gridvoting-jax 0.41.0

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
• 💾 choice of Float32 or Float64 precision
• 🔗 Better compatibility with modern ML/AI workflows

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

---

Quick Start

Open a new window at https://colab.google

Installation in Google Colab

To install, add these line at the top of the first cell:

!pip install gridvoting-jax
import gridvoting_jax as gv

Note: the pip line uses a dash '-' but the import line uses an underscore '_'

####Float64 Precision By default, JAX uses 32-bit floats for faster performance. However, larger models (g>50) should use 64-bit floats for higher accuracy and to avoid accumulation errors.

To enable 64-bit precision for higher accuracy:

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

Spatial Voting Example

import gridvoting_jax as gv

# Use a pre-built example or create your own
# 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

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)

To install into Google Colab, add these lines at the top of the first cell:

!pip install gridvoting-jax
import gridvoting_jax as gv

Local Installation

If you are using your own computer, not Google Colab, then you need to install the gridvoting-jax python module.

pip install gridvoting-jax

Pip may work; it may not. If pip issues an error about another system managing the python packages on your computer, then it may be wise to create a python virtual environment so as not to create conflicts among the python packages.

Device support

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

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

• Base Images: JAX + CUDA
• 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 BJM validation
./test_docker_bjm.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 .

---

Requirements

• Python 3.10+
• 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.

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Performance

Under review

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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 (Matrix) + Algebraic	Power (vector) + Algebraic
Tolerance	1e-10	variable, up to 1e-10 for float64
Device Detection	GPU/CPU	TPU/GPU/CPU
Import	import gridvoting	import gridvoting_jax

Numerical Accuracy: Float32 provides ~7 decimal digits of precision, which can be sufficient for some 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
• In a Spatial Voting Simulatoin, a mapping of the set of alternatives F into a 2D grid (x,y coordinates)

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 (v0.30.0)

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.device_type: Current device type ('gpu', 'tpu', or 'cpu')
• gv.use_accelerator: Boolean indicating if GPU/TPU is available

Geometric Components (gv.geometry)

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

class PolarGrid

grid = gv.PolarGrid(radius, rstep=1, thetastep=15)

Constructs a 2D polar grid for spatial voting models with radial symmetry.

Parameters:

• radius: Maximum radius of the grid
• rstep: Radial step size (default: 1)
• thetastep: Angular step size in degrees (default: 15)

Properties:

• grid.points: JAX array of shape (N, 2) containing [x, y] coordinates in Cartesian space
• grid.r, grid.theta: 1D JAX arrays of radial and angular coordinates
• grid.weights: 1D JAX array of area-based weights for each grid cell
• grid.len: Total number of grid points (1 + (n_rings * n_angular_positions))

Methods:

• index(r=None, theta=None, x=None, y=None): Find grid index from polar or Cartesian coordinates
• partition_from_rotation(angle): Create partition for rotational symmetry
  • angle=0: Continuous rotation symmetry (SO(2)) - each ring forms a partition
  • angle>0: Discrete rotation symmetry (cyclic group C_n) - rings subdivided into angular sectors
  • Angle must divide 360 and be a multiple of thetastep
• plot(z, ...): Plot scalar fields using polar contour plot

Notes:

• Grid points are arranged in concentric rings around the origin
• The origin (r=0) is a single point
• Weights represent the area of each grid cell in state space
• Useful for models with radial or rotational symmetry

Symmetry & Dimension Reduction

Reduce computational cost by exploiting spatial symmetries.

Known issue: Practicality. Time currently required to calculate symmetries and lumping is typically higher than solution time of the original model.

import gridvoting_jax as gv
import jax.numpy as jnp
from gridvoting_jax.symmetry import suggest_symmetries

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

# 2. Partition Grid
# Create partition using inverse indices (JAX array format)
# partition[i] gives the group ID for state i
partition = model.grid.partition_from_symmetry(['reflect_x'])
print(f"Partition shape: {partition.shape}")  # (N,) array
print(f"Number of groups: {int(partition.max()) + 1}")

# 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.solve()

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

# Verify Lumpability (optional)
# Check if partition preserves Markov property
is_valid = gv.is_lumpable(model.MarkovChain, partition)
print(f"Strongly lumpable: {is_valid}")

Partition Format :

• Partitions are represented as inverse indices (JAX arrays)
• Format: jnp.ndarray of shape (N,) where partition[i] is the group ID for state i
• Example: jnp.array([0, 0, 1, 1]) means states 0,1 are in group 0; states 2,3 are in group 1
• Migration helper: gv.list_partition_to_inverse(old_partition, n_states) converts from list-based partition format to inverse indices

Symmetry Types:

• 'reflect_x': Reflection across x=0 (vertical line)
• 'reflect_y': Reflection across y=0 (horizontal line)
• 'reflect_x=c': Reflection across x=c (custom vertical line)
• 'reflect_y=c': Reflection across y=c (custom horizontal line)
• 'swap_xy': Diagonal reflection (x,y) ↔ (y,x)
• ('rotate', cx, cy, angle): Rotation by angle degrees around (cx, cy)

Performance:

• Singleton symmetries (single symmetry) use optimized fast path
• Multiple symmetries use general connected components algorithm
• Lumping uses fully vectorized JAX operations)

### Pareto Efficiency
Finds the Pareto Optimal set (points where no other point is unanimously preferred).

```python
# Get a boolean mask for 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,
    weights=None  # Optional: JAX array of weights for each alternative
)

Parameters:

• utility_functions: JAX array of shape (n_voters, n_alternatives) containing utility values
• number_of_voters: Total number of voters
• number_of_feasible_alternatives: Total number of alternatives
• majority: Number of votes required to win
• zi: Boolean for Zero Intelligence (True) or Minimal Intelligence (False) challenger selection
• weights: (Optional) JAX array of shape (n_alternatives,) with positive weights for each alternative. When provided, challengers are selected with probability proportional to weights instead of uniformly. Useful for grids with non-uniform cell areas (e.g., PolarGrid)

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(solver="power_method", sec_per_digit=1.0, **kwargs) (New in v0.10.0):
  • Solvers: "full_matrix_inversion", "gmres_matrix_inversion", "power_method", "bifurcated_power_method"

class BudgetVotingModel

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

Plott's Theorem Examples

Demonstrate core existence conditions from Plott's median-in-all-directions 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)  # (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:

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 BJM research)
model = gv.bjm_spatial_triangle(g=20, zi=False)

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

Markov Chain (gv.stochastic)

class MarkovChain

mc = gv.MarkovChain(P)
mc.solve(solver="full_matrix_inversion")

# With partitions for automatic lumping/unlumping
partition = model.grid.partition_from_symmetry(['reflect_x'])
mc.solve(solver="full_matrix_inversion", partitions=partition)

Parameters:

• solver: Strategy to use (see solver options below)
• initial_guess: Optional starting distribution for iterative solvers
• partitions: Optional JAX array for automatic Markov chain lumping/unlumping. When provided, the chain is lumped using the partition, solved on the reduced state space, then unlumped back to the original space. See Symmetry & Dimension Reduction section for details.
• time_per_digit: Time budget (seconds) per digit of precision for iterative solvers (default: 1.0)

[!NOTE] API Change: The MarkovChain method find_unique_stationary_distribution has been renamed to solve for a more concise API aligned with scientific computing conventions.

Dense Solvers (constructs full transition matrix):

• "full_matrix_inversion" (default): Direct matrix inversion

  • Fastest for small grids (g≤40)
  • Memory: O(N²) where N = grid.len
  • Accuracy: Excellent (limited by float32 precision)
  • Fails: g≥80 (out of memory on some GPUs)

• "gmres_matrix_inversion": Iterative GMRES solver

  • Memory-efficient for medium grids (g=40-60)
  • Memory: O(N²) for matrix + O(N) for solver
  • Accuracy: Excellent
  • Fails: g≥80 (out of memory on some GPUs matrix construction OOM)

• "power_method": Power iteration

  • Memory: O(N²) for matrix + O(N) for vectors
  • Slower convergence than GMRES
  • Robust for difficult cases
  • Fails: g≥80 (out of memory on some GPUs, matrix construction OOM)

• "bifurcated_power_method": Dual-start power iteration

  • Starts from uniform distribution and atom at middle grid point
  • Better convergence for some models
  • Same memory requirements as power_method

Lazy Solvers (matrix-free, for large grids):

• "power_method (lazy)": Lazy power iteration

  • No matrix construction - computes P.T @ v on-the-fly
  • Memory: O(N) only
  • Works for g=80, g=100
  • Slower than dense but enables large grids
  • Use via: model.analyze_lazy(solver="power_method")

• "bifurcated_power_method (lazy)": Lazy dual-start power iteration

  • Lazy version of bifurcated_power_method
  • Memory: O(N)
  • Use via: model.analyze_lazy(solver="power_method", force_lazy=True)

Outline Solvers (New in v0.19.0) (SpatialVotingModel only):

• "outline_and_fill": Solve on coarsened grid (2x spacing), interpolate

  • Creates coarsened model with 2x grid spacing (same boundaries)
  • Solves coarsened model (4x fewer points)
  • Interpolates to original grid using sparse BCOO matrix
  • Normalizes result
  • Fast but low accuracy (L1 ~0.02-0.03)
  • Use case: Quick approximation or initial guess generation
  • Memory: O(N_coarse²) + O(N_fine) for interpolation

• "outline_and_power": Outline + power_method refinement

  • Uses outline_and_fill solution as initial guess
  • Refines with power_method solver
  • Best for large grids - never hits OOM at g=80
  • Memory: O(N²) for dense power method
  • Accuracy: Good to Excellent (L1 ~1e-06 to 5e-04)
  • Recommended for g=80 when GMRES fails

• "outline_and_gmres": Outline + GMRES refinement

  • Uses outline_and_fill solution as initial guess
  • Refines with gmres_matrix_inversion
  • Excellent accuracy when memory allows
  • Memory: O(N²) for dense GMRES
  • Fails: g≥80 (GMRES OOM)
  • Recommended for g≤60 for best accuracy

Solver Selection Guide:

Grid Size	Recommended Solver	Alternative	Notes
g=20-40	full_matrix_inversion	outline_and_gmres	Fastest, most accurate
g=60	gmres_matrix_inversion	outline_and_gmres	Balance speed/memory
g=80	outline_and_power	power_method (lazy)	Use outline or lazy solvers
g=100	outline_and_power	N/A	Requires outline solver

Pre-computed Interpolation Matrix :

from gridvoting_jax.models.spatial import create_outline_interpolation_matrix

# Pre-compute for batch processing
C = create_outline_interpolation_matrix(model.grid, coarse_grid)

# Reuse for multiple models with same grid size
model1.analyze(solver="outline_and_fill", interpolation_matrix=C)
model2.analyze(solver="outline_and_fill", interpolation_matrix=C)

Large Grid Support

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

model = gv.bjm_spatial_triangle(g=100, zi=False)
model.analyze(solver="outline_and_power")  # Recommended for large grids

Datasets (gv.datasets)

• gv.datasets.fetch_bjm_spatial_voting_2022_a100(): Downloads BJM 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.run_comparison_report()

# download the reference dataset
gv.datasets.fetch_bjm_spatial_voting_2022_a100()

# compare your computed results to the published scientific record using L1 norm
gv.benchmarks.run_comparison_report()

# 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 BJM Data

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

from gridvoting_jax.benchmarks.bjm_comparison import run_comparison_report

# Run complete comparison report
# Automatically downloads reference data to /tmp/gridvoting_bjm_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.bjm_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.

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Testing

see TESTING.md

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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.

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Contributing

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

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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}
}