib 3.10, jax 0.7).

Note: pandas and scipy are NOT required. gridvoting-jax uses only JAX for numerical operations.

---

Performance

Under review

---

Differences from Original gridvoting

This JAX version differs from the original in several ways:

Feature	Original gridvoting	gridvoting-jax
Backend	NumPy/CuPy	JAX
Precision	Float64	Float32 (default) Float64 (available)
Solver	Power + Algebraic	Algebraic only
Tolerance	1e-10	5e-5
Device Detection	GPU/CPU	TPU/GPU/CPU
Import	import gridvoting	import gridvoting_jax

Numerical Accuracy: Float32 provides ~7 decimal digits of precision, which is sufficient for many spatial voting simulations.

---

Random Sequential Voting Simulations

This follows section 2 of our research paper.

A simulation consists of:

• A sequence of times: t=0,1,2,3,...
• A finite feasible set of alternatives F
• A set of voters who have preferences over the alternatives and vote truthfully
• A rule for voting and selecting challengers
• A mapping of the set of alternatives F into a 2D grid

The active or status quo alternative at time t is called f[t].

At each t, there is a majority-rule vote between alternative f[t] and a challenger alternative c[t]. The winner of that vote becomes the next status quo f[t+1].

Randomness enters through two possible rules for choosing the challenger c[t]:

• Zero Intelligence (ZI) (zi=True): c[t] is chosen uniformly at random from F
• Minimal Intelligence (MI) (zi=False): c[t] is chosen uniformly from the status quo f[t] and the possible winning alternatives given f[t]

---

API Documentation (v0.9.0)

The package is organized into submodules, but the public API is exposed at the top level for convenience.

import gridvoting_jax as gv

Core Configuration (gv.core)

Centralized configuration and constants.

• gv.enable_float64(): Enable 64-bit floating point precision globally for JAX
• gv.TOLERANCE: Default tolerance for floating-point comparisons (5e-5 for float32)
• gv.device_type: Current device type ('gpu', 'tpu', or 'cpu')
• gv.use_accelerator: Boolean indicating if GPU/TPU is available

Spatial Components (gv.spatial)

class Grid

grid = gv.Grid(x0, x1, xstep=1, y0, y1, ystep=1)

Constructs a 2D grid for spatial voting models.

Properties:

• grid.points: JAX array of shape (N, 2) containing [x, y] coordinates
• grid.x, grid.y: 1D JAX arrays of x and y coordinates
• grid.boundary: 1D boolean mask for boundary points
• grid.len: Total number of grid points

Methods:

• spatial_utilities(voter_ideal_points, metric='sqeuclidean'): Distance-based utility calculation
• within_box/disk/triangle(...): Geometric query methods returning boolean masks
• extremes(z, valid=None): Find min/max values and their locations
• embedding(valid): Create embedding function for plotting subsets
• plot(z, ...): Plot scalar fields on the grid using Matplotlib

6. Symmetry & Dimension Reduction

Reduce computational cost by exploiting spatial symmetries.

import gridvoting_jax as gv
from gridvoting_jax.symmetry import suggest_symmetries

# 1. Detect Symmetries
# Suggest valid spatial symmetries for the mode
symmetries = suggest_symmetries(model)
print(f"Detected: {symmetries}") 

# 2. Partition Grid
# Create equivalence classes (e.g. reflection across y-axis)
partition = model.grid.partition_from_symmetry(['reflect_x'])

# 3. Lump Markov Chain
# Solve on reduced state space (e.g., 50% fewer states)
lumped_mc = gv.lump(model.MarkovChain, partition)
lumped_pi = lumped_mc.find_unique_stationary_distribution()

# 4. Unlump
# Map results back to full grid
stationary_distribution = gv.unlump(lumped_pi, partition)

7. Pareto Efficiency

Analyze the Pareto Optimal set (points where no other point is unanimously preferred).

# Get boolean mask of Pareto set
pareto_mask = model.Pareto

# Visualize
model.grid.plot(pareto_mask, title="Pareto Set")

# Create Unanimous Model
unanimous_model = model.unanimize()

Voting Models

class VotingModel

Geometry-agnostic base voting model.

vm = gv.VotingModel(
    utility_functions,
    number_of_voters,
    number_of_feasible_alternatives,
    majority,
    zi
)

Methods:

• analyze(solver="full_matrix_inversion"): Compute stationary distribution
• what_beats(index): Returns alternatives that beat the given index
• summarize_in_context(grid): Calculate entropy, mean, and covariance

Properties:

• stationary_distribution: Probability distribution over alternatives
• core_exists: Boolean indicating if a core exists
• core_points: Boolean mask of core points

class SpatialVotingModel

Geometry-aware spatial voting model (delegates to VotingModel).

model = gv.SpatialVotingModel(
    voter_ideal_points,
    grid,
    number_of_voters,
    majority,
    zi
)

Additional Methods:

• plot_stationary_distribution(**kwargs): Visualize results on grid
• analyze_lazy(solver="auto", force_lazy=False, force_dense=False, **kwargs) (New in v0.10.0):
  • Analyze using lazy matrix construction for large grids (g=80, g=100)
  • Auto-selects dense or lazy based on memory
  • Solvers: "auto", "gmres", "power_method"
  • Example: model.analyze_lazy(force_lazy=True) for g=80+

class BudgetVotingModel (New in v0.9.0)

Budget allocation voting model for dividing a fixed budget among 3 voters.

model = gv.BudgetVotingModel(budget=100, zi=False)

Features:

• Feasible set forms triangular simplex: x + y <= budget
• Number of alternatives: (budget+1)*(budget+2)//2
• Utility functions: u1=x, u2=y, u3=budget-x-y
• GiniSS inequality index: scaled to [0,1]
• Symmetry property: π[x,y] ≈ π[y,x]

Methods:

• analyze(solver="full_matrix_inversion"): Compute stationary distribution
• voter_utility_distribution(voter_index): Probability distribution of voter payoffs
• giniss_distribution(granularity=0.10): Probability distribution of GiniSS index
• plot_stationary_distribution(**kwargs): Visualize on triangular simplex

Properties:

• budget: Total budget to allocate
• u1, u2, u3: Utility for each voter at each alternative
• GiniSS: Gini-like inequality index for each alternative
• stationary_distribution: Probability distribution over allocations

Example Models (New in v0.9.0)

Plott's Theorem Examples

Demonstrate core existence conditions from Plott's median voter theorem:

Plott, C. R. (1967). A notion of equilibrium and its possibility under majority rule. American Economic Review, 57(4), 787-806.

# Core existence examples
model = gv.core1(g=20, zi=False)  # 5 voters on horizontal line
model = gv.core2(g=20, zi=False)  # 5 voters on vertical line  
model = gv.core3(g=20, zi=False)  # 5 voters on diagonal
model = gv.core4(g=20, zi=False)  # 4 corners + center
model = gv.ring_with_central_core(g=20, r=10, voters=7)  # Ring + center

# No-core example
model = gv.nocore_triangle(g=20, zi=False)  # Equilateral triangle (cycling)

Shapes Submodule

Random and geometric configurations:

# Random triangle
model = gv.shapes.random_triangle(g=20, within=10, zi=False)

# Ring of voters (must be odd)
model = gv.shapes.ring(g=20, r=10, voters=5, round_ideal_points=True)

BJM Research Examples

Examples from published research:

Brewer, P., Juybari, J. & Moberly, R. (2023). A comparison of zero- and minimal-intelligence agendas in majority-rule voting models. Journal of Economic Interaction and Coordination. https://doi.org/10.1007/s11403-023-00387-8

# Spatial voting (Triangle 1 from OSF)
model = gv.bjm_spatial_triangle(g=20, zi=False)

# Budget voting
model = gv.bjm_budget_triangle(budget=100, zi=False)

Markov Chain (gv.dynamics)

class MarkovChain

mc = gv.MarkovChain(P, tolerance=5e-5)
mc.find_unique_stationary_distribution(solver="full_matrix_inversion")

Solvers:

• "full_matrix_inversion": Direct matrix inversion (default)
• "gmres_matrix_inversion": Iterative GMRES solver
• "power_method": Power iteration method
• "grid_upscaling": Spatial upscaling (SpatialVotingModel only)

class LazyMarkovChain (New in v0.10.0)

Memory-efficient Markov chain for large grids (g=80, g=100).

from gridvoting_jax.dynamics.lazy import LazyMarkovChain, LazyTransitionMatrix

lazy_P = LazyTransitionMatrix(utility_functions, majority, zi, number_of_feasible_alternatives)
mc = LazyMarkovChain(lazy_P=lazy_P)
mc.find_unique_stationary_distribution(solver="gmres")

Solvers: "gmres" (default), "power_method"

Methods:

• find_unique_stationary_distribution(solver, initial_guess, tolerance, max_iterations, timeout)
• stationary_distribution, analyzed (properties)

class LazyTransitionMatrix (New in v0.10.0)

Methods:

• rmatvec(v): P.T @ v (non-batched, for GMRES)
• rmatvec_batched(v): P.T @ v (batched, for power method)
• matvec(v): P @ v
• todense(): Materialize full matrix

class FlexMarkovChain (New in v0.10.0)

Auto-selects dense or lazy based on memory.

from gridvoting_jax.dynamics.lazy import FlexMarkovChain

mc = FlexMarkovChain.from_voting_model(model)
mc.find_unique_stationary_distribution(solver="auto")

Large Grid Support (New in v0.10.0)

• g=80: Validated (L1 ~1e-08)
• g=100: 10,201 alternatives, uses lazy solvers + grid upscaling

model = gv.bjm_spatial_triangle(g=100, zi=False)
model.analyze(solver="grid_upscaling")  # Uses lazy GMRES

Datasets (gv.datasets)

• gv.datasets.fetch_osf_spatial_voting_2022_a100(): Downloads OSF reference dataset

---

Benchmarks

Run performance benchmarks to test solver speed across different grid sizes:

import gridvoting_jax as gv

# Print formatted benchmark results
gv.benchmarks.performance()

# Get results as dictionary for programmatic use
results = gv.benchmarks.performance(dict=True)
print(f"Device: {results['device']}")
print(f"JAX version: {results['jax_version']}")
for test in results['results']:
    print(f"{test['test_case']}: {test['time_seconds']:.4f}s")

Benchmark Test Cases:

• Grid sizes: g=20, g=40, g=60
• Voting modes: ZI (Zero Intelligence) and MI (Minimal Intelligence)
• 6 test cases total

---

Replication & Verification against OSF Data

You can automatically verify the library's output against the original A100 GPU replication data deposited on OSF. This benchmark downloads the reference data and compares stationary distributions using the L1 norm.

from gridvoting_jax.benchmarks.osf_comparison import run_comparison_report

# Run complete comparison report
# Automatically downloads reference data to /tmp/gridvoting_osf_cache
report = run_comparison_report()

# Or test specific configurations
# report = run_comparison_report([(20, False)])  # g=20, MI mode

Google Colab Usage

In a Colab notebook, you can run the full verification suite in a single cell:

!pip install gridvoting-jax

from gridvoting_jax.benchmarks.osf_comparison import run_comparison_report

# Run all 8 replication configurations (g=20, 40, 60, 80)
report = run_comparison_report()

This compares your computer's simulation results to the published scientific record.

---

Testing

Run Tests

# Install development dependencies
pip install -r requirements-dev.txt

# Run all tests (43 tests in v0.9.0)
pytest tests/

# Skip slow tests
pytest tests/ -m "not slow"

# Run only slow tests (benchmark test)
pytest tests/ -m slow

# Run with coverage
pytest tests/ --cov=gridvoting_jax -m "not slow"

Test Coverage (v0.9.0):

• Budget voting: 7 tests (symmetry, ZI/MI modes, distributions)
• Plott's theorem examples: 3 tests (core existence/absence)
• Shapes: 4 tests (random triangles, rings)
• BJM examples: 3 tests (OSF validation)
• Core functionality: 26 tests (grid, voting, solvers)

Test Markers:

• @pytest.mark.slow: Long-running tests (benchmarks)
• Use -m "not slow" to skip slow tests during development

Google Colab

!pip install gridvoting-jax
!pytest /usr/local/lib/python3.*/dist-packages/gridvoting_jax/

---

License

The software is provided under the standard MIT License.

You are welcome to try the software, read it, copy it, adapt it to your needs, and redistribute your adaptations. If you change the software, be sure to change the module name so that others know it is not the original. See the LICENSE file for more details.

---

Disclaimers

The software is provided in the hope that it may be useful to others, but it is not a full-featured turnkey system for conducting arbitrary voting simulations. Additional coding is required to define a specific simulation.

Automated tests exist and run on GitHub Actions. However, this cannot guarantee that the software is free of bugs or defects or that it will run on your computer without adjustments.

The MIT License includes this disclaimer:

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

---

Research Data

Code specific to the spatial voting and budget voting portions of our research publication -- as well as output data -- is deposited at: OSF Dataset for A comparison of zero and minimal Intelligence agendas in majority rule voting models and is freely available.

---

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

---

Citation

If you use this software in your research, please cite the original paper:

@article{brewer2023comparison,
  title={A comparison of zero-and minimal-intelligence agendas in majority-rule voting models},
  author={Brewer, Paul and Juybari, Jeremy and Moberly, Raymond},
  journal={Journal of Economic Interaction and Coordination},
  year={2023},
  publisher={Springer},
  doi={10.1007/s11403-023-00387-8}
}